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diff --git a/Turbomachines_by_A_V_Arasu/1-BASIC_CONCEPTS_OF_TURBO_MACHINES.ipynb b/Turbomachines_by_A_V_Arasu/1-BASIC_CONCEPTS_OF_TURBO_MACHINES.ipynb new file mode 100644 index 0000000..017ebbf --- /dev/null +++ b/Turbomachines_by_A_V_Arasu/1-BASIC_CONCEPTS_OF_TURBO_MACHINES.ipynb @@ -0,0 +1,571 @@ +{ +"cells": [ + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "# Chapter 1: BASIC CONCEPTS OF TURBO MACHINES" + ] + }, +{ + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 1.10: PRESSURE_RATIO_AND_EFFICIENCY.sce" + ] + }, + { +"cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], +"source": [ +"clc\n", +"clear\n", +"//input data\n", +"P=11//Overall pressure ratio in three stages of a gas turbine\n", +"nt=0.88//Overall efficiency in three stages of a gas turbine\n", +"T1=1500//Temperature at inlet of a gas turbine in K\n", +"r=1.4//ratio of specific heats for air\n", +"\n", +"//calculations\n", +"T0=nt*T1*(1-(1/P)^((r-1)/r))//Overall change in temperature in all stages in K\n", +"TN1=T1-T0//Temperature at final stage of a gas turbine in K\n", +"np=((r/(r-1))*log10(T1/TN1))/(log10(P))//Overall polytropic efficiency of the gas turbine\n", +"Ts=T0/3//Individual stage change in temperature in K\n", +"T2=T1-Ts//Exit temperature at the end of first stage in K\n", +"P1=(T1/T2)^(r/(np*(r-1)))//Pressure ratio at first stage of gas turbine \n", +"ns1=((1-(1/P1)^((np*(r-1))/r))/(1-(1/P1)^((r-1)/r)))//Stage efficiency of first stage \n", +"T3=T2-Ts//Exit temperature at the end of second stage in K\n", +"P2=(T2/T3)^(r/(np*(r-1)))//Pressure ratio at second stage of gas turbine\n", +"ns2=((1-(1/P2)^((np*(r-1))/r))/(1-(1/P2)^((r-1)/r)))//Stage efficiency of second stage\n", +"T4=T3-Ts//Exit temperature at the end of third stage in K\n", +"P3=(T3/T4)^(r/(np*(r-1)))//Pressure ratio at the third stage of gas turbine\n", +"ns3=((1-(1/P3)^((np*(r-1))/r))/(1-(1/P3)^((r-1)/r)))//Stage efficiency of third stage\n", +"\n", +"//output\n", +"printf('(a)The values for first stage are\n (1)Pressure ratio is %3.2f\n (2)stage efficiency is %3.4f\n(b)The values of second stage are\n (1)Pressure ratio is %3.3f\n (2)Stage efficiency is %3.3f\n(c)The values of third stage are\n (1)Pressure ratio is %3.2f\n (2)Stage efficiency is %3.4f\n',P1,ns1,P2,ns2,P3,ns3)" + ] + } +, +{ + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 1.11: POWER_REQUIRED.sce" + ] + }, + { +"cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], +"source": [ +"clc\n", +"clear\n", +"//input data\n", +"N=4//Number of stages in compressor\n", +"m=45//mass flow rate of air delivered by compressor in kg/s\n", +"P1=1.2//Pressure ratio at first stage\n", +"ns=0.65//Stage efficiency of first stage\n", +"r=1.4//ratio of specific heats for air\n", +"Cp=1.005//specific at heat at constant pressure in kJ/kg.K\n", +"T1=293//Temperature of air at inlet in K\n", +"\n", +"//calculations\n", +"P=(P1)^N//Overall pressure in all 4 stages\n", +"np=((r-1)/r)*((log10(P1))/(log10((((P1^((r-1)/r))-1)/ns)+1)))//Polytropic efficiency of the cycle\n", +"nc=(((P1^(N*((r-1)/r)))-1)/((P1^(N*((r-1)/(r*np))))-1))//Overall efficiency of the cycle\n", +"TN1=T1*((P1^(N))^((r-1)/(r*np)))//Final temperature at the exit of the compressor at final stage in K\n", +"W=m*Cp*(TN1-T1)//Power required to drive the compressor in kW\n", +"\n", +"//output\n", +"\n", +"printf('(a)The overall pressure ratio of the process is %3.1f\n(b)The overall efficiency of the process is %3.4f\n(c)The power required to drive the compressor is %3.2f kW',P,nc,W)" + ] + } +, +{ + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 1.12: EXIT_CONDITIONS.sce" + ] + }, + { +"cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], +"source": [ +"clc\n", +"clear\n", +"//input data\n", +"P0=0.2*9.81*(10^3)*(10^-5)//Total increase in pressure in bar\n", +"P01=1.04//Total inlet pressure of air in bar\n", +"T01=291//Total inlet temperature of air in K\n", +"ntt=0.72//Total-to-total efficiency of the process\n", +"r=1.4//ratio of specific heats for air\n", +"Cp=1.005//specific at heat at constant pressure in kJ/kg.K\n", +"\n", +"//calculations\n", +"P2=P0+P01//The total exit pressure in bar\n", +"T02=((((P2/P01)^((r-1)/r)-1)*T01)/ntt)+T01//Total temperature at the outlet in K\n", +"h0=Cp*(T02-T01)//Actual change in total enthalpy in kJ/kg\n", +"h0s=h0*ntt//Isentropic change in total enthalpy in kJ/kg\n", +"\n", +"//output\n", +"printf('(a)The total exit pressure is %3.4f bar\n and the total exit temperature is %3.2f K\n(b)The actual change in total enthalpy is %3.3f kJ/kg\n and the isentropic change in total enthalpy is %3.3f kJ/kg',P2,T02,h0,h0s)" + ] + } +, +{ + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 1.13: STATES_OF_AIR_AND_EFFICIENCIES.sce" + ] + }, + { +"cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], +"source": [ +"clc\n", +"clear\n", +"//input data\n", +"P=5//Pressure ratio in the process\n", +"ntt=0.8//Total-to-total efficiency of the process\n", +"m=5//Air flow rate through turbine in kg/s\n", +"W=500//Total power output from the turbine in kW\n", +"r=1.4//ratio of specific heats for air\n", +"Cp=1.005*10^3//specific at heat at constant pressure in J/kg.K\n", +"C2=100//Flow velocity of air in m/s\n", +"\n", +"//calculations\n", +"T=(W*10^3)/(m*Cp)//Total change in temperature in the process in K\n", +"T02s=(1/P)^((r-1)/r)//Isentropic temperature at the outlet from turvine in (K*T01)\n", +"T01=(T/ntt)*(1/(1-0.631))//Inlet total temperature in K\n", +"T02=T01-T//Actual exit total temperature in K\n", +"T2=T02-((C2^2)/(2*Cp))//Actual exit static temperature in K\n", +"T02s1=T02s*T01//Isentropic temperature at the outlet from turbine in K\n", +"T2s=T02s1-((C2^2)/(2*Cp))//Actual isentropic temperature in K\n", +"nts=(T/(T01-T2s))//Total-to-static efficiency\n", +"\n", +"//output\n", +"printf('(a)The inlet total temperature is %i K\n(b)The actual exit total temperature is %3.1f K\n(c)The actual exit static temperature is %3.1f K\n(d)The total-to-static efficiency is %3.4f',T01,T02,T2,nts)" + ] + } +, +{ + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 1.14: REHEAT_FACTOR.sce" + ] + }, + { +"cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], +"source": [ +"\n", +"clc\n", +"clear\n", +"//input data\n", +"N=3//Number of stages in turbine\n", +"P=2//Pressure ratio of each stage\n", +"ns=0.75//Stage efficiency of each stage\n", +"T1=873//Initial temperature of air in K\n", +"m=25//Flow rate of air in kg/s\n", +"r=1.4//ratio of specific heats for air\n", +"Cp=1.005//specific at heat at constant pressure in J/kg.K\n", +"\n", +"//calculations\n", +"np=(r/(r-1))*((log(1-(ns*(1-(1/P)^((r-1)/r)))))/(log(1/P)))//Polytropic efficiency of the process\n", +"nt=((1-(1/P)^(N*np*((r-1)/r)))/(1-(1/P)^(N*((r-1)/r))))//Overall efficiency of the turbine\n", +"W=m*Cp*T1*(1-(1/P)^(N*np*((r-1)/r)))//Power developed by the turbine in kW\n", +"RF=nt/ns//Reheat factor of the process\n", +"\n", +"//output\n", +"printf('(a)The overall efficiency of the turbine is %3.4f\n(b)The power developed by the turbine is %i kW\n(c)The reheat factor of the process is %3.2f',nt,W,RF)\n", +"\n", +"//comments\n", +"// the answer which i have got in scilab is correct it is showing error because the intermediate values have been approximated in textbook where as in the software it is not. if the answer is calculated in the calculator then it is same as that of obtained from the software." + ] + } +, +{ + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 1.1: COMPRESSION_WORK.sce" + ] + }, + { +"cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], +"source": [ +"clc\n", +"clear\n", +"//input data\n", +"P01=1//initial pressure of a fluid in bar\n", +"P02=10//final pressure of a fliud in bar\n", +"T01=283//initial total temperature in K\n", +"ntt=0.75//total-to-total efficiency\n", +"d=1000//density of water in kg/m^3\n", +"r=1.4//ratio of specific heats for air\n", +"Cp=1.005//specific at heat at constant pressure in kJ/kg.K\n", +"\n", +"//calculations\n", +"h0s1=(1/d)*(P02-P01)*10^2//enthalpy in kJ/kg\n", +"h01=(h0s1/ntt)//enthalpy in kJ/kg\n", +"T02s=T01*(P02/P01)^((r-1)/r)//temperature in K\n", +"h0s2=(Cp*(T02s-T01))//enthalpy in kJ/kg\n", +"h02=(h0s2/ntt)//enthalpy in kJ/kg\n", +"\n", +"//output\n", +"printf('The work of compression for adiabatic steady flow per kg of fliud if \n(a)The fliud is liquid water is %3.1f kJ/kg\n(b)The fliud is air as a perfect gas is %3.2f kJ/kg',h01,h02)\n", +"" + ] + } +, +{ + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 1.2: EFFICIENCY.sce" + ] + }, + { +"cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], +"source": [ +"clc\n", +"clear\n", +"//input data\n", +"P01=7//Total initial pressure of gases at entry in bar\n", +"T01=1100//Total initial temperature in K\n", +"P02=1.5//Total final pressure of gases at exit in bar\n", +"T02=830//Total final temperature in K\n", +"C2=250//Exit velocity in m/s\n", +"r=1.3//Ratio of specific heats of gases\n", +"M=28.7//Molecular weight of gases\n", +"R1=8.314//Gas constant of air in kJ/kg.K\n", +"\n", +"//calculations\n", +"T02s=T01*(P02/P01)^((r-1)/r)//Final temperature in K\n", +"ntt=((T01-T02)/(T01-T02s))//Total-to-total efficiency\n", +"R=(R1/M)//Gas constant of given gas in kJ/kg.K\n", +"Cp=((r*R)/(r-1))//Specific heat of given gas at constant pressure in kJ/kg.K\n", +"T2s=(T02s-((C2^2)/(2*Cp*1000)))//Temperature in isentropic process at exit in K\n", +"nts=((T01-T02)/(T01-T2s))//Total-to-static efficiency\n", +"\n", +"//output\n", +"printf('The total-to-total efficiency of gases is %3.3f\nThe total-to-static efficiency of gases is %3.3f',ntt,nts)\n", +"" + ] + } +, +{ + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 1.3: PRESSURE_RATIO.sce" + ] + }, + { +"cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], +"source": [ +"clc\n", +"clear\n", +"//input data\n", +"h0=6//Change in total enthalpy in kJ/kg\n", +"T01=303//Total inlet temperature of fluid in K\n", +"P01=1//Total inlet pressure of fliud in bar\n", +"Cp=1.005//specific at heat at constant pressure in kJ/kg.K\n", +"ntt=0.75//Adiabatic total-to-total efficiency\n", +"r=1.4//ratio of specific heats for air\n", +"\n", +"//calculations\n", +"T02=T01+(h0/Cp)//Exit total termperature of fliud in K\n", +"P1=(1+((ntt*h0)/(Cp*T01)))^(r/(r-1))//Total pressure ratio of fluid \n", +"h0s=ntt*h0//Change in enthalpy of process in kJ/kg\n", +"P0=((h0s*1000)/100)//Change in pressure in bar\n", +"P02=P0+P01//Total outlet pressure of fliud in bar\n", +"P2=(P02/P01)//Total pressure ratio of fliud\n", +"\n", +"//output\n", +"printf('(a)The exit total temperature of fliud is %3.2f K\n(b)The total pressure ratio if:\n(1)The fliud is air is %3.3f\n(2)The fliud is liquid water is %3.0i',T02,P1,P2)\n", +"" + ] + } +, +{ + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 1.4: TOTAL_PRESSURE.sce" + ] + }, + { +"cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], +"source": [ +"clc\n", +"clear\n", +"//input data\n", +"W=100//Output power developed in kW\n", +"Q=0.1//Flow through device in m^3/s\n", +"d=800//Density of oil in kg/m^3\n", +"ntt=0.75//Total-to-total efficiency\n", +"C1=3//inlet flow velocity of oil in m/s\n", +"C2=10//outlet flow velocity of oil in m/s\n", +"\n", +"//calculations\n", +"m=d*Q//Mass flow rate of oil in kg/s\n", +"h0=-(W/m)//Change in total enthalpy in kJ/kg\n", +"h0s=(h0/ntt)//Isentropic change in total enthalpy in kJ/kg\n", +"P0=((d*h0s)*(1/100))//Change in total pressure of oil in bar\n", +"P=P0-((d/(2000*100))*(C2^2-C1^2))//Change in static pressure in bar\n", +"\n", +"//output\n", +"printf('The change in total pressure of oil is %3.1f bar\nThe change in static presure is %3.1f bar',P0,P)\n", +"" + ] + } +, +{ + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 1.5: OVERALL_EFFICIENCY.sce" + ] + }, + { +"cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], +"source": [ +"clc\n", +"clear\n", +"//input data\n", +"N=4//Number of stages in turbine handling\n", +"P=0.4//Stagnation presure ratio between exit and inlet of each stage\n", +"ns1=0.86//Stage efficiency of first and second stages\n", +"ns2=0.84//Stage efficiency of third and fourth stages\n", +"r=1.4//ratio of specific heats for air\n", +"\n", +"//calculations\n", +"u=1-(P)^((r-1)/r)//constant\n", +"T03=(1-(u*ns1))^2//Temperature after the end of first two stages in (K*Cp*T01) where Cp is specific at heat at constant pressure in kJ/kg.K and T01 is initial temperature at entry of stage 1 in K\n", +"W12=u*(1+(1-(u*ns1)))*ns1//Actual work output from first two stages in (kW*Cp*T01)\n", +"W34=T03*u*(1+(1-(u*ns2)))*ns2//Actual work output from last two stages in (kW*Cp*T01)\n", +"W=(W12+W34)//Total actual work output from turbine in (kW*Cp*T01)\n", +"Ws=1-(1-u)^N//Total isentropic work due to single stage compressor in (kW*Cp*T01)\n", +"n=(W/Ws)//Overall turbine efficiency\n", +"\n", +"//output\n", +"printf('the overall efficiency of the turbine is %3.3f',n)\n", +"" + ] + } +, +{ + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 1.6: COMPRESSOR_EFFICIENCY.sce" + ] + }, + { +"cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], +"source": [ +"clc\n", +"clear\n", +"//input data\n", +"P=1400//Pressure developed by compressor in mm W.G\n", +"P1=1.01//Initial pressure of air in bar\n", +"T1=305//Initial temperature of air in K\n", +"T2=320//Final temperature of air in K\n", +"P=1400*9.81*10^-5//Pressure developed by compressor in bar\n", +"r=1.4//ratio of specific heats for air\n", +"\n", +"//calculations\n", +"P2=P1+P//Final pressure of air in bar\n", +"T2s=T1*(P2/P1)^((r-1)/r)//Isentropic temperature at exit in K\n", +"nc=((T2s-T1)/(T2-T1))//compressor efficiency\n", +"np=((r-1)/r)*((log10(P2/P1))/(log10(T2/T1)))//Infinitesimal stage efficiency\n", +"\n", +"//output\n", +"printf('(a)The compressor efficiency is %3.4f\n(b)The infinitesimal stage efficiency is %3.4f',nc,np)" + ] + } +, +{ + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 1.7: INFINITESIMAL_EFFICIENCY.sce" + ] + }, + { +"cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], +"source": [ +"clc\n", +"clear\n", +"//input data\n", +"P1=1.01//Input pressure to compressor in bar\n", +"T1=305//Input temperature to compressor in K\n", +"P2=3//Output pressure from compressor in bar\n", +"r=1.4//ratio of specific heats for air\n", +"nc=0.75//compressor efficiency\n", +"\n", +"//calculations\n", +"T2s=T1*(P2/P1)^((r-1)/r)//Isentropic output temperature from compressor in K\n", +"T2=T1+((T2s-T1)/nc)//Actual output temperature from compressor in K\n", +"np=((r-1)/r)*((log10(P2/P1))/(log10(T2/T1)))//Infinitesimal efficiency of compressor\n", +"\n", +"//output\n", +"printf('The infinitesimal efficiency of the compressor is %3.3f',np)" + ] + } +, +{ + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 1.8: POLYTROPIC_EFFICIENCY.sce" + ] + }, + { +"cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], +"source": [ +"clc\n", +"clear\n", +"//input data\n", +"P=2.2//Pressure ratio across a gas turbine\n", +"n=0.88//Efficiency of a gas turbine\n", +"T1=1500//Inlet temperature of the gas in K\n", +"r=1.4//ratio of specific heats for air\n", +"\n", +"//calculations\n", +"T2s=T1*(1/P)^((r-1)/r)//Isentropic output temperature from gas turbine in K\n", +"T2=T1-(n*(T1-T2s))//actual output temperature from gas turbine in K\n", +"np=(r/(r-1))*((log10(T1/T2))/(log10(P)))//Polytropic efficiency of the turbine\n", +"\n", +"//output\n", +"printf('The polytropic efficiency of the turbine is %3.3f',np)\n", +"" + ] + } +, +{ + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 1.9: STATES_AND_EFFICIENCIES.sce" + ] + }, + { +"cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], +"source": [ +"clc\n", +"clear\n", +"// input data\n", +"P=1.3//Pressure ratio of stages\n", +"N=8//Number of stages\n", +"m =45//The flow rate through compressor in kg/s\n", +"nc=0.8//Overall efficiency of the compressor\n", +"P1=1//Initial pressure of the air at entry in bar\n", +"T1=308//Initial temperature of the air at entry in K\n", +"r=1.4//ratio of specific heats for air\n", +"\n", +"//calculations\n", +"PN=(P)^8//Overall pressure ratio of all 8 stages\n", +"TN=PN^((r-1)/r)//Overall temperature ratio of all 8 stages\n", +"TN1s=TN*T1//Ideal exit temperature in K\n", +"TN1=((TN1s-T1)/nc)+T1//Actual exit temperature in K\n", +"PN1=PN*P1//Actual exit pressure in bar\n", +"np=((r-1)/r)*((log10(PN1/P1))/(log10(TN1/T1)))//Polytropic efficiency of the cycle\n", +"ns=((((P)^((r-1)/r))-1)/(((P)^((r-1)/(r*np)))-1))//The stage efficiency of the cycle\n", +"\n", +"//output\n", +"printf('(a)The state of air at compressor exit are\n (1)actual temperature is %3.1f K\n (2)actual pressure is %3.2f bar\n(b)The polytropic efficiency of the cycle is %3.2f\n(c)The stage efficiency of the cycle is %3.4f',TN1,PN1,np,ns)" + ] + } +], +"metadata": { + "kernelspec": { + "display_name": "Scilab", + "language": "scilab", + "name": "scilab" + }, + "language_info": { + "file_extension": ".sce", + "help_links": [ + { + "text": "MetaKernel Magics", + "url": "https://github.com/calysto/metakernel/blob/master/metakernel/magics/README.md" + } + ], + "mimetype": "text/x-octave", + "name": "scilab", + "version": "0.7.1" + } + }, + "nbformat": 4, + "nbformat_minor": 0 +} diff --git a/Turbomachines_by_A_V_Arasu/2-BLADE_THEORY.ipynb b/Turbomachines_by_A_V_Arasu/2-BLADE_THEORY.ipynb new file mode 100644 index 0000000..46bf570 --- /dev/null +++ b/Turbomachines_by_A_V_Arasu/2-BLADE_THEORY.ipynb @@ -0,0 +1,354 @@ +{ +"cells": [ + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "# Chapter 2: BLADE THEORY" + ] + }, +{ + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 2.1: WEIGHT_CARRIED.sce" + ] + }, + { +"cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], +"source": [ +"clc\n", +"clear\n", +"//input data\n", +"c =2.25//Chord length of an aerofoil in m\n", +"l=13.5//Span of the aerofoil in m\n", +"C=125//Velocity of the aerofoil in m/s\n", +"Cl=0.465//Lift coefficient\n", +"Cd=0.022//Drag coefficient\n", +"d=1.25//Density of the air in kg/m^3\n", +"\n", +"//calculations\n", +"A=c*l//Area of cross section of the aerofoil in m^2\n", +"W=Cl*d*((C^2)/2)*A*10^-3//Weight carried by the wings of aerofoil in kN\n", +"D=Cd*d*((C^2)/2)*A//Drag force on the wings of aerofoil in N\n", +"P=D*C*10^-3//Power required to the drive the aerofoil in kW\n", +"\n", +"//output\n", +"printf('(a)Weight carrried by the wings is %3.2f kN\n(b)Drag force on the wings of aerofoil is %3.2f N\n(c)Power required to drive the aerofoil is %3.3f kW',W,D,P)\n", +"\n", +"\n", +"//comments\n", +"// error in the first review is not printing the value of drag force which is corrected" + ] + } +, +{ + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 2.2: DIAMETER_OF_PARACHUTE.sce" + ] + }, + { +"cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], +"source": [ +"clc\n", +"clear\n", +"//input data\n", +"W=980//The weight of the object being dropped by parachute in N\n", +"C=5//The maximum terminal velocity of dropping in m/s\n", +"d=1.22//The density of the air in kg/m^3\n", +"Cd=1.3//The drag coefficient of the parachute\n", +"\n", +"//calculations\n", +"A=W/(Cd*d*((C^2)/2))//The area of cross section in m^2\n", +"D=((A*4)/(3.14))^(1/2)//Diameter of the parachute in m\n", +"\n", +"//output\n", +"printf('The required diameter of the parachute is %3.2f m',D)" + ] + } +, +{ + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 2.3: COEFFICIENT_OF_LIFT.sce" + ] + }, + { +"cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], +"source": [ +"clc\n", +"clear\n", +"//input data\n", +"A=10*1.2//Area of the airplane wing in m^2\n", +"C=((240*10^3)/3600)//Velocity of the wing in m/s\n", +"F=20//Total aerodynamic force acting on the wing in kN\n", +"LD=10//Lift-drag ratio\n", +"d=1.2//Density of the air in kg/m^3\n", +"\n", +"//calculations\n", +"L=(F)/(1.01)^(1/2)//The weight that the plane can carry in kN\n", +"Cl=(L*10^3)/(d*A*((C^2)/2))//Coefficient of the lift\n", +"\n", +"//output\n", +"printf('(1)The coefficient of lift is %3.3f\n(2)The total weight the palne can carry is %3.1f kN',Cl,L)" + ] + } +, +{ + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 2.4: MEAN_RADIUS.sce" + ] + }, + { +"cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], +"source": [ +"clc\n", +"clear\n", +"//input data\n", +"m=25//Mass flow rate of the air in kg/s\n", +"d=1.1//Density of the air in kg/m^3\n", +"Ca=157//Axial flow velocity of the air in m/s\n", +"N=150//Rotational speed of the air in rev/s\n", +"U=200//Mean blade speed in m/s\n", +"lc=3//Rotor blade aspect ratio \n", +"sc=0.8//Pitch chord ratio\n", +"\n", +"//calculations\n", +"rm=(U)/(2*3.145*N)//Mean radius of the blades in m\n", +"A=(m)/(d*Ca)//The annulus area of flow in m^2\n", +"l=(A)/(2*3.1*rm)//The blade height in m\n", +"C=l/lc//The chord of the blades in m\n", +"S=sc*C//The blade pitch in m\n", +"n=(2*3.141*rm)/(S)//Number of blades \n", +"\n", +"//output\n", +"\n", +"printf('(a)The mean radius of the blades is %3.3f m\n(b)The blade height is %3.2f m\n(c) (1)The pitch of the blades is %3.4f m\n (2)The chord of the blades is %3.3f m\n(d)The number of the blades are %3.f',rm,l,S,C,n)" + ] + } +, +{ + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 2.5: DEFLECTION_ANGLE.sce" + ] + }, + { +"cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], +"source": [ +"clc\n", +"clear\n", +"//input data\n", +"sc=0.8//Pitch-chord ratio of compressor blade\n", +"b1=45//Relative air angle at inlet in degree\n", +"b2=15//Relative air angle at oulet in degree\n", +"a1=b1//Cascade air angle at inlet in degree\n", +"a2=b2//Cascade air angle at outlet in degree\n", +"\n", +"//calculations \n", +"en=a1-a2//Nominal deflection angle of the blade in degree\n", +"m=((0.23*(1)^2))+(0.1*a2/50)//An emperical constant for a circular arc camber where (2*a/c)=1\n", +"t=(a1-a2)/(1-0.233)//Blade camber angle in degree\n", +"d=(m*(sc)^(1/2))*t//The deviation angle of the blade in terms of (degree*t)\n", +"ps=a1-(t/2)//The blade stagger for a given circular arc cascade in degree\n", +"\n", +"//output\n", +"printf('(a)The nominal deflection angle is %i degree\n(b)The blade camber angle is %3.2f degree\n(c)The deviation angle is %3.2f degree\n(d)The blade stagger is %3.2f degree',en,t,d,ps)" + ] + } +, +{ + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 2.6: CASCADE_BLADE_ANGLES.sce" + ] + }, + { +"cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], +"source": [ +"clc\n", +"clear\n", +"//input data\n", +"t=25//The camber angle of aero foil blades in degree\n", +"ps=30//The blade stagger angle in degree\n", +"sc=1//The pitch-chord ratio of the blades\n", +"in=5//The nominal value of incidence in degree\n", +"\n", +"//calculations\n", +"a1=ps+(t/2)//The cascade blade angle at inlet in degree\n", +"a2=a1-t//The cascade blade angle at outlet in degree\n", +"a1n=in+a1//The nominal entry air angle in degree\n", +"a2n=atand((tand(a1n))-(1.55/(1.0+(1.5*sc))))//The nominal exit air angle in degree\n", +"\n", +"//output\n", +"printf('(1)The cascade blade angles at \n (a)inlet is %3.1f degree\n (b)exit is %3.1f degree\n(2)The nominal air angles at \n (a)inlet is %3.1f degree\n (b)exit is %3.2f degree',a1,a2,a1n,a2n)" + ] + } +, +{ + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 2.7: LOSS_COEFFICIENT.sce" + ] + }, + { +"cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], +"source": [ +"clc\n", +"clear\n", +"//input data\n", +"C1=75//Velocity of air entry in m/s\n", +"a1=48//Air angle at entry in degree\n", +"a2=25//Air angle at exit in degree\n", +"cs=0.91//The chord-pitch ratio \n", +"P0m=(11*9.81*10^3)/10^3//The stagnation pressure loss in N/m^2\n", +"d=1.25//The density of the sair in kg/m^3\n", +"\n", +"//calculations\n", +"Cp=(P0m/(0.5*d*C1^2))//The pressure loss coefficient \n", +"am=atand((tand(a1)+tand(a2))/2)//The mean air angle in degree\n", +"Cd=2*(1/cs)*(P0m/(d*C1^2))*((cosd(am))^3/(cosd(a1))^2)//The drag coefficient \n", +"Cl=(2*(1/cs)*cosd(am)*(tand(a1)-tand(a2)))-(Cd*tand(am))//THe lift coefficient\n", +"\n", +"//output\n", +"printf('(a)The pressure loss coefficient is %3.4f\n(b)The drag coefficient is %3.4f\n(c)The lift coefficient is %3.3f',Cp,Cd,Cl)" + ] + } +, +{ + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 2.8: PRESSURE_LOSS_COEFFICIENT.sce" + ] + }, + { +"cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], +"source": [ +"clc\n", +"clear\n", +"//input data\n", +"a1=40//The cascade air angle at entry in degree\n", +"a2=65//The cascade air angle at exit in degree\n", +"C1=100//Air entry velocity in m/s\n", +"d=1.25//The density of the air in kg/m^3\n", +"sc=0.91//The pitch-chord ratio of the cascade\n", +"P0m=(17.5*9.81*10^3)/10^3//The average loss in stagnation pressure across cascade in N/m^2\n", +"\n", +"//calculations\n", +"Cp=(P0m/(0.5*d*C1^2))//The pressure loss coefficient in the cascade\n", +"am=atand((tand(a2)-tand(a1))/2)//The mean air angle in degree\n", +"Cd=2*(sc)*(P0m/(d*C1^2))*((cosd(am))^3/(cosd(a2))^2)//The drag coefficient \n", +"Cl=(2*(sc)*cosd(am)*(tand(a1)+tand(a2)))+(Cd*tand(am))//THe lift coefficient\n", +"\n", +"//output\n", +"printf('(a)The pressure loss coefficient is %3.4f\n(b)The drag coefficient is %3.4f\n(c)The lift coefficient is %3.3f',Cp,Cd,Cl)" + ] + } +, +{ + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 2.9: COEFFICIENT_OF_DRAG_AND_LIFT.sce" + ] + }, + { +"cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], +"source": [ +"clc\n", +"clear\n", +"//input data\n", +"W=30000//The weight of the jet plane in N\n", +"A=20//The area of the wing in m^2\n", +"C=250*5/18//The speed of the jet plane in m/s\n", +"P=750//The power delivered by the engine in kW\n", +"d=1.21//Density of the air in kg/m^3\n", +"\n", +"//calculations\n", +"L=W//The lift force on the plane is equal to the weight of the plane in N\n", +"Pd=0.65*P//The power required to overcome the drag resistance in kW\n", +"D=(Pd/C)*10^3//The drag force on the wing in N\n", +"Cd=D/(0.5*d*A*C^2)//The coefficient of drag for the wing \n", +"Cl=L/(0.5*d*A*C^2)//The coefficient of lift for the wing \n", +"\n", +"//output\n", +"printf('(a)The coefficient of lift on the wing is %3.3f\n(b)The coefficient of drag on the wing is %3.3f',Cl,Cd)" + ] + } +], +"metadata": { + "kernelspec": { + "display_name": "Scilab", + "language": "scilab", + "name": "scilab" + }, + "language_info": { + "file_extension": ".sce", + "help_links": [ + { + "text": "MetaKernel Magics", + "url": "https://github.com/calysto/metakernel/blob/master/metakernel/magics/README.md" + } + ], + "mimetype": "text/x-octave", + "name": "scilab", + "version": "0.7.1" + } + }, + "nbformat": 4, + "nbformat_minor": 0 +} diff --git a/Turbomachines_by_A_V_Arasu/3-CENTRIFUGAL_COMPRESSORS_AND_FANS.ipynb b/Turbomachines_by_A_V_Arasu/3-CENTRIFUGAL_COMPRESSORS_AND_FANS.ipynb new file mode 100644 index 0000000..d593eda --- /dev/null +++ b/Turbomachines_by_A_V_Arasu/3-CENTRIFUGAL_COMPRESSORS_AND_FANS.ipynb @@ -0,0 +1,716 @@ +{ +"cells": [ + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "# Chapter 3: CENTRIFUGAL COMPRESSORS AND FANS" + ] + }, +{ + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 3.10: FAN_EFFICIENCY.sce" + ] + }, + { +"cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], +"source": [ +"clc\n", +"clear\n", +"//input data\n", +"H=0.075//Pressure developed by a fan in m W.G\n", +"D2=0.89//The impeller diameter in m\n", +"N=720//The running speed of the fan in rpm\n", +"b22=39//The blade air angle at the tip in degree\n", +"b2=0.1//The width of the impeller in m\n", +"Cr=9.15//The constant radial velocity in m/s\n", +"d=1.2//Density of air in kg/m^3\n", +"r=1.4//The ratio of specific heats of air\n", +"R=287//The universal gas constant in J/kg.K\n", +"Cp=1005//The specific heat of air at constant pressure in J/kg.K\n", +"g=9.81//Acceleration due to gravity in m/s^2\n", +"dw=1000//Density of water in kg/m^3\n", +"\n", +"//calculations\n", +"IW=(dw*g*H)/d//Ideal work done in J/kg\n", +"U2=(3.1415*D2*N)/60//The impeller tip speed in m/s\n", +"Wx2=Cr/tand(b22)//Relative whirl component of velocity at outlet in m/s\n", +"Cx2=U2-(Wx2)//Outlet absolute velocity of air in tangential direction in m/s\n", +"Wm=U2*Cx2//Actual work done per unit mass flow rate in J/kg\n", +"nf=IW/Wm//Fan efficiency\n", +"Q=3.1415*D2*b2*Cr//The discharge of the air by fan in m^3/s\n", +"m=d*Q//Mass flow rate of the air by the fan in kg/s\n", +"W=m*Wm*10^-3//Power required to drive the fan in kW\n", +"R=1-(Cx2/(2*U2))//Stage reaction of the fan\n", +"sp=2*Cx2/U2//The pressure coefficient\n", +"\n", +"//output\n", +"printf('(a)The fan efficiency is %3.3f\n(b)The Discharge of air by the fan is %3.3f m^3/s\n(c)The power required to drive the fan is %3.4f kW\n(d)The stage reaction of the fan is %3.4f\n(e)The pressure coefficient of the fan is %3.3f',nf,Q,W,R,sp)" + ] + } +, +{ + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 3.11: FAN_EFFICIENCY_AND_PRESSURE_COEFFICIENT.sce" + ] + }, + { +"cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], +"source": [ +"clc\n", +"clear\n", +"//input data\n", +"\n", +"b22=30//The blade air angle at the tip in degrees\n", +"D2=0.466//The impeller diameter in m\n", +"Q=3.82//The discharge of the air by fan in m^3/s\n", +"m=4.29//Mass flow rate of the air by the fan in kg/s\n", +"H=0.063//Pressure developed by a fan in m W.G\n", +"pi2=0.25//Flow coefficient at impeller exit\n", +"W=3//Power supplied to the impeller in kW\n", +"r=1.4//The ratio of specific heats of air\n", +"R=287//The universal gas constant in J/kg.K\n", +"Cp=1005//The specific heat of air at constant pressure in J/kg.K\n", +"g=9.81//Acceleration due to gravity in m/s^2\n", +"dw=10^3//Density of water in kg/m^3\n", +"\n", +"//calculations\n", +"IW=Q*dw*g*H*(10^-3)//Ideal work done in kW\n", +"nf=IW/W//Fan efficiency\n", +"U2=(((W*10^3)/m)/(1-(pi2/tand(b22))))^(1/2)//The impeller tip speed in m/s\n", +"Cr2=pi2*U2//The radial velocity at exit in m/s\n", +"Cx2=U2-(Cr2/tand(b22))//Outlet absolute velocity of air in tangential direction in m/s\n", +"sp=2*Cx2/U2//Presuure coefficient of the fan\n", +"R=1-(Cx2/(2*U2))//Degree of reaction of the fan\n", +"N=(U2*60)/(3.141592*D2)//Rotational speed of the fan in rpm\n", +"b2=Q/(3.14*D2*Cr2)//Impeller width at the exit in m\n", +"\n", +"//output\n", +"printf('(a)The fan efficiency is %3.3f\n(b)The pressure coefficient is %3.3f\n(c)The degree of reaction of the fan is %3.3f\n(d)The rotational speed of the fan is %3.1f rpm\n(e)The impeller width at exit is %3.3f m',nf,sp,R,N,b2)" + ] + } +, +{ + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 3.12: POWER_INPUT_AND_ANGLES.sce" + ] + }, + { +"cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], +"source": [ +"clc\n", +"clear\n", +"//input data\n", +"N=3000//The running speed of the blower in rpm\n", +"D2=0.75//The impeller diameter in m\n", +"Cr2=57//The radial velocity at exit in m/s\n", +"Cx1=0//Inlet absolute velocity of air in tangential direction in m/s\n", +"DR=0.58//Degree of reaction of the blower\n", +"nc=0.75//Total-to-total efficiency\n", +"r=1.4//The ratio of specific heats of air\n", +"R=287//The universal gas constant in J/kg.K\n", +"Cp=1.005//The specific heat of air at constant pressure in J/kg.K\n", +"T01=298//The inlet stagnation temperature in K\n", +"P01=1*101.325//The inlet stagnation pressure in kPa\n", +"\n", +"//calculations\n", +"U2=(3.1415*D2*N)/60//The impeller tip speed in m/s\n", +"Cx2=2*(1-DR)*U2//Outlet absolute velocity of air in tangential direction in m/s\n", +"Wx2=U2-Cx2//Relative whirl component of velocity at outlet in m/s\n", +"b22=atand(Cr2/Wx2)//The blade air angle at the tip in degree\n", +"Wm=U2*Cx2*10^-3//Actual work done per unit mass flow rate when Cx1=0 in kW/(kg/s)\n", +"T=Wm/Cp//Total change in temperature in blower in K\n", +"P=(1+(nc*(T/T01)))^(r/(r-1))//Total pressure ratio in the blower\n", +"P02=P*P01//The outlet stagnation pressure from blower in kPa\n", +"\n", +"//output\n", +"printf('(a)The exit blade angle is %3.1f degree\n(b)The power input to the blower is %3.3f kW/(kg/s)\n(c)The exit stagnation pressure is %3.2f kPa',b22,Wm,P02)" + ] + } +, +{ + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 3.13: STAGE_PRESSURE_RISE.sce" + ] + }, + { +"cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], +"source": [ +"clc\n", +"clear\n", +"//input data\n", +"D1=0.18//The impeller inner diameter in m\n", +"D2=0.2//The impeller outer diameter in m\n", +"C1=21//The absolute velocity at the entry in m/s\n", +"C2=25//The absolute velocity at the exit in m/s\n", +"W1=20//The relative velocity at the entry in m/s\n", +"W2=17//The relative velocity at the exit in m/s\n", +"N=1450//The running speed of the fan in rpm\n", +"m=0.5//The mass flow rate of the air in fan in kg/s\n", +"nm=0.78//The motor efficiency of the fan \n", +"d=1.25//The density of the air in kg/m^3\n", +"r=1.4//The ratio of specific heats of air\n", +"R=287//The universal gas constant in J/kg.K\n", +"Cp=1.005//The specific heat of air at constant pressure in J/kg.K\n", +"\n", +"//calculations\n", +"U1=(3.14*D1*N)/60//Peripheral velocity of impeller at inlet in m/s\n", +"U2=(3.14*D2*N)/60//The impeller tip speed in m/s\n", +"dH=(((U2^2)-(U1^2))/2)+(((W1^2)-(W2^2))/2)//The actual total rise in enthalpy in kJ/kg\n", +"dH0=dH+(((C2^2)-(C1^2))/2)//The stage total isentropic rise in enthalpy in kJ/kg\n", +"dP0=d*dH0//The stage total pressure rise in N/m^2\n", +"dP=d*dH//The actual total rise in pressure in N/m^2\n", +"R=dP/dP0//The degree of reaction of the fan\n", +"W=m*(dH0)//The work done by the fan per second in W\n", +"P=W/nm//The power input to the fan in W\n", +"\n", +"//output\n", +"printf('(a)The stage total pressure rise is %3.1f N/m^2\n(b)The degree of reaction of the fan is %3.3f\n(c)The power input to the fan is %3.1f W',dP0,R,P)" + ] + } +, +{ + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 3.14: VOLUME_FLOW_RATE.sce" + ] + }, + { +"cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], +"source": [ +"clc\n", +"clear\n", +"//input data\n", +"dH=0.14//Rise in static pressure of the air by fan in m of water\n", +"N=650//The running speed of the fan in rpm\n", +"P=85*0.735//Power consumed by the fan in kW\n", +"H1=0.75//The static pressure of the air at the fan in m of Hg\n", +"T1=298//The static pressure at the fan of air in K\n", +"m=260//Mass flow rate of air in kg/min\n", +"dHg=13590//Density of mercury in kg/m^3\n", +"dw=1000//Density of water in kg/m^3\n", +"g=9.81//Acceleration due to gravity in m/s^2\n", +"R=287//The universal gas constant in J/kg.K\n", +"\n", +"//calculations\n", +"P1=dHg*g*H1*10^-3//The inlet static pressure in kPa\n", +"dP=dw*g*dH*10^-3//The total change in static pressures at inlet and outlet in kPa\n", +"P2=P1+dP//The exit static pressure in kPa\n", +"d1=(P1*10^3)/(R*T1)//The inlet density of the air in kg/m^3\n", +"Q=m/d1//The volume flow rate of air in fan in m^3/min\n", +"\n", +"//output\n", +"printf('(a)The exit static pressure of air in the fan is %3.2f kPa\n(b)The volume flow rate of the air is %3.1f m^3/min',P2,Q)" + ] + } +, +{ + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 3.1: RISE_IN_TOTAL_TEMPERATURE.sce" + ] + }, + { +"cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], +"source": [ +"clc\n", +"clear\n", +"//input data\n", +"m=10//The mass flow rate of air into compressor in kg/s\n", +"P1=1//The ambient air pressure in compressor in bar\n", +"T1=293//The ambient air temperature in compressor in K\n", +"N=20000//The running speed of the compressor in rpm\n", +"nc=0.8//The isentropic efficiency of the compressor\n", +"P02=4.5//The total exit pressure from the compressor in bar\n", +"C1=150//The air entry velocity into the impeller eye in m/s\n", +"Cx1=0//The pre whirl speed in m/s\n", +"WS=0.95//The ratio of whirl speed to tip speed\n", +"Cp=1005//The specific heat of air at constant pressure in J/kg.K \n", +"R=287//The universal gas constant in J/kg.K\n", +"Dh=0.15//The eye internal diamater in m\n", +"r=1.4//Ratio of specific heats of air \n", +"d=1.189//The density of the air in kg/m^3\n", +"\n", +"//calculations\n", +"T01=T1+((C1^2)/(2*Cp))//The stagnation temperature at inlet in K\n", +"P01=P1*(T01/T1)^(r/(r-1))//The stagnation pressure at inlet in bar\n", +"T02s=(T01)*(P02/P01)^((r-1)/r)//The temperature after isentropic compression from P01 to P02 in K\n", +"T=(T02s-T01)/nc//The actual rise in total temperature in K\n", +"W=Cp*(10^-3)*(T)//The work done per unit mass in kJ/kg\n", +"U2=((W*(10^3))/(WS))^(1/2)//The impeller tip speed in m/s\n", +"Dt=(U2*60)/(3.1415*N)//The impeller tip diameter in m\n", +"P=m*W//Power required to drive the compressor in kW\n", +"d1=((P1*10^5)/(R*T1))//The density of the air entry in kg/m^3\n", +"De=(((4*m)/(d*C1*3.14))+(Dh^2))^(1/2)//The eye external diameter in m\n", +"\n", +"//output\n", +"printf('(a)The actual rise in total temperature of the compressor is %3.1f K\n(b)\n (1)The impeller tip speed is %3.2f m/s\n (2)The impeller tip diameter is %3.2f m\n(c)The power required to drive the compressor is %3.1f kW\n(d)The eye external diameter is %3.3f m',T,U2,Dt,P,De)" + ] + } +, +{ + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 3.2: BLADE_ANGLES_AND_DIMENSIONS.sce" + ] + }, + { +"cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], +"source": [ +"clc\n", +"clear\n", +"//input data\n", +"Q1=20//Discharge of air to the centrifugal compressor in m^3/s\n", +"V1=Q1//Volume of rate is equal to the discharge in m^3/s\n", +"P1=1//Initial pressure of the air to the centrifugal compressor in bar\n", +"T1=288//Initial temperature of the air to the centrifugal compressor in K\n", +"P=1.5//The pressure ratio of compression in centrifugal compressor\n", +"C1=60//The velocity of flow of air at inlet in m/s\n", +"Cr2=C1//The radial velocity of flow of air at outlet in m/s\n", +"Dh=0.6//The inlet impeller diameter in m\n", +"Dt=1.2//The outlet impeller diameter in m\n", +"N=5000//The speed of rotation of centrifugal compressor in rpm\n", +"n=1.5//polytropic index constant in the given law PV^n\n", +"Cp=1005//The specific heat of air at constant pressure in J/kg.K \n", +"\n", +"//calculations\n", +"U1=(3.14*Dh*N)/60//Peripheral velocity of impeller at inlet in m/s\n", +"b11=atand(C1/U1)//The blade angle at impeller inlet in degree\n", +"U2=(3.14*Dt*N)/60//Peripheral velocity of impeller top at outlet in m/s\n", +"T2=T1*(P)^((n-1)/n)//Final temperature of the air to the centrifugal compressor in K\n", +"Cx2=((Cp*(T2-T1))/U2)//The whirl component of absolute velocity in m/s\n", +"Wx2=U2-Cx2//The exit relative velocity in m/s\n", +"a2=atand(Cr2/Cx2)//The blade angle at inlet to casing in degree\n", +"b22=atand(Cr2/Wx2)//The blade angle at impeller outlet in degree\n", +"b1=Q1/(2*3.14*(Dh/2)*C1)//The breadth of impeller blade at inlet in m \n", +"V2=(P1*V1*T2)/(T1*P*P1)//Volume flow rate of air at exit in m^3/s\n", +"Q2=V2//Volume flow rate is equal to discharge in m^3/s\n", +"b2=Q2/(2*3.14*(Dt/2)*Cr2)//The breadth of impeller blade at outlet in m\n", +"\n", +"//output\n", +"printf('(a)The blade and flow angles\n (1)The blade angle at impeller inlet is %3.1f degree\n (2)The blade angle at inlet to casing is %3.1f degree\n (3)The blade angle at impeller outlet is %3.2f degree\n(b)Breadth of the impeller blade at inlet and outlet\n (1)The breadth of impeller blade at inlet is %3.3f m\n (2)The Volume flow rate of air at exit is %3.2f m^3/s\n (3)The breadth of impeller blade at outlet is %3.4f m',b11,a2,b22,b1,V2,b2)\n", +"\n", +"\n", +"//comments\n", +"//error in the first review is not printing the value of V2 which is corrected" + ] + } +, +{ + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 3.3: OVERALL_DIAMETER.sce" + ] + }, + { +"cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], +"source": [ +"clc\n", +"clear\n", +"//input data\n", +"m=14//The mass flow rate of air delivered to centrifugal compressor in kg/s\n", +"P01=1//The inlet stagnation pressure in bar\n", +"T01=288//The inlet stagnation temperature in K\n", +"P=4//The stagnation pressure ratio\n", +"N=200//The speed of centrifygal compressor in rps\n", +"ss=0.9//The slip factor\n", +"ps=1.04//The power input factor\n", +"ntt=0.8//The overall isentropic efficiency\n", +"r=1.4//The ratio of specific heats of air\n", +"Cp=1005//The specific heat of air at constant pressure in J/kg.K\n", +"\n", +"//calculations\n", +"pp=ss*ps*ntt//The pressure coefficient\n", +"U2=((Cp*T01*((P^((r-1)/r))-1))/pp)^(1/2)//Peripheral velocity of impeller top at outlet in m/s\n", +"D2=U2/(3.14*N)//The overall diameter of the impeller in m\n", +"\n", +"//output\n", +"printf('The overall diameter of the impeller is %3.2f m',D2)" + ] + } +, +{ + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 3.4: INLET_RELATIVE_MACH_NUMBER.sce" + ] + }, + { +"cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], +"source": [ +"clc\n", +"clear\n", +"//input data\n", +"D1=0.457//Impeller diameter at inlet in m\n", +"D2=0.762//Impeller diameter at exit in m\n", +"Cr2=53.4//Radial component of velocity at impeller exit in m/s\n", +"ss=0.9//Slip factor\n", +"N=11000//Impeller speed in rpm\n", +"P2=2.23//Static pressure at impeller exit in bar\n", +"T01=288//The inlet stagnation temperature in K\n", +"P01=1.013//The inlet stagnation pressure in bar\n", +"C1=91.5//Velocity of air leaving the guide vanes in m/s\n", +"a11=70//The angle at which air leaves the guide vanes in degrees\n", +"r=1.4//The ratio of specific heats of air\n", +"R=287//The universal gas constant in J/kg.K\n", +"Cp=1005//The specific heat of air at constant pressure in J/kg.K\n", +"\n", +"//calculations\n", +"Cx1=C1*cosd(a11)//Inlet absolute velocity of air in tangential direction in m/s\n", +"Ca1=Cx1*tand(a11)//Radial component of absolute velocity at inlet in m/s\n", +"U1=(3.14*D1*N)/(60)//Peripheral velocity of impeller at inlet in m/s\n", +"Wx1=U1-Cx1//Relative whirl component of velocity at inlet in m/s\n", +"W1=((Wx1^2)+(Ca1^2))^(1/2)//Relative velocity at inlet in m/s\n", +"T1=T01-((C1^2)/(2*Cp))//The inlet air temperature in K\n", +"a1=(r*R*T1)^(1/2)//The velocity of air in m/s\n", +"M1r=W1/a1//Initial relative mach number\n", +"U2=(3.14*D2*N)/60//Peripheral velocity of impeller top at exit in m/s\n", +"W=(ss*U2^2)-(U1*Cx1)//Work done by the compressor in kJ/kg\n", +"T02=(W/Cp)+T01//The outlet stagnation temperature in K\n", +"Cx21=ss*U2//Absolute whirl component of velocity with slip consideration in m/s\n", +"C2=((Cx21^2)+(Cr2^2))^(1/2)//The absolute velocity of air at exit in m/s\n", +"T2=T02-((C2^2)/(2*Cp))//The exit temperature of air in K\n", +"P02=P2*(T02/T2)^(r/(r-1))//The exit stagnation pressure of compressor in bar\n", +"nc=(T01/(T02-T01))*(((P02/P01)^((r-1)/r))-1)//Total head isentropic efficiency\n", +"\n", +"//output\n", +"printf('(1)The inlet relative mach number is %3.3f\n(2)The impeller total head efficiency is %3.3f',M1r,nc)" + ] + } +, +{ + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 3.5: DIMENSIONS_OF_IMPELLER.sce" + ] + }, + { +"cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], +"source": [ +"clc\n", +"clear\n", +"//input data\n", +"N=16500//The running speed ofradial blade of a centrifugal compressor in rpm\n", +"P=4//The total pressure ratio\n", +"P01=1//The atmospheric pressure in bar\n", +"T01=298//THe atmospheric temperature in K\n", +"Dh=0.16//The hub diameter at impeller eye in m\n", +"Ca=120//The axial velocity at inlet in m/s\n", +"C1=Ca//The absolute velocity at inlet in m/s\n", +"sp=0.7//The pressure coefficient\n", +"C3=120//The absolute velocity at diffuser exit in m/s\n", +"m=8.3//The mass flow rate in kg/s\n", +"nc=0.78//The adiabatic total-to-total efficiency\n", +"r=1.4//The ratio of specific heats of air\n", +"R=287//The universal gas constant in J/kg.K\n", +"Cp=1005//The specific heat of air at constant pressure in J/kg.K\n", +"\n", +"//calculations\n", +"T1=T01-((C1^2)/(2*Cp))//The inlet temperature in K\n", +"P1=P01*(T1/T01)^(r/(r-1))//The inlet pressure in bar\n", +"d1=(P1*10^5)/(R*T1)//The inlet density of air in kg/m^3\n", +"Dt=(((4*m)/(3.14*d1*Ca))+(0.16^2))^(1/2)//The eye tip diameter in m\n", +"T=((T01)*((P^((r-1)/r))-1))/nc//The overall change in temperature in K\n", +"ssps=sp/nc//The product of slip factor and power factor\n", +"U2=(T*Cp/ssps)^(1/2)//Peripheral velocity of impeller top at exit in m/s\n", +"D2=(U2*60)/(3.14*N)//The impeller tip diameter in m\n", +"Uh=(3.14*Dh*N)/60//Peripheral velocity of eye hub in m/s\n", +"bh=atand(C1/Uh)//Blade angle at eye hub in degree\n", +"Ut=(3.14*Dt*N)/60//Peripheral velocity of eye tip in m/s\n", +"bt=atand(C1/Ut)//Blade angle at eye tip in degree\n", +"T03=T01+T//Temperature at the exit in K\n", +"T3=T03-((C3^2)/(2*Cp))//Exit static temperature in K\n", +"P3=(P*P01)*(T3/T03)^(r/(r-1))//Exit static pressure in bar\n", +"W=m*Cp*(T03-T01)*10^-6//Power required to drive the compressor in mW\n", +"//output\n", +"printf('(a)The main dimensions of the impeller are\n (1)Eye tip diameter is %3.3f m\n (2)Impeller tip diameter is %3.3f m\n (3)Blade angle at the eye hub is %3.2f degree\n Blade angle at the eye tip is %3.2f degree\n(b) (1)The static exit temperature is %3.1f K\n (2)The static exit pressure is %3.3f bar\n(c)The power required is %3.3f MW',Dt,D2,bh,bt,T3,P3,W)" + ] + } +, +{ + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 3.6: AIR_ANGLES.sce" + ] + }, + { +"cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], +"source": [ +"clc\n", +"clear\n", +"//input data\n", +"Dt=0.25//Tip diameter of the eye in m\n", +"Dh=0.1//Hub diameter of the eye in m\n", +"N=120//Speed of the compressor in rps\n", +"m=5//Mass of the air handled in kg/s\n", +"P01=102//Inlet stagnation pressure in kPa\n", +"T01=335//Inlet total temperature in K\n", +"r=1.4//The ratio of specific heats of air\n", +"R=287//The universal gas constant in J/kg.K\n", +"Cp=1005//The specific heat of air at constant pressure in J/kg.K\n", +"\n", +"//calculations\n", +"d1=(P01*10^3)/(R*T01)//Density at the inlet of inducer in kg/m^3\n", +"Dm=(Dh+Dt)/2//Mean impeller diameter in m\n", +"b=(Dt-Dh)/2//Impeller blade height in m\n", +"C1=m/(d1*3.14*Dm*b)//Axial velocity component at the inlet in m/s\n", +"T11=T01-((C1^2)/(2*Cp))//Inlet temperature in K\n", +"P11=P01*(T11/T01)^(r/(r-1))//Inlet pressure in kPa\n", +"d11=(P11*10^3)/(R*T11)//Inlet density with mean impeller diameter an blade height in kg/m^3\n", +"C11=m/(d11*3.14*Dm*b)//Axial velocity component at inlet using mean blade values in m/s\n", +"T12=T01-((C1^2)/(2*Cp))//Initial temperature using modified axial velocity in K\n", +"P12=P01*(T12/T01)^(r/(r-1))//Initial pressure at inlet usin modified axial velocity in kPa\n", +"d12=(P12*10^3)/(R*T12)//Inlet density with modified axial velocity in kg/m^3\n", +"C12=m/(d12*3.14*Dm*b)//Axial velocity component at inlet using modified axial velocity in m/s\n", +"U1=3.14*Dm*N//Peripheral velocity of impeller at inlet in m/s\n", +"b1=atand(C12/U1)//The blade angle at impeller inlet in degree\n", +"W11=C12/sind(b1)//Relative velocity at inlet in m/s\n", +"Mr11=W11/(r*R*T12)^(1/2)//Initial relative mach number\n", +"Ca=C12//Axial velocity at IGV in m/s\n", +"W12=Ca//Relative velocity at inlet usin IGV in m/s\n", +"a1=atand(Ca/U1)//Air angle at IGV exit in degree\n", +"C13=Ca/sind(a1)//The velocity of flow of air at inlet in m/s\n", +"T13=T01-((C13^2)/(2*Cp))//Initial temperature using IGV in K\n", +"Mr12=W12/(r*R*T13)^(1/2)//Initial relative mach number using IGV \n", +"\n", +"//output5\n", +"printf('(1)Without using IGV\n (a)The air angle at inlet of inducer blade is %3.2f degree\n (b)The inlet relative mach number is %3.3f\n(2)With using IGV\n (a))The air angle at inlet of inducer blade is %3.2f degree\n (b)The inlet relative mach number is %3.3f',b1,Mr11,a1,Mr12)" + ] + } +, +{ + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 3.7: ABSOLUTE_MACH_NUMBER.sce" + ] + }, + { +"cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], +"source": [ +"clc\n", +"clear\n", +"//input data\n", +"Cr2=28//Radial component of velocity at impeller exit in m/s\n", +"ss=0.9//The slip factor\n", +"U2=350//The impeller tip speed in m/s\n", +"A=0.08//The impeller area in m^2\n", +"nc=0.9//Total head isentropic efficiency\n", +"T01=288//The ambient air temperature in K\n", +"P01=1//The ambient air pressure in bar\n", +"r=1.4//The ratio of specific heats of air\n", +"R=287//The universal gas constant in J/kg.K\n", +"Cp=1005//The specific heat of air at constant pressure in J/kg.K\n", +"\n", +"//calculations\n", +"Cx2=ss*U2//outlet absolute velocity of air in tangential direction in m/s\n", +"C2=((Cx2^2)+(Cr2^2))^(1/2)//Axial velocity component at the outlet in m/s\n", +"T=(ss*(U2^2))/Cp//Total change in temperature in K\n", +"T02=T+T01//The final ambient air temperature in K\n", +"T2=T02-((C2^2)/(2*Cp))//The actual final air temperature in K\n", +"M2=(C2)/(r*R*T2)^(1/2)//Exit absolute mach number\n", +"P=((1+(ss*T/T01))^(r/(r-1)))//The overall pressure ratio\n", +"P02=P*P01//The final ambient pressure in bar\n", +"P2=P02*(T2/T02)^(r/(r-1))//The absolute final pressure in bar\n", +"d2=(P2*10^5)/(R*T2)//The final density of air at exit in kg/m^3\n", +"m=d2*A*Cr2//The mass flow rate in kg/s\n", +"\n", +"//output\n", +"printf('(a)The exit absolute mach number is %3.4f\n(b)The mass flow rate is %3.4f kg/s',M2,m)" + ] + } +, +{ + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 3.8: MAXIMUM_MACH_NUMBER.sce" + ] + }, + { +"cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], +"source": [ +"clc\n", +"clear\n", +"//input data\n", +"Dh=0.175//Hub diameter of the eye in m\n", +"Dt=0.3125//Tip diameter of the eye in m\n", +"m=20//Mass of the air handled in kg/s\n", +"N=16000//Speed of the compressor in rpm\n", +"T01=288//The ambient air temperature in K\n", +"P01=100//The ambient air pressure in kPa\n", +"Ca=152//The axial component of inlet velocity of eye in m/s\n", +"r=1.4//The ratio of specific heats of air\n", +"R=287//The universal gas constant in J/kg.K\n", +"Cp=1005//The specific heat of air at constant pressure in J/kg.K\n", +"\n", +"\n", +"//calculations\n", +"A=(3.14/4)*((Dt^2)-(Dh^2))//Annulus area of flow at the impeller eye in m^2\n", +"Ut=(3.1415*Dt*N)/60//Impeller eye tip speed in m/s\n", +"Uh=(3.1415*Dh*N)/60//Impeller eye hub speed in m/s\n", +"a1=90-20//Blade angle at inlet in degree \n", +"C1=Ca/sind(a1)//The air entry velocity into the impeller eye in m/s\n", +"T1=T01-((C1^2)/(2*Cp))//The actual inlet air temperature in K\n", +"P1=P01*(T1/T01)^(r/(r-1))//The actual inlet air pressure in kPa\n", +"d1=P1/(R*T1)//The initial density of air at entry in kg/m^3\n", +"b1h=atand(Ca/(Uh-(Ca/tand(a1))))//Impeller angle at the hub in degree\n", +"b1t=atand(Ca/(Ut-(Ca/tand(a1))))//Impeller angle at the tip of eye in degree\n", +"Cx1=Ca/tand(a1)//Inlet absolute velocity of air in tangential direction in m/s\n", +"Wx1=Ut-Cx1//Relative whirl component of velocity at inlet in m/s\n", +"W1=((Wx1^2)+(Ca^2))^(1/2)//Relative velocity at inlet in m/s\n", +"Mr1=W1/(r*R*T1)^(1/2)//Maximum mach number at the eye\n", +"\n", +"//output\n", +"printf('(a)\n (1)The impeller eye tip speed is %3.2f m/s\n (2)The impeller eye hub speed is %3.2f m/s\n (3)The impeller angle at the hub is %i degree\n (4)Impeller angle at the tip of eye is %3.2f degree\n(b)The maximum mach number at the eye is %3.2f',Ut,Uh,b1h,b1t,Mr1)" + ] + } +, +{ + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 3.9: MASS_AND_VOLUME_RATE.sce" + ] + }, + { +"cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], +"source": [ +"clc\n", +"clear\n", +"//input data\n", +"P1=100//The air in take pressure in kPa\n", +"T1=309//The air in take temperature in K\n", +"H=0.750//Pressure head developed in mm W.G\n", +"P=33//Input power to blower in kW\n", +"nb=0.79//Blower efficiency\n", +"nm=0.83//Mechanical efficiency\n", +"r=1.4//The ratio of specific heats of air\n", +"R=287//The universal gas constant in J/kg.K\n", +"Cp=1005//The specific heat of air at constant pressure in J/kg.K\n", +"g=9.81//Acceleration due to gravity in m/s^2\n", +"dw=1000//Density of water in kg/m^3\n", +"\n", +"//calculations\n", +"d=(P1*10^3)/(R*T1)//Density of air flow at inlet in kg/m^3\n", +"dP=dw*g*H//Total change in pressure in N/m^2\n", +"IW=dP/d//Ideal work done in J/kg\n", +"Wm=IW/nb//Actual work done per unit mass flow rate in J/kg\n", +"W=P*nm//Actual power input in kW\n", +"m=(W*10^3)/Wm//Mass flow rate in kg/s\n", +"Q=m/d//Volume flow rate in m^3/s\n", +"P2=P1+(dP/10^3)//The exit pressure of air in kPa\n", +"T2=T1+(Wm/(Cp))//The exit temperature of air in K\n", +"\n", +"//output\n", +"printf('(a)The mass flow rate of air is %3.3f kg/s\n(b)The volume flow rate of air is %3.2f m^3/s\n(c)\n (1)The exit pressure of air is %3.2f kPa\n (2)The exit temperature of air is %3.2f K',m,Q,P2,T2)" + ] + } +], +"metadata": { + "kernelspec": { + "display_name": "Scilab", + "language": "scilab", + "name": "scilab" + }, + "language_info": { + "file_extension": ".sce", + "help_links": [ + { + "text": "MetaKernel Magics", + "url": "https://github.com/calysto/metakernel/blob/master/metakernel/magics/README.md" + } + ], + "mimetype": "text/x-octave", + "name": "scilab", + "version": "0.7.1" + } + }, + "nbformat": 4, + "nbformat_minor": 0 +} diff --git a/Turbomachines_by_A_V_Arasu/4-AXIAL_FLOW_COMPRESSORS_AND_FANS.ipynb b/Turbomachines_by_A_V_Arasu/4-AXIAL_FLOW_COMPRESSORS_AND_FANS.ipynb new file mode 100644 index 0000000..4795e42 --- /dev/null +++ b/Turbomachines_by_A_V_Arasu/4-AXIAL_FLOW_COMPRESSORS_AND_FANS.ipynb @@ -0,0 +1,820 @@ +{ +"cells": [ + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "# Chapter 4: AXIAL FLOW COMPRESSORS AND FANS" + ] + }, +{ + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 4.10: AIR_AND_BLADE_ANGLES.sce" + ] + }, + { +"cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], +"source": [ +"clc\n", +"clear\n", +"//input data\n", +"Uh=150//The blade root velocity in m/s\n", +"Um=200//The mean velocity in m/s\n", +"Ut=250//The tip velocity in m/s\n", +"dT0=20//The total change in temperature in K\n", +"Ca1m=150//The axial velocity in m/s\n", +"l=0.93//The work done factor \n", +"Rm=0.5//Reaction at mean radius\n", +"N=9000//Rotational speed in rpm\n", +"R=287//The universal gas constant in J/kg.K\n", +"Cp=1005//The specific heat of air at constant pressure in J/kg.K\n", +"r=1.4//The ratio of specific heats of air\n", +"\n", +"//calculations\n", +"dtb1tb2=((Cp*dT0)/(l*Um*Ca1m))//The difference between the tangent angles of blade angles at mean\n", +"atb1tb2=((2*Rm*Um)/(Ca1m))//The sum of the tangent angles of blade angles at mean\n", +"b1m=atand((atb1tb2+dtb1tb2)/2)//The inlet blade angle in degree at mean\n", +"a2m=b1m//The exit air angle in degree as the Reaction at mean radius is 0.5\n", +"b2m=atand(tand(b1m)-dtb1tb2)//The exit blade angle in degree at mean\n", +"a1m=b2m//The inlet air angle in degree as the reaction at mean radius is 0.5\n", +"Dh=(Uh*60)/(3.141*N)//Hub diameter in m\n", +"Dm=(Um*60)/(3.141*N)//Mean diameter in m\n", +"Cx1m=Ca1m*tand(a1m)//The whirl velocity at inlet at mean in m/s\n", +"Cx2m=Ca1m*tand(a2m)//The whirl velocity at exit at mean in m/s\n", +"Cx1h=(Cx1m*(Dh/2)/(Dm/2))//The whirl velocity at inlet at hub in m/s\n", +"Cx2h=(Cx2m*(Dh/2)/(Dm/2))//The whirl velocity at exit at hub in m/s\n", +"K1=(Ca1m^2)+(2*(Cx1m^2))//Sectional velocity in m/s\n", +"Ca1h=((K1)-(2*(Cx1h^2)))^(1/2)//The axial velocity at hub inlet in (m/s)^2\n", +"w=(2*3.141*N)/60//Angular velocity of blade in rad/s\n", +"K2=(Ca1m^2)+(2*(Cx2m^2))-(2*((Cx2h/(Dh/2))-(Cx1m/(Dm/2))))*(w*(Dm/2)^(2))//Sectional velocity in (m/s)^2\n", +"Ca2h=(K2-(2*Cx2h^2)+(2*((Cx2h/(Dh/2))-(Cx1h/(Dh/2))))*(w*(Dh/2)^(2)))^(1/2)//Axial velocity at hub outlet in m/s\n", +"a1h=atand(Cx1h/Ca1h)//Air angle at inlet in hub in degree\n", +"b1h=atand((Uh-Cx1h)/Ca1h)//Blade angle at inlet in hub in degree\n", +"a2h=atand(Cx2h/Ca2h)//Air angle at exit in hub in degree\n", +"b2h=atand((Uh-Cx2h)/Ca2h)//Blade angle at exit in hub in degree\n", +"W1=Ca1h/cosd(b1h)//Relative velocity at entry in hub in m/s\n", +"W2=Ca2h/cosd(b2h)//Relative velocity at exit in hub in m/s\n", +"Rh=((W1^2)-(W2^2))/(2*Uh*(Cx2h-Cx1h))//The degree of reaction at hub\n", +"Dt=(Ut*60)/(3.141*N)//Tip diameter in m\n", +"Cx1t=(Cx1m*(Dt/2)/(Dm/2))//The whirl velocity at inlet at tip in m/s\n", +"Cx2t=(Cx2m*(Dt/2)/(Dm/2))//The whirl velocity at exit at tip in m/s\n", +"Ca1t=(K1-(2*Cx1t^2))^(1/2)//Axial velocity at tip inlet in m/s\n", +"Ca2t=(K2-(2*Cx2t^2)+(2*((Cx2t/(Dt/2))-(Cx1t/(Dt/2))))*(w*(Dt/2)^(2)))^(1/2)//Axial velocity at tip outlet in m/s\n", +"a1t=atand(Cx1t/Ca1t)//Air angle at inlet in tip in degree\n", +"b1t=atand((Ut-Cx1t)/Ca1t)//Blade angle at inlet in tip in degree\n", +"a2t=atand(Cx2t/Ca2t)//Air angle at exit in tip in degree\n", +"b2t=atand((Ut-Cx2t)/Ca2t)//Blade angle at exit in tip in degree\n", +"W1=Ca1t/cosd(b1t)//Relative velocity at entry in tip in m/s\n", +"W2=Ca2t/cosd(b2t)//Relative velocity at exit in tip in m/s\n", +"Rt=((W1^2)-(W2^2))/(2*Ut*(Cx2t-Cx1t))//The degree of reaction at tip\n", +"\n", +"//output\n", +"printf('(a)At the mean\n (1)The inlet blade angle is %3.2f degree\n (2)The inlet air angle is %3.2f degree\n (3)The outlet blade angle is %3.2f degree\n (4)The outlet air angle is %3.2f degree\n (5)Degree of reaction is %3.1f \n(b)At the root\n (1)The inlet blade angle is %3.2f degree\n (2)The inlet air angle is %3.1f degree\n (3)The outlet blade angle is %3.1f degree\n (4)The outlet air angle is %3.1f degree\n (5)Degree of reaction is %3.1f\n(c)At the tip\n (1)The inlet blade angle is %3.2f degree\n (2)The inlet air angle is %3.2f degree\n (3)The outlet blade angle is %3.2f degree\n (4)The outlet air angle is %3.2f degree\n (5)Degree of reaction is %3.1f\n',b1m,a1m,b2m,a2m,Rm,b1h,a1h,b2h,a2h,Rh,b1t,a1t,b2t,a2t,Rt)\n", +"" + ] + } +, +{ + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 4.11: TOTAL_PRESSURE_OF_AIR.sce" + ] + }, + { +"cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], +"source": [ +"clc\n", +"clear\n", +"//input data\n", +"N=3600//Running speed of blower in rpm\n", +"Dt=0.2//The rotor tip diameter in m\n", +"Dh=0.125//The rotor hub diameter in m\n", +"P1=1.013//The atmospheric pressure in bar\n", +"T1=298//The atmospheric temperature in K\n", +"m=0.5//Mass flow rate of air in kg/s\n", +"db=20//The turning angle of the rotor in degree\n", +"b1=55//The inlet blade angle in degree \n", +"R=287//The universal gas constant in J/kg.K\n", +"nc=0.9//Total-to-total efficiency\n", +"P=0.25//Total pressure drop across the intake in cm of water\n", +"Cp=1005//The specific heat of air at constant pressure in J/kg.K\n", +"r=1.4//The ratio of specific heats of air\n", +"g=9.81//Acceleration due to gravity in m/s^2\n", +"ns=0.75//The stator efficiency\n", +"dw=1000//Density of water in kg/m^3\n", +"\n", +"//calculations\n", +"d1=(P1*10^5)/(R*T1)//The density of air at inlet in kg/m^3\n", +"A=(3.141/4)*((Dt^2)-(Dh^2))//The area of flow in m^2\n", +"Ca=m/(d1*A)//The axial velocity of air in m/s\n", +"U=((3.141*(Dt+Dh)*N)/(2*60))//Mean rotor blade velocity in m/s\n", +"b2=b1-db//The outlet blade angle in degree\n", +"Cx2=U-(Ca*tand(b2))//The whirl velocity at exit in m/s \n", +"Cx1=0//The whirl velocity at entry in m/s as flow at inlet is axial \n", +"dh0r=U*(Cx2-Cx1)//The actual total enthalpy rise across the rotor in J/kg\n", +"dh0sr=nc*dh0r//The isentropic total enthalpy rise across the rotor in J/kg\n", +"dP0r=(d1*dh0sr)*((10^-1)/(g))//The total pressure rise across the rotor in cm of water\n", +"P0=dP0r-P//Stagnation pressure at the rotor exit in cm of water\n", +"C2=((Ca^2)+(Cx2^2))^(1/2)//The absolute velocity at the exit in m/s\n", +"dPr=dP0r-((d1*((C2^2)-(Ca^2)))/2)*((10^-1)/g)//The static pressure across the rotor in cm of water\n", +"dhs=((C2^2)-(Ca^2))/2//The actual enthalpy change across the stator in J/kg\n", +"dhss=ns*dhs//The theoretical enthalpy change across the stator in J/kg\n", +"dPs=(d1*dhss)*((10^-1)/g)//The static pressure rise across the stator in cm of water\n", +"dP0s=-((dPs/((10^-1)/g))+((d1/2)*(Ca^2-C2^2)))*(10^-1/g)//The change in total pressure across the stator in cm of water\n", +"P03=P0-dP0s//Total pressure at stator inlet in cm of water\n", +"dh0ss=((dw*g*(P03/100))/d1)//Theoretical total enthalpy change across the stage in J/kg\n", +"ntt=dh0ss/dh0r//The overall total-to-total efiiciency\n", +"DR=dPr/(dPr+dPs)//The degree of reaction for the stage\n", +"\n", +"//output\n", +"printf('(a)Total pressure of air exit of rotor is %3.2f cm of water\n(b)The static pressure rise across the rotor is %3.2f cm of water\n(c)The static pressure rise across the stator os %3.2f cm of water\n(d)The change in total pressure across the stator is %3.2f cm of water\n(e)The overall total-to-total efficiency is %3.3f\n(f)The degree of reaction for the stage is %3.3f',P0,dPr,dPs,dP0s,ntt,DR)" + ] + } +, +{ + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 4.12: POWER_REQUIRED_TO_DRIVE_THE_FAN.sce" + ] + }, + { +"cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], +"source": [ +"clc\n", +"clear\n", +"//input data\n", +"Q=2.5//The amount of air which fan takes in m^3/s\n", +"P1=1.02//The inlet pressure of air in bar\n", +"T1=315//The inlet temperature of air in K\n", +"dH=0.75//The pressure head delivered by axial flow fan in m W.G\n", +"T2=325//The delivery temperature of air in K\n", +"R=287//The universal gas constant in J/kg.K\n", +"Cp=1.005//The specific heat of air at constant pressure in kJ/kg.K\n", +"r=1.4//The ratio of specific heats of air\n", +"g=9.81//Acceleration due to gravity in m/s^2\n", +"\n", +"//calculations\n", +"d=(P1*10^5)/(R*T1)//The density of air in kg/m^3\n", +"m=d*Q//The mass flow rate of air in kg/s\n", +"W=m*Cp*(T2-T1)//Power required to drive the fan in kW\n", +"dP=((10^3)*g*dH)/(10^5)//The overall pressure difference in bar\n", +"P2=P1+(dP)//The exit pressure in bar\n", +"nf=((T1*(((P2/P1)^((r-1)/r))-1))/(T2-T1))//Static fan efficiency\n", +"\n", +"//output\n", +"printf('(a)Mass flow rate through the fan is %3.2f kg/s\n(b)Power required to drive the fan is %3.2f kW\n(c)Static fan efficiency is %3.4f',m,W,nf)" + ] + } +, +{ + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 4.13: FLOW_RATE.sce" + ] + }, + { +"cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], +"source": [ +"clc\n", +"clear\n", +"//input data\n", +"b2=10//Rotor blade air angle at exit in degree\n", +"Dt=0.6//The tip diameter in m\n", +"Dh=0.3//The hub diameter in m\n", +"N=960//The speed of the fan in rpm\n", +"P=1//Power required by the fan in kW\n", +"pi=0.245//The flow coefficient\n", +"P1=1.02//The inlet pressure in bar\n", +"T1=316//The inlet temperature in K\n", +"R=287//The universal gas constant in J/kg.K\n", +"Cp=1.005//The specific heat of air at constant pressure in kJ/kg.K\n", +"r=1.4//The ratio of specific heats of air\n", +"g=9.81//Acceleration due to gravity in m/s^2\n", +"\n", +"//calculations\n", +"A=(3.141/4)*((Dt^2)-(Dh^2))//Area of the fan at inlet in m^2\n", +"Dm=(Dt+Dh)/2//The mean rotor diameter in m\n", +"U=(3.141*Dm*N)/60//The mean blade speed in m/s\n", +"Ca=pi*U//The axial velocity in m/s\n", +"Q=A*Ca//The flow rate of air in m^3/s\n", +"d=(P1*10^5)/(R*T1)//Density of air in kg/m^3\n", +"dPst=((d*(U^2)*(1-((pi*tand(b2))^2)))/2)*((10^5)/(g*(10^3)))*10^-5//Static pressure across the stage in m W.G\n", +"Wm=U*(U-(Ca*tand(b2)))//Work done per unit mass in J/kg\n", +"m=d*Q//Mass flow rate in kg/s\n", +"W=m*Wm//Work done in W\n", +"no=W/(P*10^3)//Overall efficiency \n", +"\n", +"//output\n", +"printf('(a)THe flow rate is %3.3f m^3/s\n(b)Static pressure rise across the stage is %3.3f m W.G\n(c)The overall efficiency is %3.4f',Q,dPst,no)" + ] + } +, +{ + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 4.14: ROTOR_BLADE_ANGLE.sce" + ] + }, + { +"cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], +"source": [ +"clc\n", +"clear\n", +"//input data\n", +"b2=10//Rotor blade air angle at exit in degree\n", +"Dt=0.6//The tip diameter in m\n", +"Dh=0.3//The hub diameter in m\n", +"N=960//The speed of the fan in rpm\n", +"P=1//Power required by the fan in kW\n", +"pi=0.245//The flow coefficient\n", +"P1=1.02//The inlet pressure in bar\n", +"T1=316//The inlet temperature in K\n", +"R=287//The universal gas constant in J/kg.K\n", +"Cp=1.005//The specific heat of air at constant pressure in kJ/kg.K\n", +"r=1.4//The ratio of specific heats of air\n", +"g=9.81//Acceleration due to gravity in m/s^2\n", +"\n", +"//calculations\n", +"A=(3.141/4)*((Dt^2)-(Dh^2))//Area of the fan at inlet in m^2\n", +"Dm=(Dt+Dh)/2//The mean rotor diameter in m\n", +"U=(3.141*Dm*N)/60//The mean blade speed in m/s\n", +"Ca=pi*U//The axial velocity in m/s\n", +"Q=A*Ca//The flow rate of air in m^3/s\n", +"d=(P1*10^5)/(R*T1)//Density of air in kg/m^3\n", +"b1=atand(U/Ca)//Rotor blade angle at entry in degree\n", +"dPst=((d*(U^2)*(1-((pi*tand(b2))^2)))/2)//Static pressure rise across the stage in N/m^2\n", +"dPr=dPst//Static pressure rise across the rotor in N/m^2\n", +"Wm=U*(U-(Ca*tand(b2)))//Work done per unit mass in J/kg\n", +"dP0st=d*Wm//Stagnation pressure of the stage in N/m^2\n", +"DR1=dPr/dP0st//Degree of reaction\n", +"DR2=(Ca/(2*U))*(tand(b1)+tand(b2))//Degree of reaction\n", +"\n", +"//output\n", +"printf('(a)Rotor blade angle at entry is %3.2f degree\n(b)Degree of reaction is %3.3f',b1,DR1)" + ] + } +, +{ + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 4.15: OVERALL_EFFICIENCY.sce" + ] + }, + { +"cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], +"source": [ +"clc\n", +"clear\n", +"//input data\n", +"m=3//Mass flow rate of air in kg/s\n", +"P1=100*10^3//The atmospheric pressure in Pa\n", +"T1=310//The atmospheric temperature in K\n", +"nb=0.8//The efficiency of the blower\n", +"nm=0.85//The mechanical efficiency\n", +"P=30//The power input in kW\n", +"R=287//The universal gas constant in J/kg.K\n", +"g=9.81//Acceleration due to gravity in m/s^2\n", +"dw=1000//Density of water in kg/m^3\n", +"\n", +"//calculations\n", +"no=nb*nm//Overall efficiency of the blower\n", +"d=(P1)/(R*T1)//The density of the air in kg/m^3\n", +"dP=((no*P*10^3)/m)*d//The pressure developed in N/m^2\n", +"dH=((dP)/(g*dw))*(10^3)//The pressure developed in mm W.G\n", +"\n", +"//output\n", +"printf('(a)Overall efficiency of the blower is %3.2f\n(b)The pressure developed is %3.2f mm W.G',no,dH)" + ] + } +, +{ + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 4.16: OVERALL_EFFICIENCY_AND_POWER.sce" + ] + }, + { +"cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], +"source": [ +"clc\n", +"clear\n", +"//input data\n", +"psi=0.4//Pressure coefficient \n", +"m=3.5//Mass flow rate of air in kg/s\n", +"N=750//The speed of fan in rpm\n", +"T1=308//The static temperature at the entry in K\n", +"Dh=0.26//The hub diameter in m\n", +"DhDt=1/3//The hub to tip ratio\n", +"P1=98.4*10^3//The static pressure at entry in Pa\n", +"nm=0.9//The mechanical efficiency\n", +"nf=0.79//Static fan efficiency\n", +"R=287//The universal gas constant in J/kg.K\n", +"Cp=1.005//The specific heat of air at constant pressure in kJ/kg.K\n", +"r=1.4//The ratio of specific heats of air\n", +"g=9.81//Acceleration due to gravity in m/s^2\n", +"dw=1000//Density of water in kg/m^3\n", +"\n", +"//calculations\n", +"no=nm*nf//Overall efficiency\n", +"Dt=Dh/DhDt//The tip diameter in m\n", +"Dm=(Dt+Dh)/2//Mean rotor diameter in m\n", +"U=(3.141*Dm*N)/60//The mean blade speed in m/s\n", +"dPd=((U^2)/2)*psi//The ratio of change in pressure to density in J/kg\n", +"Wi=dPd*m//The ideal work in W\n", +"P=Wi/nm//The power required by the fan in W\n", +"d=P1/(R*T1)//The density of the air in kg/m^3\n", +"A=(3.141/4)*((Dt^2)-(Dh^2))//Area of cross section of the fan in m^2\n", +"Ca=m/(d*A)//The axial velocity of air in m/s\n", +"pi=Ca/U//The flow coefficient\n", +"tb1tb2=psi/(2*pi)//The difference between tangent angles of rotor inlet and exit angles\n", +"b2=atand((1-(dPd/U^2))/pi)//The exit rotor angle in degree\n", +"b1=atand((tand(b2))+(tb1tb2))//The inlet rotor angle in degree\n", +"dP=d*dPd//The pressure developed in N/m^2\n", +"dH=(dP/(dw*g))*10^3//Pressure developed in mm of W.G\n", +"\n", +"//output\n", +"printf('(a)The overall efficiency is %3.3f\n,(b)The power required by the fan is %3.2f W\n(c)The flow coefficient is %3.2f\n(d)\n (1)The rotor inlet angle is %3.2f degree\n (2)The rotor exit angle is %3.2f degree\n(e)The pressure developed is %3.2f mm of W.G',no,P,pi,b1,b2,dH)" + ] + } +, +{ + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 4.1: PRESSURE_RISE.sce" + ] + }, + { +"cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], +"source": [ +"clc\n", +"clear\n", +"//input data\n", +"b1=60//The angle made by the relative velocity vector at exit in degree\n", +"db=30//The turning angle in degree\n", +"dCx=100//The change in the tangential velocities in m/s\n", +"DR=0.5//Degree of reaction\n", +"N=36000//The speed of the compressor in rpm\n", +"D=0.14//Mean blade diameter in m\n", +"P1=2//Inlet pressure in bar\n", +"T1=330//Inlet temperature in K\n", +"b=0.02//Blade height in m\n", +"R=287//The universal gas constant in J/kg.K\n", +"Cp=1.005//The specific heat of air at constant pressure in kJ/kg.K\n", +"r=1.4//The ratio of specific heats of air\n", +"\n", +"//calculations\n", +"b2=b1-db//The angle made by the relative velocity vector at entry in degree\n", +"a1=b2//Air flow angle at exit in degree as DR=0.5\n", +"U=(3.1415*D*N)/60//The blade mean speed in m/s\n", +"T2=((U*dCx)/(Cp*1000))+T1//The exit air temperature in K\n", +"P2=P1*(T2/T1)^(r/(r-1))//The exit air pressure in bar\n", +"dP=P2-P1//The pressure rise in bar\n", +"Ca=(2*U*DR)/(tand(b2)+tand(b1))//The axial velocity in m/s\n", +"A1=3.1415*D*b//The inlet flow area in m^2\n", +"d1=(P1*10^5)/(R*T1)//The inlet air density in kg/m^3\n", +"m=d1*A1*Ca//The amount of air handled in kg/s\n", +"W=m*Cp*(T2-T1)//The power developed in kW\n", +"\n", +"//output\n", +"printf('(a)Air flow angle at exit is %3i degree\n(b)The pressure rise is %3.2f bar\n(c)The amount of air handled is %3.2f kg/s\n(d)The power developed is %3.1f kW',a1,dP,m,W)" + ] + } +, +{ + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 4.2: TOTAL_HEAD_ISENTROPIC_EFFICIENCY.sce" + ] + }, + { +"cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], +"source": [ +"clc\n", +"clear\n", +"//input data\n", +"P01=1//Atmospheric pressure at inlet in bar\n", +"T01=291//Atmospheric temperature at inlet in K\n", +"T02=438//Total head temperature in delivery pipe in K \n", +"P02=3.5//Total head pressure in delivery pipe in bar\n", +"P2=3//Staic pressure in delivery pipe in bar\n", +"R=287//The universal gas constant in J/kg.K\n", +"Cp=1005//The specific heat of air at constant pressure in J/kg.K\n", +"r=1.4//The ratio of specific heats of air\n", +"\n", +"//calculations \n", +"T02s=T01*(P02/P01)^((r-1)/r)//Total isentropic head temperature in delivery pipe in K \n", +"nc=(T02s-T01)/(T02-T01)//Total head isentropic efficiency\n", +"np=((log10(P02/P01))/((r/(r-1))*(log10(T02/T01))))//Polytropic efficiency\n", +"T2=T02*(P2/P02)^((r-1)/r)//Static temperature in delivery pipe in K\n", +"C2=(2*Cp*(T02-T2))^(1/2)//The air velocity in delivery pipe in m/s\n", +"\n", +"//output\n", +"printf('(a)Total head isentropic efficiency is %3.3f\n(b)Polytropic efficiency %3.3f\n(c)The air velocity in delivery pipe is %3.2f m/s',nc,np,C2)" + ] + } +, +{ + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 4.3: POWER_REQUIRED.sce" + ] + }, + { +"cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], +"source": [ +"clc\n", +"clear\n", +"//input data\n", +"N=8//Number of stages\n", +"Po=6//Overall pressure ratio \n", +"T01=293//Temperature of air at inlet in K\n", +"nc=0.9//Overall isentropic efficiency\n", +"DR=0.5//Degree of reaction \n", +"U=188//Mean blade speed in m/s\n", +"Ca=100//Constant axial velocity in m/s\n", +"R=287//The universal gas constant in J/kg.K\n", +"Cp=1005//The specific heat of air at constant pressure in J/kg.K\n", +"r=1.4//The ratio of specific heats of air\n", +"\n", +"//calculations\n", +"T0n1s=T01*(Po)^((r-1)/r)//The isentropic temperature of air leaving compressor stage in K\n", +"T0n1=((T0n1s-T01)/nc)+T01//The temperature of air leaving compressor stage in K\n", +"dta2ta1=(Cp*(T0n1-T01))/(N*U*Ca)//The difference between tan angles of air exit and inlet\n", +"sta1tb1=U/Ca//The sum of tan of angles of air inlet and the angle made by the relative velocity \n", +"b1=atand((dta2ta1+sta1tb1)/2)//The angle made by the relative velocity vector at exit in degree as the DR=1 then a2=b1\n", +"a1=atand(tand(b1)-dta2ta1)//Air flow angle at exit in degree\n", +"W=Cp*(T0n1-T01)*10^-3//Power required per kg of air/s in kW\n", +"\n", +"//output\n", +"printf('(a)Power required is %3.2f kW\n(b)\n (1)Air flow angle at exit is %3i degree \n (2)The angle made by the relative velocity vector at exit is %3i degree',W,a1,b1)" + ] + } +, +{ + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 4.4: PRESSURE_AT_OUTLET.sce" + ] + }, + { +"cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], +"source": [ +"clc\n", +"clear\n", +"//input data\n", +"W=4.5//Power absorbed by the compressor in MW\n", +"m=20//Amount of air delivered in kg/s\n", +"P01=1//Stagnation pressure of air at inlet in bar\n", +"T01=288//Stagnation temperature of air at inlet in K\n", +"np=0.9//Polytropic efficiency of compressor\n", +"dT0=20//Temperature rise in first stage in K\n", +"R=287//The universal gas constant in J/kg.K\n", +"Cp=1.005//The specific heat of air at constant pressure in kJ/kg.K\n", +"r=1.4//The ratio of specific heats of air\n", +"\n", +"\n", +"//calculations\n", +"T02=T01+dT0//Stagnation temperature of air at outlet in K\n", +"T0n1=((W*10^3)/(m*Cp))+T01//The temperature of air leaving compressor stage in K\n", +"P0n1=P01*(T0n1/T01)^((np*r)/(r-1))//Pressure at compressor outlet in bar\n", +"P1=(T02/T01)^((np*r)/(r-1))//The pressure ratio at the first stage \n", +"N=((log10(P0n1/P01)/log10(P1)))//Number of stages \n", +"T0n1T01=(P0n1/P01)^((r-1)/(np*r))//The temperature ratio at the first stage\n", +"T0n1sT01=(P0n1/P01)^((r-1)/r)//The isentropic temperature ratio at the first stage\n", +"nc=((T0n1sT01-1)/(T0n1T01-1))//The overall isentropic efficiency\n", +"\n", +"//output\n", +"printf('(a)Pressure at compressor outlet is %3.2f bar\n(b)Number of stages is %3.f\n(c)The overall isentropic efficiency is %3.3f',P0n1,N,nc)" + ] + } +, +{ + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 4.5: NUMBER_OF_STAGES.sce" + ] + }, + { +"cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], +"source": [ +"clc\n", +"clear\n", +"//input data\n", +"DR=0.5//Degree of reaction\n", +"b1=44//Blade inlet angle in degree\n", +"b2=13//Blade outlet angle in degree\n", +"Po=5//The pressure ratio produced by the compressor\n", +"nc=0.87//The overall isentropic efficiency\n", +"T01=290//Inlet temperature in K\n", +"U=180//Mean blade speed in m/s\n", +"l=0.85//Work input factor\n", +"R=0.287//The universal gas constant in kJ/kg.K\n", +"Cp=1005//The specific heat of air at constant pressure in J/kg.K\n", +"r=1.4//The ratio of specific heats of air\n", +"\n", +"//calculations\n", +"a2=b1//Air flow angle at entry in degree as DR=0.5\n", +"a1=b2//Air flow angle at exit in degree as DR=0.5\n", +"T0n1s=T01*(Po)^((r-1)/r)//The isentropic temperature of air leaving compressor stage in K\n", +"T0n1=((T0n1s-T01)/nc)+T01//The temperature of air leaving compressor stage in K\n", +"Ca=U/(tand(b2)+tand(b1))//The axial velocity in m/s\n", +"N=((Cp*(T0n1-T01))/(l*U*Ca*(tand(a2)-tand(a1))))//The number of stages \n", +"ds=(Cp*(10^-3)*log(T0n1/T01))-(R*log(Po))//Change in entropy in kJ/kg.K\n", +"\n", +"//output\n", +"printf('(a)The number of stages are %3.f\n(b)The change in entropy is %3.3f kJ/kg-K',N,ds)" + ] + } +, +{ + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 4.6: DEGREE_OF_REACTION.sce" + ] + }, + { +"cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], +"source": [ +"clc\n", +"clear\n", +"//input data\n", +"D=0.6//Mean diameter of compressor in m\n", +"N=15000//Running speed of the compressor in rpm\n", +"dT=30//Actual overall temperature raise in K\n", +"PR=1.3//Pressure ratio of all stages\n", +"m=57//Mass flow rate of air in kg/s\n", +"nm=0.86//Mechanical efficiency\n", +"T1=308//Initial temperature in K\n", +"T2=328//Temperature at rotor exit in K\n", +"r=1.4//The ratio of specific heats of air\n", +"Cp=1.005//The specific heat of air at constant pressure in kJ/kg.K\n", +"\n", +"//calculations\n", +"W=m*Cp*dT//Work done in kW\n", +"P=W/nm//Power required in kW\n", +"ns=((T1*((PR^((r-1)/r))-1))/(dT))//Stage efficiency\n", +"R=(T2-T1)/(dT)//Reaction ratio\n", +"\n", +"//output\n", +"printf('(a)Power required to drive the compressor is %3.3f kW\n(b)The stage efficiency is %3.4f\n(c)The degree of reaction is %3.2f',P,ns,R)" + ] + } +, +{ + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 4.7: COMPRESSOR_SPEED.sce" + ] + }, + { +"cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], +"source": [ +"clc\n", +"clear\n", +"//input data\n", +"Pr=2//The pressure ratio of first stage\n", +"P1=1.01//The inlet pressure in bar\n", +"T1=303//The inlet temperature in K\n", +"nc=0.83//Overall efficency of the compressor\n", +"pi=0.47//The flow coefficient\n", +"dCxCa=0.5//Ratio of change of whirl velocity to axial velocity\n", +"D=0.5//Mean diameter in m\n", +"r=1.4//The ratio of specific heats of air\n", +"Cp=1005//The specific heat of air at constant pressure in J/kg.K\n", +"\n", +"//calculations\n", +"dT=T1*((Pr^((r-1)/r))-1)/nc//The Actual overall temperature raise in K\n", +"dCx=dCxCa*pi//The change of whirl velocity in m/s\n", +"U=(dT*Cp/dCx)^(1/2)//The mean blade speed in m/s\n", +"N=(U*60)/(3.1415*D)//Speed at which compressor runs in rpm\n", +"Cx2=(U+(dCx*U))/2//The whirl velocity at exit in m/s\n", +"Cx1=U-Cx2//The whirl velocity at entry in m/s\n", +"Ca=pi*U//The axial velocity in m/s\n", +"C1=((Ca^2)+(Cx1^2))^(1/2)//The inlet absolute velocity of air in m/s\n", +"\n", +"//output\n", +"printf('(a)The compressor speed is %3i rpm\n(b)The absolute velocity of air is %3.2f m/s',N,C1)" + ] + } +, +{ + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 4.8: TIP_RADIUS_AND_ANGLES.sce" + ] + }, + { +"cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], +"source": [ +"clc\n", +"clear\n", +"//input data\n", +"N=9000//The rotational speed in rpm\n", +"dT0=20//The stagnation temperature rise in K\n", +"DhDt=0.6//The hub to tip ratio\n", +"l=0.94//The work donee factor\n", +"ns=0.9//The isentropic efficiency of the stage\n", +"C1=150//Inlet velocity in m/s\n", +"P01=1//The ambient pressure in bar\n", +"T01=300//The ambient temperature in K\n", +"Mr1=0.92//Mach number relative to tip \n", +"R=287//The universal gas constant in J/kg.K\n", +"Cp=1005//The specific heat of air at constant pressure in kJ/kg.K\n", +"r=1.4//The ratio of specific heats of air\n", +"g=9.81//Acceleration due to gravity in m/s^2\n", +"\n", +"//calculations\n", +"T1=T01-((C1^2)/(2*Cp))//The inlet temperature in K\n", +"W1=Mr1*(r*R*T1)^(1/2)//The relative velocity at entry in m/s\n", +"b11=acosd((C1)/(W1))//The inlet rotor angle at tip in degree\n", +"Ut=W1*sind(b11)//Tip speed in m/s\n", +"rt=(Ut*60)/(2*3.1415*N)//The tip radius in m\n", +"b12=atand((tand(b11))-((Cp*dT0)/(l*Ut*C1)))//The outlet rotor angle at tip in degree\n", +"P1=P01*(T1/T01)^(r/(r-1))//The inlet pressure in bar\n", +"d1=(P1*10^5)/(R*T1)//The density of air at the entry in kg/m^3\n", +"Dt=2*rt//The tip diameter in m\n", +"Dh=DhDt*(Dt)//The hub diameter in m\n", +"A1=(3.141/4)*((Dt^2)-(Dh^2))//The area of cross section at the entry in m^2\n", +"rm=((Dt/2)+(Dh/2))/2//The mean radius in m\n", +"h=((Dt/2)-(Dh/2))//The height of the blade in m\n", +"A=2*3.1415*rm*h//The area of the cross section in m^2\n", +"m=d1*A*C1//The mass flow rate in kg/s\n", +"P03P01=(1+((ns*dT0)/T01))^(r/(r-1))//The stagnation pressure ratio \n", +"P=m*Cp*dT0*10^-3//The power required in kW\n", +"Uh=(3.1415*Dh*N)/60//The hub speed in m/s\n", +"b21=atand(Uh/C1)//The rotor air angle at entry in degree\n", +"b22=atand(tand(b21)-((Cp*dT0)/(l*Uh*C1)))//The rotor air angle at exit in degree\n", +"\n", +"//output\n", +"printf('(a)\n (1)The tip radius is %3.3f m\n (2)The rotor entry angle at tip section is %3.1f degree\n (3)The rotor exit angle at tip section is %3.2f degree\n(b)Mass flow entering the stage is %3.3f kg/s\n(c)\n (1)The stagnation pressure ratio is %3.3f\n (2)The power required is %3.2f kW\n(d)\n (1)The rotor air angle at entry is %3.2f degree\n (2)The rotor air angle at exit is %3.2f degree',rt,b11,b12,m,P03P01,P,b21,b22)\n", +"" + ] + } +, +{ + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 4.9: STAGE_AIR_AND_BLADE_ANGLES.sce" + ] + }, + { +"cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], +"source": [ +"clc\n", +"clear\n", +"//input data\n", +"Ur=150//The blade root velocity in m/s\n", +"Um=200//The mean velocity in m/s\n", +"Ut=250//The tip velocity in m/s\n", +"dT0=20//The total change in temperature in K\n", +"Ca=150//The axial velocity in m/s\n", +"l=0.93//The work done factor \n", +"Rm=0.5//Reaction at mean radius\n", +"R=287//The universal gas constant in J/kg.K\n", +"Cp=1005//The specific heat of air at constant pressure in J/kg.K\n", +"r=1.4//The ratio of specific heats of air\n", +"\n", +"//calculations\n", +"dtb1tb2=((Cp*dT0)/(l*Um*Ca))//The difference between the tangent angles of blade angles at mean\n", +"atb1tb2=((2*Rm*Um)/(Ca))//The sum of the tangent angles of blade angles at mean\n", +"b1m=atand((atb1tb2+dtb1tb2)/2)//The inlet blade angle in degree at mean\n", +"a2m=b1m//The exit air angle in degree as the Reaction at mean radius is 0.5\n", +"b2m=atand(tand(b1m)-dtb1tb2)//The exit blade angle in degree at mean\n", +"a1m=b2m//The inlet air angle in degree as the reaction at mean radius is 0.5\n", +"rmrh=Um/Ur//The ratio of radii of mean and root velocities at hub\n", +"a1h=atand(tand(a1m)*(rmrh))//The inlet air angle in degree at hub\n", +"b1h=atand((Ur/Ca)-(tand(a1h)))//The inlet blade angle in degree at hub\n", +"a2h=atand(tand(a2m)*(rmrh))//The outlet air angle in degree at hub\n", +"b2h=atand((Ur/Ca)-(tand(a2h)))//The outlet blade angle in degree at hub\n", +"Rh=((Ca*(tand(b1h)+tand(b2h)))/(2*Ur))//The degree of reaction at the hub\n", +"rmrt=Um/Ut//The ratio of radii of mean and tip velocities at tip\n", +"a1t=atand(tand(a1m)*(rmrt))//The inlet air angle in degree at tip\n", +"b1t=atand((Ut/Ca)-(tand(a1t)))//The inlet blade angle in degree at tip\n", +"a2t=atand(tand(a2m)*(rmrt))//The outlet air angle in degree at tip\n", +"b2t=atand((Ut/Ca)-(tand(a2t)))//The outlet blade angle in degree at tip\n", +"Rt=((Ca*(tand(b1t)+tand(b2t)))/(2*Ut))//The degree of reaction at tip\n", +"\n", +"//output\n", +"printf('(a)At the mean\n (1)The inlet blade angle is %3.2f degree\n (2)The inlet air angle is %3.2f degree\n (3)The outlet blade angle is %3.2f degree\n (4)The outlet air angle is %3.2f degree\n (5)Degree of reaction is %3.1f \n(b)At the root\n (1)The inlet blade angle is %3.2f degree\n (2)The inlet air angle is %3.2f degree\n (3)The outlet blade angle is %3.2f degree\n (4)The outlet air angle is %3.2f degree\n (5)Degree of reaction is %3.3f\n(c)At the tip\n (1)The inlet blade angle is %3.2f degree\n (2)The inlet air angle is %3.2f degree\n (3)The outlet blade angle is %3.2f degree\n (4)The outlet air angle is %3.2f degree\n (5)Degree of reaction is %3.3f\n',b1m,a1m,b2m,a2m,Rm,b1h,a1h,b2h,a2h,Rh,b1t,a1t,b2t,a2t,Rt)" + ] + } +], +"metadata": { + "kernelspec": { + "display_name": "Scilab", + "language": "scilab", + "name": "scilab" + }, + "language_info": { + "file_extension": ".sce", + "help_links": [ + { + "text": "MetaKernel Magics", + "url": "https://github.com/calysto/metakernel/blob/master/metakernel/magics/README.md" + } + ], + "mimetype": "text/x-octave", + "name": "scilab", + "version": "0.7.1" + } + }, + "nbformat": 4, + "nbformat_minor": 0 +} diff --git a/Turbomachines_by_A_V_Arasu/5-AXIAL_FLOW_STEAM_AND_GAS_TURBINES.ipynb b/Turbomachines_by_A_V_Arasu/5-AXIAL_FLOW_STEAM_AND_GAS_TURBINES.ipynb new file mode 100644 index 0000000..83c71a5 --- /dev/null +++ b/Turbomachines_by_A_V_Arasu/5-AXIAL_FLOW_STEAM_AND_GAS_TURBINES.ipynb @@ -0,0 +1,906 @@ +{ +"cells": [ + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "# Chapter 5: AXIAL FLOW STEAM AND GAS TURBINES" + ] + }, +{ + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 5.10: ACTUAL_STAGE_POWER_OUTPUT.sce" + ] + }, + { +"cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], +"source": [ +"clc\n", +"clear\n", +"//input data\n", +"R=0.5//Degree of reaction\n", +"P0=2.2//Inlet pressure in bar\n", +"T0=443//Inlet temperature in K\n", +"N=2400//Rotor running speed in rpm\n", +"Dm=0.5//Rotor mean diameter in m\n", +"a1=36//Rotor inlet angle in degree\n", +"a2=19//Stator exit angle in degree\n", +"ns=0.88//Stage efficiency\n", +"m=1//Mass flow rate of steam in kg/s\n", +"\n", +"//calculations\n", +"b2=a1//Outlet angle of the rotor blade in degree\n", +"b1=a2//Inlet angle of the rotor blade in degree\n", +"U=(3.1415*Dm*N)/60//Mean blade speed in m/s\n", +"Ca=(2*U*R)/(tand(b2)-tand(b1))//Axial velocity in m/s\n", +"W=m*U*Ca*(tand(a1)+tand(a2))*10^-3//Power output in kW\n", +"dh=W/ns//Stage enthalpy drop in kJ/kg\n", +"\n", +"//output\n", +"printf('(a)Power output is %3.2f kW\n(b)Stage enthalpy drop is %3.2f kJ/kg',W,dh)" + ] + } +, +{ + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 5.11: ROTOR_BLADE_ANGLES.sce" + ] + }, + { +"cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], +"source": [ +"clc\n", +"clear\n", +"//input data\n", +"P0=800//Inlet pressure of hot gas in kPa\n", +"T1=973//Inlet temperature of hot gas in K\n", +"P2=100//Final pressure of hot gas in kPa\n", +"a1=73//Nozzle angle in degree\n", +"m=35//Mass flow rate in kg/s\n", +"ns=0.9//Nozzle efficiency\n", +"Cp=1.005//Specific heat of gas at constant pressure in kJ/kg.K\n", +"r=1.4//Ratio of specific heats of air\n", +"\n", +"//calculations\n", +"b1=atand(tand(a1)/2)//Inlet angle of the rotor blade in degree\n", +"b2=b1//Outlet angle of the rotor blade in degree\n", +"pi=2/tand(a1)//Flow coefficient\n", +"psil=pi*(tand(b1)+tand(b2))//Blade loading coefficient\n", +"dh=ns*Cp*T1*(1-(P2/P0)^((r-1)/r))//Change in enthalpy in kJ/kg\n", +"W=m*dh*10^-3//Power developed in MW\n", +"\n", +"//output\n", +"printf('(a)Rotor blade angles\n Inlet angle of the rotor blade is %3.2f degree\n Outlet angle of the rotor blade is %3.2f degree\n(b)Flow coefficient is %3.3f\n(c)Blade loading coefficient is %3.f\n(d)Power developed is %3.1f MW',b1,b2,pi,psil,W)" + ] + } +, +{ + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 5.12: POWER_DEVELOPED_AND_ANGLES.sce" + ] + }, + { +"cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], +"source": [ +"clc\n", +"clear\n", +"//input data\n", +"P0=100//Initial pressure of steam in bar\n", +"T0=773//Initial temperature of steam in K\n", +"D=1//Turbine diameter in m\n", +"N=3000//Speed of turbine in rpm\n", +"m=100//Mass flow rate of steam in kg/s\n", +"a1=70//Exit angle of the first stage nozzle in degree\n", +"ns1=0.78//Stage efficiency of first stage \n", +"ns2=ns1//Stage efficiency of second stage\n", +"\n", +"//calculations\n", +"U=(3.1415*D*N)/60//Mean blade speed in m/s\n", +"C1=(2*U)/sind(a1)//Velocity of steam at exit from nozzle in m/s \n", +"b11=atand(tand(a1)/2)//Inlet angle of the rotor blade in degree\n", +"b21=b11//Outlet angle of the rotor blade in degree\n", +"b12=b21//Inlet angle of the rotor blade in second stage in degree\n", +"b22=b12//Outlet angle of the rotor blade in second stage in degree\n", +"W=4*m*U^2*10^-6//Total work done in both the stages in MW\n", +"dh02=2*U^2*10^-3//Change in enthalpy in first stage of turbine in kJ/kg\n", +"dh02s=(dh02/ns1)//Change in enthalpy isentropically of turine first stage in kJ/kg\n", +"printf('The values of enthalpy and specific volume are taken from the mollier chart at inlet and exit conditions respectively')\n", +"h0=3370//Enthalpy at beginning of first stage in kJ/kg\n", +"h2=h0-dh02//Enthalpy at the end of first stage in kJ/kg\n", +"h2s=h0-dh02s//Isentropic enthalpy at the end of first stage in kJ/kg\n", +"v2=0.041//Specific volume at the end of first stage in m^3/kg\n", +"dh24=2*U^2*10^-3//Change in enthalpy in second stage of turbine in kJ/kg\n", +"dh24s=dh24/ns2//Change in enthalpy isentropically of turine second stage in kJ/kg\n", +"h4=h2-dh24//Enthalpy at beginning of second stage in kJ/kg\n", +"h4s=h2-dh24s//Isentropic enthalpy at the end of second stage in kJ/kg\n", +"v4=0.05//Specific volume at the end of second stage in m^3/kg\n", +"\n", +"Ca=C1*cosd(a1)//Axial velocity in m/s\n", +"h1r=(m*v2)/(3.1415*D*Ca)//Blade height at first stage rotor exit in m\n", +"h2r=(m*v4)/(3.1415*D*Ca)//Blade height at second stage rotor exit in m\n", +"\n", +"//output\n", +"printf('\n\n(a)rotor blade angles\n Inlet angle of the rotor blade is %3.2f degree\n Outlet angle of the rotor blade is %3.2f degree\n Inlet angle of the rotor blade in second stage is %3.2f degres\n Outlet angle of the rotor blade in second stage is %3.2f degree\n(b)Total work done or Power developed in both the stages is %3.2f MW\n(c)final state of steam\n Enthalpy at beginning of first stage is %3i kJ/kg\n Enthalpy at the end of first stage is %3.2f kJ/kg\n Isentropic enthalpy at the end of first stage is %3.2f kJ/kg\n Specific volume at the end of first stage is %3.3f m^3/kg\n Enthalpy at beginning of second stage is %3.1f kJ/kg\n Isentropic enthalpy at the end of second stage is %3.2f kJ/kg\n Specific volume at the end of second stage is %3.2f m^3/kg\n(d)blade height\n Blade height at first stage rotor exit is %3.4f m\n Blade height at second stage rotor exit is %3.4f m',b11,b21,b12,b22,W,h0,h2,h2s,v2,h4,h4s,v4,h1r,h2r)" + ] + } +, +{ + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 5.13: ROTOR_BLADE_ANGLES.sce" + ] + }, + { +"cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], +"source": [ +"clc\n", +"clear\n", +"//input data\n", +"P0=100//Initial pressure of steam in bar\n", +"T0=773//Initial temperature of steam in K\n", +"D=1//Turbine diameter in m\n", +"N=3000//Speed of turbine in rpm\n", +"m=100//Mass flow rate of steam in kg/s\n", +"a1=70//Exit angle of the first stage nozzle in degree\n", +"ns=0.65//Stage efficiency of first stage \n", +"\n", +"//calculations\n", +"U=(3.1415*D*N)/60//Mean blade speed in m/s\n", +"C1=(4*U)/sind(a1)//Velocity of steam at exit from nozzle in m/s\n", +"Ca=C1*cosd(a1)//Axial velocity in m/s\n", +"Wx1=3*U//Inlet whirl velocity in m/s\n", +"b11=atand(Wx1/Ca)//Inlet angle of the rotor blade in degree\n", +"b21=b11//Outlet angle of the rotor blade in degree\n", +"C2=Ca//Velocity of steam at exit from stage in m/s\n", +"b22=atand(U/Ca)//Outlet angle of the rotor blade in degree\n", +"b12=b22//Inlet angle of the rotor blade in in degree\n", +"W=m*8*U^2*10^-6//Total work done or power developed in MW\n", +"printf('The values of enthalpy and specific volume are taken from the mollier chart at inlet and exit conditions respectively')\n", +"h0=3370//Enthalpy at beginning of stage in kJ/kg\n", +"dh04=(W*10^3)/m//Change in enthalpy of turbine in kJ/kg\n", +"dh04s=dh04/ns//Change in enthalpy isentropically of turine in kJ/kg\n", +"h4=h0-dh04//Enthalpy at beginning of stage in kJ/kg\n", +"h4s=h0-dh04s//Isentropic enthalpy at the end of stage in kJ/kg\n", +"v4=0.105//Specific volume at the end of stage in m^3/kg\n", +"h=(m*v4)/(3.1415*D*Ca)//Rotor blade height in m\n", +"\n", +"printf('\n\n(a)rotor blade angles\n Inlet angle of the rotor blade is %3.2f degree\n Outlet angle of the rotor blade is %3.2f degree\n Inlet angle of the rotor blade in second stage is %3.2f degres\n Outlet angle of the rotor blade in second stage is %3.2f degree\n(b)Total work done or Power developed in both the stages is %3.2f MW\n(c)final state of steam\n Enthalpy at beginning of first stage is %3i kJ/kg\n Enthalpy at beginning of stage is %3.1f kJ/kg\n Isentropic enthalpy at the end of stage is %3.2f kJ/kg\n Specific volume at the end of stage is %3.3f m^3/kg\n(d)rotor blade height is %3.4f m',b11,b21,b12,b22,W,h0,h4,h4s,v4,h)" + ] + } +, +{ + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 5.14: ROTOR_BLADE_ANGLE_FOR_DEGREE_OF_REACTION_50.sce" + ] + }, + { +"cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], +"source": [ +"clc\n", +"clear\n", +"//input data\n", +"a1=(90-30)//Nozzle angle in axial direction in degree\n", +"Ca=180//Axial velocity in m/s\n", +"U=280//Rotor blade speed in m/s\n", +"R=0.25//Degree of reaction\n", +"\n", +"//calculations\n", +"Cx1=Ca*tand(a1)//Velocity of whirl at inlet in m/s\n", +"b1=atand((Cx1-U)/Ca)//Blade angle at inlet in degree\n", +"b2=a1//Blade angle at exit in degree as degree of reaction is 0.5\n", +"\n", +"//output\n", +"printf('(a)Blade angle at inlet is %3i degree\n(b)Blade angle at exit is %3i degree',b1,b2)" + ] + } +, +{ + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 5.15: POWER_AND_BLADE_ANGLES.sce" + ] + }, + { +"cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], +"source": [ +"clc\n", +"clear\n", +"//input data\n", +"R=0.5//Degree of reaction\n", +"ns=0.85//Stage efficiency\n", +"P0=800//Inlet pressure of hot gas in kPa\n", +"T0=900//Inlet temperature of hot gas in K\n", +"U=160//Blade speed in m/s\n", +"m=75//Mass flow rate of hot gas in kg/s\n", +"a1=70//Absolute air angle at first stage nozzle exit in degree\n", +"\n", +"//calculations\n", +"C1=U/sind(a1)//Velocity of steam at exit from nozzle in m/s\n", +"Ca=C1*cosd(a1)//Axial velocity of hot gas in m/s\n", +"C2=Ca//Velocity of steam at exit from stage in m/s\n", +"b1=0//Blade angle at inlet in degree as Wx1=0 \n", +"a2=b1//Stator exit angle in degree as degree of reaction is 0.5\n", +"b2=a1//Blade angle at outlet in degree as degree of reaction is 0.5\n", +"Cx2=0//Velocity of whirl at outlet in m/s\n", +"Cx1=U//Velocity of whirl at inlet in m/s\n", +"W=m*U*(Cx1+Cx2)*10^-6//Power developed in MW\n", +"Wm=W*10^3/m//Work done per unit mass flow rate in kJ/kg\n", +"dhs=Wm/ns//Isentropic enthalpy drop in kJ/kg\n", +"\n", +"//output\n", +"printf('(a)Rotor blade angles\n Absolute air angle at first stage nozzle exit is %3i degree\n Blade angle at outlet is %3i degree\n Blade angle at inlet is %3i degree\n Stator exit angle is %3i degree\n(b)Power developed is %3.2f MW\n(c)Isentropic enthalpy drop is %3.2f kJ/kg',a1,b2,b1,a2,W,dhs)" + ] + } +, +{ + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 5.16: DEGREE_OF_REACTION.sce" + ] + }, + { +"cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], +"source": [ +"clc\n", +"clear\n", +"//input data\n", +"b1m=46//Rotor blade angle at entry at mean section in degree\n", +"b2m=75//Rotor blade angle at exit at mean section in degree\n", +"a1m=75//Nozzle angle at exit at mean section in degree\n", +"DhDt=0.6//Hub to tip ratio\n", +"N=7500//Mean rotor speed in rpm\n", +"Dh=0.45//Hub diameter in m\n", +"\n", +"//calculations\n", +"R=0.5//Degree of reaction as a1m=b2m\n", +"a2m=b1m//Stator angle at exit at mean section in degree\n", +"Dm=(Dh+(Dh/DhDt))/2//Mean diameter of turbine at mean section in m\n", +"Um=(3.1415*DhDt*N)/60//Mean blade speed in m/s\n", +"Ca=Um/(tand(a1m)-tand(b1m))//Axial velocity in m/s\n", +"pi=Ca/Um//Flow coefficient\n", +"psil=pi*(tand(b1m)+tand(b2m))//Blade loading coefficient\n", +"a1h=atand(tand(a1m)*((Dm/2)/(Dh/2)))//Nozzle angle at inlet at root section in degree\n", +"Uh=(3.14*Dh*N)/60//Blade speed at root section in m/s\n", +"b1h=atand(tand(a1h)-(Uh/Ca))//Rotor blade angle at entry at root section in degree\n", +"a2h=atand(tand(a2m)*((Dm/2)/(Dh/2)))//Stator angle at exit at root section in degree\n", +"b2h=atand((Uh/Ca)+tand(a2h))//Rotor blade angle at exit at root section in degree\n", +"pih=Ca/Uh//Flow coefficient at root section\n", +"Rh=(pih/2)*(tand(b2h)-tand(b1h))//Degree of reaction at root section\n", +"psilh=pih*(tand(b1h)+tand(b2h))//Blade loading coefficient at root section\n", +"\n", +"//output\n", +"printf('Mean section\n (a)Degree of reaction is %3.1f\n (b)Blade loading coefficient is %3.2f\nRoot section (a)Degree of reaction is %3.2f\n (b)Blade loading coefficient is %3.2f',R,psil,Rh,psilh)" + ] + } +, +{ + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 5.17: GAS_VELOCITIES.sce" + ] + }, + { +"cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], +"source": [ +"clc\n", +"clear\n", +"//input data\n", +"T00=973//Total head inlet temperature in K\n", +"P00=4.5//Total head inlet pressure in bar\n", +"P2=1.6//Static head outlet pressure in bar\n", +"m=20//Gas flow rate in kg/s\n", +"a1=(90-28)//Nozzle outlet angle measured perpendicular to blade velocity in degree\n", +"Dmh=10//Mean blade diameter to blade height ratio \n", +"NLC=0.1//Nozzle loss coefficient\n", +"Cp=1155.6//Specific heat of gas at a constant pressure in kJ/kg\n", +"R=289//Gas constant in J/kg\n", +"r=1.333//Ratio of specific heats of gas \n", +"\n", +"//calculations\n", +"T2ss=T00*(P2/P00)^((r-1)/r)//Isentropic temperature at outlet in mid section in K here T00=T01\n", +"T1s=T2ss//Isentropic temperature at inlet at mid section in K\n", +"C1m=(2*Cp*(T00-T1s)/1.1)^(1/2)//Velocity of steam at exit from nozzle at mid section in m/s\n", +"T1=T00-((C1m^2)/(2*Cp))//Gas temperature at mid section in K\n", +"d=(P2*10^5)/(R*T1)//Density of gas in kg/m^3\n", +"Rg=(Cp*(r-1)/r)//Gas constant of the gas in kJ/kg\n", +"Ca=C1m*cosd(a1)//Axial velocity in m/s\n", +"h=((m/(d*Ca))*(1/(Dmh*3.1415)))^(1/2)//Hub height in m\n", +"Dm=Dmh*h//Mean blade diameter in m\n", +"Dh=Dm-h//Hub diameter in m\n", +"a1h=atand(((Dm/2)/(Dh/2))*tand(a1))//Discharge angle at hub in degree\n", +"C1h=Ca/cosd(a1h)//Gas velocity at hub section in m/s\n", +"T1h=T00-((C1h^2)/(2*Cp))//Gas temperature at hub in K here T01=T00\n", +"Dt=Dm+h//Tip diameter in m\n", +"a1t=atand(((Dm/2)/(Dt/2))*tand(a1))//Gas discharge angle at tip in degree\n", +"C1t=Ca/cosd(a1t)//Gas velocity at tip in m/s\n", +"T1t=T00-((C1t^2)/(2*Cp))//Gas temperature in K here T00=T01\n", +"\n", +"//output\n", +"printf('(a)At mid section\n Gas velocity is %3.1f m/s\n Gas temperature is %3.1f K\n Gas discharge angle is %3i degree\n(b)At hub section\n Gas velocity is %3.1f m/s\n Gas temperature is %3.2f K\n Gas discharge angle is %3.2f degree\n(c)At tip section\n Gas velocity is %3.1f m/s\n Gas temperature is %3.2f K\n Gas discharge angle is %3.2f degree',C1m,T1,a1,C1h,T1h,a1h,C1t,T1t,a1t)" + ] + } +, +{ + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 5.18: ABSOLUTE_AND_RELATIVE_ANGLES.sce" + ] + }, + { +"cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], +"source": [ +"clc\n", +"clear\n", +"//input data\n", +"a1=75//Nozzle air angle in degree\n", +"Rh=0//Degree of reaction\n", +"N=6000//Running speed of hub in rpm\n", +"Dh=0.45//Hub diameter in m\n", +"Df=0.75//Tip diameter in m\n", +"\n", +"\n", +"//calculations\n", +"Uh=(3.1415*Dh*N)/60//Hub speed in m/s\n", +"C1h=Uh/((sind(a1))/2)//Velocity of steam at exit from nozzle in hub in m/s\n", +"Cah=C1h*cosd(a1)//Axial velocity at hub in m/s\n", +"Cx1h=C1h*sind(a1)//Whirl component of velocity at inlet in hub in m/s\n", +"b1h=atand((Cx1h-Uh)/Cah)//Rotor blade angle at entry at hub section in degree\n", +"b2h=b1h//Rotor blade angle at exit at mean section in degree as zero reaction section\n", +"sopt=sind(a1)/2//Blade to gas speed ratio at hub\n", +"rm=((Dh/2)+(Df/2))/2//Mean radius in m\n", +"rmrh=(rm/(Dh/2))^((sind(a1))^2)//Ratio of inlet velocity at hub and mean for constant nozzle air angle at hub section\n", +"C1m=C1h/rmrh//Velocity of steam at exit from nozzle at mean section in m/s\n", +"Cx1m=Cx1h/rmrh//Velocity of whirl at inlet at mean section in m/s\n", +"Ca1m=Cah/rmrh//Axial velocity at mean section in m/s\n", +"Um=(3.1415*2*rm*N)/60//Mean blade speed in m/s\n", +"b1m=atand((Cx1m-Um)/Ca1m)//Rotor blade angle at entry at mean section in degree\n", +"b2m=atand(Um/Ca1m)//Rotor blade angle at exit at mean section in degree for axial exit Cx2=0\n", +"s=Um/C1m//Blade to gas ratio at mean\n", +"Rm=(Ca1m/(2*Um))*(tand(b2m)-tand(b1m))//Degree of reaction of mean section\n", +"rmrt=((rm)/(Df/2))^((sind(a1))^2)//Ratio of inlet velocity at tip and mean for constant nozzle air angle at tip section\n", +"C1t=C1m*rmrt//Velocity of steam at exit from nozzle at tip section in m/s\n", +"Cx1t=Cx1m*rmrt//Velocity of whirl at inlet at tip section in m/s\n", +"Ca1t=Ca1m*rmrt//Axial velocity at tip section in m/s\n", +"Ut=(3.1415*Df*N)/60//Mean tip speed in m/s\n", +"b1t=atand((Cx1t-Ut)/Ca1t)//Rotor blade angle at entry at tip section in degree\n", +"b2t=atand(Ut/Ca1t)//Rotor blade angle at exit at tip section in degree for axial exit Cx2=0\n", +"st=Ut/C1t//Blade to gas ratio at tip\n", +"Rf=(Ca1t/(2*Ut))*(tand(b2t)-tand(b1t))//Degree of reaction of tip section\n", +"\n", +"//output\n", +"printf('(1)Hub section\n (a)\n Absolute air angle is %3.2f degree\n Relative air angle is %3.2f degree\n (b)Blade to gas speed ratio is %3.3f\n (c)Degree of reaction is %3i\n(2)Mean section\n (a)\n Absolute air angle is %3.2f degree\n Relative air angle is %3.2f degree\n (b)Blade to gas speed ratio is %3.3f\n (c)Degree of reaction is %3.3f\n(3)Tip section\n (a)\n Absolute air angle is %3.2f degree\n Relative air angle is %3.2f degree\n (b)Blade to gas speed ratio is %3.3f\n (c)Degree of reaction is %3.3f\n',b1h,b2h,sopt,Rh,b1m,b2m,s,Rm,b1t,b2t,st,Rf)" + ] + } +, +{ + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 5.1: INLET_ANGLE_OF_MOVING_BLADE.sce" + ] + }, + { +"cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], +"source": [ +"clc\n", +"clear\n", +"//input data\n", +"C1=500//Steam velocity in m/s\n", +"U=200//Blade speed in m/s\n", +"b2=(90-25)//Exit angle of moving blade measured in axial direction in degree\n", +"a1=(90-20)//Nozzle angle in axial direction in degree\n", +"m=5//Steam flow rate in kg/s\n", +"\n", +"printf('The scale of the velocity vector diagram is 1:50\n\nThe following values are obtained from the velocity vector diagram')\n", +"\n", +"b1=33//Moving blade inlet angle in degree\n", +"a2=56//Direction of steam at the exit in degree\n", +"C2=160//Exit velocity of the steam in m/s\n", +"Wx1=270//Inlet whirl velocity in m/s\n", +"Wx2=285//Exit whirl velocity in m/s\n", +"Ca1=175//Inlet axial velocity in m/s\n", +"Ca2=135//Exit axial velocity in m/s\n", +"\n", +"//calculations\n", +"Wm=U*(Wx1+Wx2)*10^-3//Work done per kg of steam in kW/kg\n", +"AT=m*(Ca1-Ca2)//Axial thrust in N\n", +"W=m*Wm//Power developed in kW\n", +"Ndia=((U*(Wx1+Wx2))/((C1^2)/2))//Diagram or blade efficiency \n", +"\n", +"//output\n", +"printf('\n\n(a)Moving blade inlet angle is %3i degree\n(b)\n Exit velocity of the steam is %3i m/s\n Direction of steam at the exit is %3i degree\n(c)Work done per kg of steam is %3i kW/kg\n(d)\n Axial thrust is %3i N\n Power developed is %3i kW\n(e)Diagram or blade efficiency is %3.3f',b1,C2,a2,Wm,AT,W,Ndia)" + ] + } +, +{ + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 5.2: AXIAL_THRUST_ON_BLADING.sce" + ] + }, + { +"cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], +"source": [ +"clc\n", +"clear\n", +"//input data\n", +"U=300//Blade speed in m/s\n", +"a=20//Nozzle angle in degree\n", +"dhs=473//Isentropic heat drop in kJ/kg\n", +"Nn=0.85//Nozzle efficiency\n", +"W2W1=0.7//Blade velocity coefficient\n", +"nM=0.9//Mechanical efficiency\n", +"\n", +"//initial calculations\n", +"dh=Nn*dhs//Useful heat drop converted into kinetic energy in kJ/kg\n", +"C1=(2*1000*dh)^(1/2)//Velocity of steam at exit from nozzle in m/s\n", +"\n", +"printf('The scale of the velocity vector diagram is 1:100\n\nThe following values are obtained from the velocity vector diagram')\n", +"\n", +"Ca1=310//Inlet axial velocity in m/s\n", +"Ca2=210//Exit axial velocity in m/s\n", +"Wx1=550//Inlet whirl velocity in m/s\n", +"Wx2=380//Exit whirl velocity in m/s\n", +"W1=620//inlet Blade velocity in m/s\n", +"\n", +"//calculations\n", +"W2=W2W1*W1//Exit bladde velocity in m/s\n", +"AT=Ca1-Ca2//Axial thrust in N/kg\n", +"Wm=U*(Wx1+Wx2)*10^-3//Work developed per kg of steam/sec in kW/(kg/s)\n", +"P=Wm*nM//Power developed per kg of steam/sec in kW/(kg/s)\n", +"m=3600/P//Steam rate per kW.hr in kg\n", +"Ndia=((U*(Wx1+Wx2))/((C1^2)/2))//Diagram or blade efficiency \n", +"MNdia=(sind(90-a))^(2)//Maximum blade efficiency under optimum conditions \n", +"Ns1=Wm/dhs//Stage efficiency\n", +"Ns2=Ndia*Nn//Stage efficiency in other method\n", +"E=(((W1^2)-(W2^2))/2)*10^-3//Energy loss in blade friction in kJ/kg\n", +"\n", +"//output\n", +"printf('\n\n(a)Axial thrust is %3i N/kg\n(b)\n Work developed per kg of steam/sec is %3i kW/(kg/s)\n Power developed per kg of steam/sec is %3.1f kW/(kg/s)\n Steam rate per kW.hr is %3.1f kg\n(c)\n Diagram or blade efficiency is %3.3f\n Maximum blade efficiency under optimum conditions is %3.3f\n Stage efficiency is %3.4f\n(d)Energy loss in blade friction is %3.3f kJ/kg',AT,Wm,P,m,Ndia,MNdia,Ns1,E)" + ] + } +, +{ + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 5.3: VELOCITY_OF_STEAM_AT_EXIT.sce" + ] + }, + { +"cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], +"source": [ +"clc\n", +"clear\n", +"//input data\n", +"P1=5//Input pressure of steam in bar\n", +"P2=3//Exhaust pressure of steam in bar\n", +"C0=75//Carry over velocity of steam in m/s\n", +"a1=20//Nozzle angle in degree\n", +"UC1=0.4//The direction of blade rotation and blade speed ratio\n", +"b2=20//Blade exit angle in degree\n", +"m=2.5//Steam flow rate in kg/s\n", +"W=206//Power Output of the stage in kW\n", +"Nn=0.9//Efficiency of the nozzle\n", +"\n", +"printf('Assuming isentropic expansion the enthalpy drop can be found from steam table\n\nThe following values are obtained from steam tables')\n", +" \n", +"h1=2747.5//Enthalpy at initial pressure in kJ/kg\n", +"s1=6.819//Entropy at initial pressure in kJ/kg.K\n", +"s2=s1//Entropy at final pressure in kJ/kg.K\n", +"sfp2=1.647//Entropy of fliud at final pressure in kJ/kg.K\n", +"sfgp2=5.367//Entropy of fliud-gas mixture at final pressure in kJ/kg.K\n", +"hfg=2170.1//Enthalpy of fliud-gas mixture in kJ/kg\n", +"hf=551.5//Enthalpy of fliud in kJ/kg\n", +"\n", +"printf('\n\nThe scale of the velocity vector diagram is 1:50\n\nThe following values are obtained from the velocity vector diagram')\n", +"\n", +"W1=280//Relative velocity at inlet in m/s\n", +"W2=240//Relative velocity at exit in m/s\n", +"\n", +"//calculations\n", +"x2=(s2-sfp2)/sfgp2//The percentage of wet steam \n", +"h2s=hf+(x2*hfg)//The isentropic enthalpy at the second stage in kJ/kg\n", +"dhs=h1-h2s//Isentropic heat drop in kJ/kg\n", +"C1=((2000*Nn*dhs)+(C0^2))^(1/2)//Velocity of steam at exit from nozzle in m/s\n", +"U=UC1*C1//Blade speed in m/s\n", +"Wx1Wx2=(W*10^3)/(m*U)//The sum of whirl components of velocity in m/s\n", +"Ndia=(U*Wx1Wx2)/((C1^2)/2)//Diagram efficiency \n", +"RV=W2/W1//Relative velocity ratio \n", +"E=dhs+((C0^2)/2000)//Energy supplied per kg in kJ/kg\n", +"Ns1=(U*Wx1Wx2)/(E*10^3)//Stage efficiency\n", +"Ns2=Ndia*Nn//Stage efficiency in other method\n", +"\n", +"//output\n", +"printf('\n\n(a)Velocity of steam at exit from nozzle is %3.2f m/s\n(b)Diagram efficiency is %3.4f\n(c)Relative velocity ratio is %3.3f\n(d)\n Stage efficiency in method 1 is %3.4f\n Stage efficiency in method 2 is %3.4f',C1,Ndia,RV,Ns1,Ns2)" + ] + } +, +{ + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 5.4: BLADE_INLET_ANGLE_FOR_EACH_ROW.sce" + ] + }, + { +"cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], +"source": [ +"clc\n", +"clear\n", +"//input data\n", +"C1=600//Velocity of steam at exit from nozzle in m/s\n", +"U=120//Blade speed in m/s\n", +"a1=16//Nozzle angle in degree\n", +"b2=18//Discharge angle for first moving ring in degree \n", +"a11=21//Discharge angle for the fixed ring in degree \n", +"b22=35//Discharge angle for the second moving ring in degree\n", +"Wr=0.9//Blade velocity coefficient\n", +"m=1//Mass flow rate in kg/s\n", +"\n", +"printf('\n\nThe scale of the velocity vector diagram is 1:50\n\nThe following values are obtained from the velocity vector diagram')\n", +"\n", +"W1=485//Relative velocity at inlet for first stage in m/s\n", +"W2=Wr*W1//Relative velocity for first stage at exit in m/s\n", +"Wx1=460//Inlet whirl velocity for first stage in m/s\n", +"Wx2=410//Exit whirl velocity for first stage in m/s\n", +"Ca1=170//Inlet axial velocity for first stage in m/s\n", +"Ca2=135//Exit axial velocity for first stage in m/s\n", +"C2=325//Exit velocity of the steam for first stage in m/s\n", +"b1=20//Blade inlet angle for first row of moving blade in degree\n", +"C11=Wr*C2//Steam velocity at inlet to second row of moving blades in m/s\n", +"W12=190//Relative velocity at inlet for second stage in m/s\n", +"W22=Wr*W12//Relative velocity at exit for second stage in m/s\n", +"Wx11=155//Inlet whirl velocity for second stage in m/s\n", +"Wx22=140//Exit whirl velocity for second stage in m/s\n", +"Ca11=110//Inlet axial velocity for second stage in m/s\n", +"Ca22=100//Exit axial velocity for second stage in m/s\n", +"b11=35//Blade inlet angle for second row of moving blade in degree\n", +"dWx1=Wx1+Wx2//Driving force for first stage in m/s\n", +"dWx11=Wx11+Wx22//Driving force for second stage in m/s\n", +"dW=(dWx1+dWx11)*1//Total driving force for unit mass flow rate in N\n", +"AT1=Ca1-Ca2//Axial thrust for first stage in m/s\n", +"AT2=Ca11-Ca22//Axial thrust for second stage in m/s\n", +"AT=(AT1+AT2)*1//Total axial thrust for unit mass flow rate in N\n", +"DP=m*U*(dWx1+dWx11)*10^-3//Diagram power in kW\n", +"DE=(U*(dWx1+dWx11))/((C1^2)/2)//Diagram efficiency\n", +"MDE=(sind(90-a1))^2//Maximum diagram efficiency\n", +"\n", +"//output\n", +"printf('\n\n(a)\n Blade inlet angle for first row of moving blade is %3.i degree\n Blade inlet angle for second row of moving blade is %3i degree\n(b)\n Driving force for first stage is %3i m/s\n Driving force for second stage is %3i m/s\n Total driving force for unit mass flow rate is %3i N\nTotal axial thrust for unit mass flow rate is %3i N\n(c)Diagram power is %3.1f kW\n(d)Diagram efficiency is %3.3f\n(e)Maximum diagram efficiency is %3.3f',b1,b11,dWx1,dWx11,dW,AT,DP,DE,MDE)" + ] + } +, +{ + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 5.5: ROTOR_SPEED.sce" + ] + }, + { +"cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], +"source": [ +"clc\n", +"clear\n", +"//input data\n", +"C1=100//Velocity of steam at exit from nozzle in m/s\n", +"h=0.04//Mean blade height in m\n", +"b2=20//Exit angle of moving blade in degree\n", +"CaU=3/4//Ratio of flow velocity and blade speed at mean radius\n", +"m=10000/3600//steam flow rate in kg/s\n", +"\n", +"//calculations\n", +"a1=b2//Nozzle angle in degree\n", +"Ca=C1*cosd(90-a1)//Flow velocity in m/s\n", +"U=Ca/CaU//Mean blade velocity in m/s\n", +"v=0.60553//Specific volume of steam from steam table at 3 bar with dry saturated steam in m^3/kg\n", +"A=(m*v)/Ca//Annulus area in m^2\n", +"D=A/(3.1415*h)//Mean blade diameter in m\n", +"N=(U*60)/(3.14*D)//Rotor speed in rpm\n", +"\n", +"printf('\n\nThe scale of the velocity vector diagram is 1:10\n\nThe following values are obtained from the velocity vector diagram')\n", +"\n", +"W1=59//Relative velocity at inlet for first stage in m/s\n", +"Wx1Wx2=142//Sum of whirl components of velocity in m/s\n", +"DP=m*U*Wx1Wx2*10^-3//Diagram power in kW\n", +"Wm=U*(Wx1Wx2)//Work done per kg of steam in kJ/kg\n", +"W2=C1//Relative velocity at exit for first stage in m/s\n", +"E=((C1^2)/2)+(((W2^2)-(W1^2))/2)//Energy input per kg in kJ/kg when W2=C1\n", +"Ndia=Wm/E//Diagram efficiency \n", +"RV=(W2-W1)/W1//Percentage increase in relative velocity \n", +"dH=((W2^2)-(W1^2))/2*10^-3//Enthalpy drop in the moving blades in kJ/kg\n", +"H=2*dH//Total enthalpy drop in two stages in kJ/kg\n", +"\n", +"//output\n", +"printf('\n\n(a)The rotor speed is %3i rpm\n(b)The diagram power is %3.2f kW\n(c)The diagram efficiency is %3.3f\n(d)Percentage increase in relative velocity is %3.3f\n(e)\n Enthalpy drop in the moving blades is %3.3f kJ/kg\n Total enthalpy drop in two stages is %3.3f kJ/kg',N,DP,Ndia,RV,dH,H)" + ] + } +, +{ + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 5.6: STEAM_FLOW_RATE.sce" + ] + }, + { +"cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], +"source": [ +"clc\n", +"clear\n", +"//input data\n", +"R=0.5//Degree of reaction\n", +"P1=14//Initial pressure in bar\n", +"T1=588//Initial temperature in K\n", +"P2=0.14//Final pressure in bar\n", +"Ns=0.75//Stage efficiency \n", +"RF=1.04//Reheat factor \n", +"N=20//No. of stages\n", +"W=11770//Total power output in kW\n", +"a1=20//Exit blade angle in degree\n", +"hD=1/12//Ratio of blade height to blade mean diameter \n", +"\n", +"//calculations\n", +"hs1=3080//Isentropic enthalpy at initial condition from mollier chart in kJ/kg\n", +"hs2=2270//Isentropic enthalpy at final condition from mollier chart in kJ/kg\n", +"dhs=hs1-hs2//Isentropic enthalpy change in kJ/kg\n", +"Nt=Ns*RF//Overall efficiency\n", +"dh=Nt*dhs//Actual enthalpy drop in kJ/kg\n", +"hs=dh/N//Enthalpy drop per stage in kJ/kg\n", +"m=W/dh//Mass flow rate in kg/s\n", +"C11=1.43*1//Velocity of steam at exit from nozzle in m/s in terms of U for 0.5 degree of reaction\n", +"Wm=1*((2*C11*sind(90-a1))-1)//Work done per mass of steam in terms of U^2 in kJ/kg\n", +"U=((hs*10^3)/Wm)^(1/2)//Mean blade velocity in m/s as work done equals enthalpy drop per stage \n", +"C1=1.43*U//Velocity of steam at exit from nozzle in m/s \n", +"Ca=C1*cosd(90-a1)//Flow velocity in m/s\n", +"v=1.618//Specific volume of steam from steam table at 1.05 bar with dry saturated steam in m^3/kg\n", +"D=((m*v)/(hD*3.14*Ca))^(1/2)//Blade mean diameter in m\n", +"N=(U*60)/(3.14*D)//Rotor speed in rpm\n", +"\n", +"//output\n", +"printf('(a)Mass flow rate of steam is %3.2f kg/s\n(b)Mean blade velocity is %3.1f m/s \n(c)Blade mean diameter is %3.3f m \n(d)Rotor speed is %3i rpm',m,U,D,N)" + ] + } +, +{ + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 5.7: NOZZLE_EXIT_ANGLE.sce" + ] + }, + { +"cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], +"source": [ +"clc\n", +"clear\n", +"//input data\n", +"rh=0.225//Blade roof radius in m\n", +"rt=0.375//Blade tip radius in m\n", +"b1m=45//Inlet angle of the rotor blade at mid height in degree\n", +"a1m=76//Outlet angle of the nozzle blade at mid height in degree\n", +"b2m=75//Outlet angle of the rotor blade at mid height in degree\n", +"N=6000//Speed of turbine in rpm\n", +"\n", +"//calculations\n", +"rm=(rh+rt)/2//Mean radius in m\n", +"Um=(2*3.14*rm*N)/60//Mean blade speed at mean radius in m/s\n", +"Ca=Um/((tand(a1m))-(tand(b1m)))//Flow velocity in m/s\n", +"Cx1m=Ca*tand(a1m)//Velocity of whirl at inlet at mid height in m/s\n", +"Cx2m=Ca*tand(b2m)-Um//Velocity of whirl at inlet at mid height in m/s\n", +"Cx1h=(Cx1m*rm)/rh//Velocity of whirl at inlet at hub height in m/s\n", +"a1h=atand(Cx1h/Ca)//Inlet angle of the nozzle blade at hub height in degree\n", +"Uh=(2*3.1415*rh*N)/60//Mean blade speed at hub in m/s\n", +"b1h=atand(tand(a1h)-(Uh/Ca))//Inlet angle of the rotor blade at hub in degree\n", +"Cx2h=Cx2m*rm/rh//Velocity of whirl at outlet at hub in m/s\n", +"b2h=atand((Uh+Cx2h)/Ca)//Outlet angle of the rotor blade at hub in degree\n", +"Cx1t=Cx1m*rm/rt//Velocity of whirl at inlet at tip in m/s\n", +"a1t=atand(Cx1t/Ca)//Inlet angle of the nozzle blade at tip height in degree\n", +"Ut=(2*3.14*rt*N)/60//Mean blade speed at tip in m/s\n", +"b1t=atand(tand(a1t)-(Ut/Ca))//Inlet angle of the rotor blade at tip in degree\n", +"Cx2t=Cx2m*rm/rt//Velocity of whirl at outlet at tip in m/s\n", +"b2t=atand((Ut+Cx2t)/Ca)//Outlet angle of the rotor blade at hub in degree\n", +"Rh=(Ca/(2*Uh))*(tand(b2h)-tand(b1h))//Degree of reaction at hub\n", +"Rt=(Ca/(2*Ut))*(tand(b2t)-tand(b1t))//Degree of reaction at tip\n", +"\n", +"//output\n", +"printf('(a)for hub\n (1)Inlet angle of the nozzle blade at hub height is %3.1f degree\n (2)Inlet angle of the rotor blade at hub is %3i degree\n (3)Outlet angle of the rotor blade at hub is %3.2f degree\n (4)Degree of reaction at hub is %3.3f\n(b)for tip\n (1)Inlet angle of the nozzle blade at tip height is %3.2f degree\n (2)Inlet angle of the rotor blade at tip is %3i degree\n (3)Outlet angle of the rotor blade at tip is %3i degree\n (4)Degree of reaction at tip is %3.3f',a1h,b1h,b2h,Rh,a1t,b1t,b2t,Rt)" + ] + } +, +{ + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 5.8: BLADE_ANGLES.sce" + ] + }, + { +"cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], +"source": [ +"clc\n", +"clear\n", +"//input data\n", +"Ca=180//Air velocity at the exit of nozzle in m/s\n", +"a1=(90-27)//Nozzle inclination perpendicular to direction of rotation in degree\n", +"R=0.5//Degree of reaction\n", +"U=180//Blade speed in m/s\n", +"\n", +"//calculations\n", +"Cx1=Ca*tand(a1)//Inlet whirl velocity in m/s\n", +"b11=atand((Cx1-U)/Ca)//Inlet angle of the rotor blade at inlet velocity triangle in degree\n", +"pi=Ca/U//Ratio of air velocity and blade velocity \n", +"b21=atand((2*R/pi)+tand(b11))//Outlet angle of the rotor blade at inlet velocity triangle in degree\n", +"C2=Ca//Exit velocity of the steam in m/s\n", +"b22=atand(U/C2)//Outlet angle of the rotor blade at outlet velocity triangle in degree\n", +"b12=b11//Inlet angle of the rotor blade at outlet velocity triangle in degree as np change in rotor inlet conditions \n", +"R=(pi*(tand(b22)-tand(b12)))/2//Degree of reaction \n", +"\n", +"//output\n", +"printf('(a)blade angles\n Inlet angle of the rotor blade at inlet velocity triangle is %3.1f degree\n Outlet angle of the rotor blade at inlet velocity triangle is %3.f degree\n(b)Degree of reaction is %3.4f\n(c)Inlet angle of the rotor blade at outlet velocity triangle is %3.f degree\n(d)Outlet angle of the rotor blade at outlet velocity triangle is %3.1f degree',b11,b21,R,b22,b12)" + ] + } +, +{ + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 5.9: POWER_DEVELOPED.sce" + ] + }, + { +"cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], +"source": [ +"clc\n", +"clear\n", +"//input data\n", +"U=300//Blade speed of turbine in m/s\n", +"m=2.5//Mass flow rate in kg/s\n", +"T0=773//Gas temperature at turbine inlet in K\n", +"T2=573//Gaas temperature at turbine outlet in K\n", +"a1=70//Fixed blade outlet angle in degree\n", +"Ca=200//Axial velocity in m/s\n", +"Cp=1.005//Specific heat of gas at constant pressure in kJ/kg.K\n", +"//calculations\n", +"W=m*Cp*(T0-T2)//Power developed by turbine in kW\n", +"Wm=Cp*(T0-T2)//Stage work done per unit mass flow rate in kJ/kg\n", +"Wx1Wx2=Wm*10^3/U//Sum of whirl components of velocity at inlet and outlet in m/s\n", +"Wx1=(Ca*tand(a1))-U//Inlet whirl velocity in m/s\n", +"Wx2=Wx1Wx2-Wx1//Outlet whirl velocity in m/s\n", +"R=(Wx2-Wx1)/(2*U)//Degree of reaction\n", +"Wx2Wx1=Wm*10^3*R//Energy input due to whirl component velocity in (m/s)^2\n", +"C1=Ca/cosd(a1)//Velocity of steam at exit from nozzle in m/s \n", +"nb=(Wm*10^3)/(((C1^2)/2)+Wx2Wx1)//Blade efficiency\n", +"\n", +"//output\n", +"printf('(a)Power developed by turbine is %3.1f kW\n(b)Degree of reaction is %3.3f\n(c)Blade efficiency is %3.4f\n',W,R,nb)" + ] + } +], +"metadata": { + "kernelspec": { + "display_name": "Scilab", + "language": "scilab", + "name": "scilab" + }, + "language_info": { + "file_extension": ".sce", + "help_links": [ + { + "text": "MetaKernel Magics", + "url": "https://github.com/calysto/metakernel/blob/master/metakernel/magics/README.md" + } + ], + "mimetype": "text/x-octave", + "name": "scilab", + "version": "0.7.1" + } + }, + "nbformat": 4, + "nbformat_minor": 0 +} diff --git a/Turbomachines_by_A_V_Arasu/6-RADIAL_FLOW_GAS_AND_STEAM_TURBINES.ipynb b/Turbomachines_by_A_V_Arasu/6-RADIAL_FLOW_GAS_AND_STEAM_TURBINES.ipynb new file mode 100644 index 0000000..8cde82e --- /dev/null +++ b/Turbomachines_by_A_V_Arasu/6-RADIAL_FLOW_GAS_AND_STEAM_TURBINES.ipynb @@ -0,0 +1,366 @@ +{ +"cells": [ + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "# Chapter 6: RADIAL FLOW GAS AND STEAM TURBINES" + ] + }, +{ + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 6.1: FLOW_AND_LOADING_COEFFICIENTS.sce" + ] + }, + { +"cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], +"source": [ +"clc\n", +"clear\n", +"//input data\n", +"P00=3//The pressure at which air is received in bar\n", +"T00=373//The temperature at which air is received in K\n", +"rt=0.5//The rotor tip diameter of turbine in m\n", +"rh=0.3//The rotor exit diameter of the turbine in m\n", +"b=0.03//The rotor blade width at entry in m\n", +"b11=60//The air angle at rotor entry in degree\n", +"a11=25//The air angle at nozzle exit in degree\n", +"Ps=2//The stage pressure ratio\n", +"nn=0.97//The nozzle efficiency\n", +"N=7200//The speed of the turbine rotation in rpm\n", +"R=287//The universal gas constant in J/kg.K\n", +"Cp=1005//The specific heat of air at constant pressure in J/kg.K\n", +"r=1.4//The ratio of specific heats of air\n", +"\n", +"//calculations\n", +"U1=(3.14*rt*N)/60//Peripheral velocity of impeller at inlet in m/s\n", +"Cr=U1/(cotd(a11)-cotd(b11))//The radial velocity at inlet in m/s\n", +"ps1=Cr/U1//Flow coefficient \n", +"sl=1+(ps1*cotd(b11))//Loading coefficient\n", +"DR=((1-(ps1*cotd(b11)))/2)//Degree of reaction\n", +"nts=((sl*U1^2)/(Cp*T00*(1-((1/Ps)^((r-1)/r)))))//Stage efficiency of the turbine\n", +"C2=Cr//Absolute velocity at the exit in m/s\n", +"U2=(3.1415*rh*N)/60//Peripheral velocity of impeller at exit in m/s\n", +"b22=atand(C2/U2)//The air angle at rotor exit in degree\n", +"dT=DR*U1*Cr*cotd(a11)/Cp//Total actual change in temperature in a stage turbine in K\n", +"dT0=(U1*Cr*cotd(a11))/Cp//The total change in temperature in turbine in K\n", +"T02=T00-dT0//The exit absolute temperature in K\n", +"T2=T02-((C2^2)/(2*Cp))//The actual exit temperature in K\n", +"T1=dT+T2//The actual inlet temperature in K\n", +"Cx1=Cr*cotd(a11)//Inlet absolute velocity of air in tangential direction in m/s\n", +"C1=Cx1/cosd(a11)//Absolute velocity at the inlet in m/s\n", +"dT1=(C1^2/2)/(Cp*nn)//The absolute change in temperature at the first stage in K\n", +"dP1=(1-(dT1/T00))^(r/(r-1))//The absolute pressure ratio in first stage \n", +"P1=dP1*P00//The inlet pressure in bar\n", +"d1=(P1*10^5)/(R*T1)//The inlet density in kg/m^3\n", +"A1=3.1415*rt*b//The inlet area of the turbine in m^2\n", +"m=d1*A1*Cr//The mass flow rate of air at inlet in kg/s\n", +"P2=P00/Ps//The exit pressure in bar\n", +"d2=(P2*10^5)/(R*T2)//The exit density of air in kg/m^3\n", +"bh=(m/(d2*3.1415*rh*Cr))//Rotor width at the exit in m\n", +"W=m*U1*Cx1*10^-3//The power developed by the turbine in kW\n", +"\n", +"//output\n", +"printf('(a)\n (1)The flow coefficient is %3.3f\n (2)The loading coefficient is %3.3f\n(b)\n (1)The degree of reaction is %3.4f \n (2)The stage efficiency of the turbine is %3.4f \n(c)\n (1)The air angle at the rotor exit is %3.2f degree\n (2)The width at the rotor exit is %3.4f m\n(d)\n (1)The mass flow rate is %3.2f kg/s\n (2)The power developed is %3.2f kW',ps1,sl,DR,nts,b22,bh,m,W)" + ] + } +, +{ + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 6.2: NOZZLE_EXIT_AIR_ANGLE.sce" + ] + }, + { +"cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], +"source": [ +"clc\n", +"clear\n", +"//input data\n", +"P0=4//Overall stage pressure ratio \n", +"T00=557//Temperature at entry in K\n", +"P3=1//Diffuser exit pressure in bar\n", +"m=6.5//Mass flow rate of air in kg/s\n", +"ps1=0.3//Flow coefficient \n", +"N=18000//Speed of the turbine in rpm\n", +"Dt=0.42//Rotor tip diameter in m\n", +"D2m=0.21//Mean diameter at rotor exit in m\n", +"R=287//The universal gas constant in J/kg.K\n", +"Cp=1.005//The specific heat of air at constant pressure in kJ/kg.K\n", +"r=1.4//The ratio of specific heats of air\n", +"\n", +"//calculations\n", +"U1=(3.1415*Dt*N)/60//Peripheral velocity of impeller at inlet in m/s\n", +"Cr1=ps1*U1//The radial velocity at inlet in m/s\n", +"a11=atand(Cr1/U1)//The nozzle exit air angle in degree\n", +"W=m*U1^2*10^-3//Power developed by turbine in kW\n", +"dT=(1/P0)^((r-1)/r)//The total isentropic temperature ratio in entire process \n", +"T3s=dT*T00//The final isentropic temperature at exit in K\n", +"dh2=W/m//The absolute enthalpy change in the first two stages in kJ/kg\n", +"ns=dh2/(Cp*(T00-T3s))//The stage efficiency of the turbine\n", +"T02=T00-(W/(m*Cp))//The absolute temperature at the entry of second stage in K\n", +"T03=T02//The absolute temperature at exit of second stage in K\n", +"dH=Cp*(T02-T3s)//The total enthalpy loss in kJ/kg\n", +"dHn=dH/2//The enthalpy loss in the nozzle in kJ/kg\n", +"C1=Cr1/sind(a11)//Absolute velocity at the inlet in m/s\n", +"dH0=((C1^2)/(2000*Cp))+(dHn)//The isentropic absolute enthalpy loss in nozzle in kJ/kg\n", +"dT0=dH0/Cp//The isentropic absolute temperature loss in nozzle in K\n", +"T1s=T00-dT0//The isentropic temperature at the entry in K\n", +"P1=P0*(T1s/T00)^(r/(r-1))//The pressure at the entry of turbine in bar\n", +"T1=T00-((C1^2)/(2000*Cp))//The temperature at the entry of turbine in K\n", +"d1=(P1*10^5)/(R*T1)//The density of the air at inlet in kg/m^3\n", +"b1=m/(d1*Cr1*3.141*Dt)//The width of the rotor at inlet in m\n", +"C2=Cr1//The avsolute velocity at the second stage entry in m/s\n", +"T2=T02-((C2^2)/(2000*Cp))//The temperature at the second stage entry in K\n", +"P23=(T2/T03)^(r/(r-1))//The pressure ratio at the second stage\n", +"P2=P23*P3//The pressure at the second stage in bar\n", +"d2=(P2*10^5)/(R*T2)//The density of the air at second stage in kg/m^3\n", +"C2=Cr1//The absolute velocity at the second stage in m/s\n", +"A2=m/(d2*C2)//The area of cross section at the second stage in m^2\n", +"h2=(A2/(3.14*D2m))//The rotor blade height at the exit in m\n", +"M1=C1/(r*R*T1)^(1/2)//The mach number at the nozzle\n", +"U2=(3.14*D2m*N)/60//The Peripheral velocity of impeller at exit in m/s\n", +"M2r=(((C2^2)+(U2^2))^(1/2))/(r*R*T2)^(1/2)//The mach number at the rotor exit \n", +"Ln=(dHn*10^3)/((C1^2)/2)//The nozzle loss coefficient\n", +"Lr=(dHn*10^3)/(((((C2^2)+(U2^2))^(1/2))^2)/2)//The rotor loss coefficient\n", +"\n", +"//output\n", +"printf('(a)The nozzle exit air angle is %3.2f degree\n(b)The power developed is %3.1f kW\n(c)The stage efficiency is %3.4f \n(d)The rotor width at the entry is %3.5f m\n(e)The rotor blade height at the exit is %3.4f m\n(f)\n (1)The mach number at the nozzle exit is %3.4f\n (2)The mach number at the rotor exit is %3.2f\n(g)\n (1)The nozzle loss coefficient is %3.4f\n (2)The rotor loss coefficient is %3.3f',a11,W,ns,b1,h2,M1,M2r,Ln,Lr)" + ] + } +, +{ + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 6.3: IMPELLER_TIP_SPEED.sce" + ] + }, + { +"cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], +"source": [ +"clc\n", +"clear\n", +"//input data\n", +"ntt=0.9//Total-to-total efficiency\n", +"P00=300//The pressure at entry to the nozzle in kPa\n", +"T00=1150//The temperature at entry to the nozzle in K\n", +"T1=1013//The static temperature at the outlet of the nozzle in K\n", +"P03=100//The pressure at the outlet of the diffuser in kPa\n", +"R=284.5//The universal gas constant in J/kg.K\n", +"Cp=1.147//The specific heat of air at constant pressure in kJ/kg.K\n", +"r=1.33//The ratio of specific heats of given gas\n", +"\n", +"//calculations\n", +"U1=(ntt*Cp*1000*T00*(1-((P03/P00)^((r-1)/r))))^(1/2)//The impeller tip speed in m/s\n", +"T01=T00//The absolute temperature at the entry in K\n", +"C1=(2000*Cp*(T01-T1))^(1/2)//The absolute velocity at the inletof turbine in m/s\n", +"a11=acosd(U1/C1)//The flow angle at the nozzle oulet in degree\n", +"M1=C1/(r*R*T1)^(1/2)//The mach number at the nozzle outlet \n", +"\n", +"//output\n", +"printf('(a)The impeller tip speed is %3.1f m/s\n(b)The flow angle at the nozzle oulet is %3.2f degrees\n(c)The mach number at the nozzle outlet is %3.2f',U1,a11,M1)" + ] + } +, +{ + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 6.4: VOLUME_FLOW_RATE.sce" + ] + }, + { +"cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], +"source": [ +"clc\n", +"clear\n", +"//input data\n", +"D1=0.09//Rotor inlet tip diameter in m\n", +"D2t=0.062//Rotor outlet tip diameter in m\n", +"D2h=0.025//Rotor outlet hub diameter in m\n", +"N=30000//Blade speed in rpm\n", +"d2=1.8//Density of exhaust gases at impeller exit in kg/m^3\n", +"C2s=0.447//Ratio of absolute velocity and isentropic velocity at exit\n", +"U1Cs=0.707//Ratio of impeller tip velocity and isentropic velocity\n", +"\n", +"//calculations\n", +"U1=(3.1415*D1*N)/60//The impeller tip speed in m/s\n", +"Cs=U1/U1Cs//Isentropic velocity in m/s\n", +"C2=C2s*Cs//Absolute velocity at the exit in m/s\n", +"A2=(3.141/4)*((D2t^2)-(D2h^2))//Area at the exit in m^2\n", +"Q2=A2*C2//Volume flow rate at the impeller exit in m^3/s\n", +"M=d2*Q2//Mass flow rate in kg/s\n", +"W=M*U1^2//Power developed in W\n", +"\n", +"//output\n", +"printf('(a)Volume flow rate at the impeller exit is %3.3f m^3/s\n(b)Power developed is %i W',Q2,W)" + ] + } +, +{ + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 6.5: ROTOR_DIAMETER.sce" + ] + }, + { +"cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], +"source": [ +"clc\n", +"clear\n", +"//input data\n", +"P00=3.5//Total-to-static pressure ratio\n", +"P2=1//Exit pressure in bar\n", +"T00=923//Inlet total temperature in K\n", +"U1Cs=0.66//Blade to isentropic speed ratio\n", +"D=0.45//Rotor diameter ratio\n", +"N=16000//Speed from nozzle in rpm\n", +"a11=20//Nozzle exit angle in degree\n", +"nn=0.95//Nozzle efficiency\n", +"b1=0.05//Rotor width at inlet in m\n", +"R=287//The universal gas constant in J/kg.K\n", +"Cp=1005//The specific heat of air at constant pressure in J/kg.K\n", +"r=1.4//The ratio of specific heats of air\n", +"\n", +"\n", +"//Calculations\n", +"T2s=T00*(1/P00)^((r-1)/r)//Isentropic temperature at the exit in K\n", +"Cs=(2*Cp*(T00-T2s))^(1/2)//The isentropic velocity in m/s\n", +"U1=U1Cs*Cs//The impeller tip speed in m/s\n", +"D1=(U1*60)/(3.14*N)//Rotor inlet diameter in m\n", +"D2=D*D1//Rotor outlet diameter in m\n", +"Cr2=U1*tand(a11)//The relative velocity at the exit in m/s\n", +"U2=(3.1415*D2*N)/60//Peripheral velocity of impeller at exit in m/s\n", +"b22=atand(Cr2/U2)//The air angle at rotor exit in degree\n", +"T02=T00-((U1^2)/(Cp))//The absolute temperature at the exit in K\n", +"T2=T02-((Cr2^2)/(2*Cp))//The temperature at the exit of turbine in K\n", +"T1=T2+((U1^2)/(2*Cp))//The temperature at the entry of turbine in K\n", +"T1s=T00-((T00-T1)/nn)//Isentropic temperature at the entry in K\n", +"P1=P00*(T1s/T00)^(r/(r-1))//The pressure at the entry stage in bar\n", +"d1=(P1*10^5)/(R*T1)//The density of the air at the inlet in kg/m^3\n", +"A1=3.1415*D1*b1//The area at the inlet in m^2\n", +"Cr1=Cr2//The relative velocity at the entry in m/s\n", +"m=d1*A1*Cr1//The mass flow rate for a 90degree IFR turbine Degree of Reaction is 0.5 in kg/s\n", +"W=(m*U1^2)*10^-6//Power developed in MW\n", +"d2=(P2*10^5)/(R*T2)//The density of the air at the exit in kg/m^3\n", +"b2=m/(d2*3.141*D2*Cr2)//Rotor width at the exit in m\n", +"D2h=D2-b2//Hub diameter at the exit in m\n", +"D2t=D2+b2//Tip diameter at the exit in m\n", +"nts=(W*10^6)/(m*Cp*(T00-T2s))//Total-to-static efficiency\n", +"C1=U1/cosd(a11)//Absolute velocity at the entry in m/s\n", +"Ln=(Cp*(T1-T1s))/((C1^2)/2)//Nozzle enthalpy loss coefficient\n", +"W2=((U2^2)+(Cr2^2))^(1/2)//Resultant relative velocity at the exit in m/s\n", +"T2s=T1*(P2/P1)^((r-1)/r)//Isentropic temperature at the exit in K\n", +"Lr=(Cp*(T2-T2s))/((W2^2)/2)//Rotor enthalpy loss coefficient\n", +"\n", +"//output\n", +"printf('(a)\n (1)Rotor inlet diameter is %3.2f m\n (2)Rotor outlet diameter is %3.3f m\n(b)The air angle at rotor exit is %3.2f degree\n(c)The mass flow rate for a 90degree IFR turbine Degree of Reaction is 0.5 is %3.2f kg/s\n(d)Power developed is %3.3f MW\n(e)\n (1)Hub diameter at the exit is %3.4f m\n (2)Tip diameter at the exit is %3.4f m\n(f)Total-to-static efficiency is %3.4f\n(g)Nozzle enthalpy loss coefficient is %3.4f\n(h)Rotor enthalpy loss coefficient is %3.4f',D1,D2,b22,m,W,D2h,D2t,nts,Ln,Lr)" + ] + } +, +{ + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 6.6: TOTAL_TO_STATIC_EFFICIENCY.sce" + ] + }, + { +"cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], +"source": [ +"clc\n", +"clear\n", +"//input data\n", +"P00=700//Total-to-static pressure ratio\n", +"T00=1145//Inlet total temperature in K\n", +"P1=527//The pressure at the entry stage in bar\n", +"T1=1029//The temperature at the entry of turbine in K\n", +"P2=385//The pressure at the second stage in bar\n", +"T2=915//The temperature at the second stage entry in K\n", +"T02=925//The absolute temperature at the exit in K\n", +"D2mD1=0.49//The ratio of rotor exit mean diameter to rotor inlet diameter\n", +"N=24000//Blade speed in rpm\n", +"R1=8.314//The gas constant of given gas in kJ/kg.K\n", +"r=1.67//The ratio of specific heats of the gas\n", +"m=39.94//Molecular weight of a gas \n", +"\n", +"//calculations\n", +"R=R1/m//The universal gas constant in kJ/kg.K\n", +"Cp=(r*R)/(r-1)//The specific heat of air at constant pressure in kJ/kg.K\n", +"T2ss=T00*(P2/P00)^((r-1)/r)//Isentropic stage temperature at the exit in K\n", +"nts=(T00-T02)/(T00-T2ss)//Total-to-static efficiency of the turbine\n", +"U1=(Cp*1000*(T00-T02))^(1/2)//The impeller tip speed in m/s\n", +"D1=(U1*60)/(3.1415*N)//Rotor inlet diameter in m\n", +"D2m=D1*D2mD1//Rotor exit mean diameter in m\n", +"C1=(2*Cp*(T00-T1))^(1/2)//Absolute velocity at the entry in m/s\n", +"T1s=T00*(P1/P00)^((r-1)/r)//Isentropic temperature at the entry in K\n", +"Ln=(Cp*(T1-T1s))/((C1^2)/2)//Nozzle enthalpy loss coefficient\n", +"C2=(2*Cp*1000*(T02-T2))^(1/2)//The temperature at the exit of turbine in K\n", +"U2=(3.14*D2m*N)/(60)//Peripheral velocity of impeller at exit in m/s\n", +"W2=((C2^2)+(U2^2))^(1/2)//Resultant relative velocity at the exit in m/s\n", +"T2s=T1*(P2/P1)^((r-1)/r)//stage temperature at the exit in K\n", +"Lr=(Cp*1000*(T2-T2s))/((W2^2)/2)//Rotor enthalpy loss coefficient\n", +"ntt=1/((1/nts)-((C2^2)/(2*U1^2)))//Total-to-total efficiency\n", +"\n", +"//output\n", +"printf('(a)Total-to-static efficiency of the turbine is %3.3f\n(b)\n (1)Rotor inlet diameter is %3.3f m\n (2)Rotor exit mean diameter is %3.3f m\n(c)\n (1)Nozzle enthalpy loss coefficient is %3.4f\n (2)Rotor enthalpy loss coefficient is %3.4f\n(d)Total-to-total efficiency is %3.4f',nts,D1,D2m,Ln,Lr,ntt)" + ] + } +], +"metadata": { + "kernelspec": { + "display_name": "Scilab", + "language": "scilab", + "name": "scilab" + }, + "language_info": { + "file_extension": ".sce", + "help_links": [ + { + "text": "MetaKernel Magics", + "url": "https://github.com/calysto/metakernel/blob/master/metakernel/magics/README.md" + } + ], + "mimetype": "text/x-octave", + "name": "scilab", + "version": "0.7.1" + } + }, + "nbformat": 4, + "nbformat_minor": 0 +} diff --git a/Turbomachines_by_A_V_Arasu/7-DIMENSIONAL_AND_MODEL_ANALYSIS.ipynb b/Turbomachines_by_A_V_Arasu/7-DIMENSIONAL_AND_MODEL_ANALYSIS.ipynb new file mode 100644 index 0000000..5a9869a --- /dev/null +++ b/Turbomachines_by_A_V_Arasu/7-DIMENSIONAL_AND_MODEL_ANALYSIS.ipynb @@ -0,0 +1,357 @@ +{ +"cells": [ + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "# Chapter 7: DIMENSIONAL AND MODEL ANALYSIS" + ] + }, +{ + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 7.10: SPEED_DISCHARGE_AND_POWER.sce" + ] + }, + { +"cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], +"source": [ +"clc\n", +"clear\n", +"//input data\n", +"DmDp=1/10//The model ratio to prototype\n", +"Hm=5//The head developed by the model in m\n", +"Hp=8.5//The head developed by the prototype in m\n", +"Pp=8000*10^3//The power developed by the prototype in W\n", +"Np=120//The speed of running of the prototype in rpm\n", +"d=1000//density of the water in kg/m^3\n", +"g=9.81//Acceleration due to gravity in m/s^2\n", +"n0=0.85//Overall efficiency of the prototype\n", +"\n", +"//calculations\n", +"Nm=((Hm/Hp)^(1/2))*(1/DmDp)*(Np)//Speed of the mpdel in rpm\n", +"Qp=Pp/(d*g*n0*Hp)//Discharge from the prototype in m^3/s\n", +"Qm=((DmDp)^(3))*(Nm/Np)*(Qp)//Discharge from the model in m^3/s\n", +"Pm=((DmDp)^(5))*((Nm/Np)^(3))*(Pp)*10^-3//Power of the model in kW\n", +"\n", +"//output\n", +"printf('(a)Speed of the model is %3.1f rpm\n(b)Discharge from the model is %3.3f m^3/s\n(c)Power of the model is %3.1f kW',Nm,Qm,Pm)" + ] + } +, +{ + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 7.11: SPEED_AND_POWER_DEVELOPED.sce" + ] + }, + { +"cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], +"source": [ +"clc\n", +"clear\n", +"//input data\n", +"P1=6600//Initial power developed by the turbine in kW\n", +"N1=100//Initial speed of the turbine in rpm\n", +"H1=30//Initial head of the turbine in m\n", +"H2=18//Final head of the turbine in m\n", +"\n", +"//calculations\n", +"N2=N1*((H2/H1)^(1/2))//The final speed of the turbine in rpm\n", +"P2=P1*((H2/H1)^(3/2))//The final power developed by the turbine in kW\n", +"\n", +"//output\n", +"printf('(1)The final speed of the turbine is %3.2f rpm\n(2)The final power developed by the turbine is %3i kW',N2,P2)" + ] + } +, +{ + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 7.12: PERFORMANCE_OF_TURBINE.sce" + ] + }, + { +"cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], +"source": [ +"clc\n", +"clear\n", +"//input data\n", +"H1=25//The initial head on the turbine in m\n", +"N1=200//The initial speed of the turbine in rpm \n", +"Q1=9//The initial discharge of the turbine in m^3/s\n", +"n0=0.9//Overall efficiency of the turbine \n", +"H2=20//The final head on the turbine in m\n", +"d=1000//density of the water in kg/m^3\n", +"g=9.81//Acceleration due to gravity in m/s^2\n", +"\n", +"//calculations\n", +"N2=N1*((H2/H1)^(1/2))//The final speed of the turbine in rpm\n", +"Q2=Q1*((H2/H1)^(1/2))//The final discharge of the turbine in m^3/s\n", +"P1=n0*d*g*Q1*H1*10^-3//Power produced by the turbine initially in kW\n", +"P2=P1*((H2/H1)^(3/2))//Power produced by the turbine finally in kW\n", +"\n", +"//output\n", +"printf('(a)The final speed of the turbine is %3.2f rpm\n(b)The final discharge of the turbine is %3.2f m^3/s\n(c)Power produced by the turbine initially is %3.3f kW\n(d)Power produced by the turbine finally is %3.2f kW',N2,Q2,P1,P2)" + ] + } +, +{ + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 7.13: SPECIFIC_SPEED.sce" + ] + }, + { +"cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], +"source": [ +"clc\n", +"clear\n", +"//input data\n", +"P1=5000*10^3//The initial power produced in W\n", +"H1=250//The initial head produced in m\n", +"N1=210//The initial speed of turbine in rpm\n", +"n0=0.85//Overall efficiency of the turbine \n", +"H2=160//The final head produced in m\n", +"d=1000//density of the water in kg/m^3\n", +"g=9.81//Acceleration due to gravity in m/s^2\n", +"\n", +"\n", +"//calculations\n", +"Nu=N1/((H1)^(1/2))//The unit speed of the turbine \n", +"Pu=P1/((H1)^(3/2))*10^-3//The unit power of the turbine \n", +"Q1=P1/(d*g*n0*H1)//The initial discharge of the turbine in m^3/s\n", +"Qu=Q1/((H1)^(1/2))//The unit discharge of the turbine \n", +"Q2=Qu*((H2)^(1/2))//The final discharge of the turbine in m^3/s\n", +"N2=Nu*((H2)^(1/2))//The final speed of the turbine in rpm\n", +"P2=Pu*((H2)^(3/2))//The final power of the turbine in kW\n", +"Ns=(N2*((P2)^(1/2)))/((H2)^(5/4))//The specific speed of the turbine\n", +"\n", +"//output\n", +"printf('(a)The unit speed of the turbine is %3.2f\n(b)The unit power of the turbine is %3.3f\n(c)The unit discharge of the turbine is %3.3f\n(d)The final discharge of the turbine is %3.2f m^3/s\n(e)The final speed of the turbine is %3.2f rpm\n(f)The final power of the turbine is %3.1f kW\n(g)The specific speed of the turbine is %3.2f',Nu,Pu,Qu,Q2,N2,P2,Ns)" + ] + } +, +{ + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 7.5: SPEED_OF_PROTOTYPE.sce" + ] + }, + { +"cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], +"source": [ +"clc\n", +"clear\n", +"//input data\n", +"Nm=1000//Speed of the model in rpm\n", +"Hm=8//Head of the model in m\n", +"Pm=30//Power of the model in kW\n", +"Hp=25//Head of the prototype in m\n", +"DmDp=1/5//The scale of the model to original\n", +"\n", +"//calculations\n", +"Np=((Hp/Hm)^(1/2))*(DmDp)*(Nm)//Speed of the prototype in rpm\n", +"Pp=(Pm)*((1/DmDp)^(5))*(Np/Nm)^(3)//Power developed by the prototype in kW\n", +"QpQm=((1/DmDp)^(3))*(Np/Nm)//Ratio of the flow rates of two pump(model and prototype)\n", +"\n", +"//output\n", +"printf('(1)Speed of prototype pump is %3.1f rpm\n(2)Power developed by the prototype pump is %3i kW\n(3)Ratio of the flow rates of two pumps is %3.4f',Np,Pp,QpQm)" + ] + } +, +{ + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 7.6: HEAD_SPEED_AND_SCALE_RATIO.sce" + ] + }, + { +"cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], +"source": [ +"clc\n", +"clear\n", +"//input data\n", +"Hp=85//Head of the prototype in m\n", +"Qp=(20000/3600)//Flow rate of the prototype in m^3/s\n", +"Np=1490//Speed of the prototype in rpm\n", +"Dp=1.2//Diameter of the prototype in m\n", +"dp=714//Density of the prototype fluid in kg/m^3\n", +"Pp=4//Power of the prototype in MW\n", +"Pm=500*10^-3//Power of the model in MW\n", +"Qm=0.5//Flow rate of the prototype in m^3/s\n", +"dm=1000//Density of the model fluid (water) in kg/m^3\n", +"\n", +"//calculations\n", +"NpNm=(Qp/Qm)//Ratio of the speeds of the prototype and the model in terms of (Dm/Dp)^(3)\n", +"DmDp=1/(((NpNm)^(3))*(dp/dm)*(Pm/Pp))^(1/4)//The ratio of the diameters of model and the prototype or the scale ratio \n", +"NmNp=1/(NpNm*((DmDp)^(3)))//The speed ratio or the ratio of speeds of the model and the prototype\n", +"HmHp=((1/NmNp)^(2))*((1/DmDp)^(2))//The head ratio or the ratio of heads of the model and the prototype \n", +"\n", +"//output\n", +"printf('(1)The head ratio of the model is %3.1f\n(2)The speed ratio of the model is %3.1f\n(3)The scale ratio of the model is %3.1f',HmHp,NmNp,DmDp)" + ] + } +, +{ + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 7.7: SPEED_AND_DISCHARGE_OF_THE_MODEL.sce" + ] + }, + { +"cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], +"source": [ +"clc\n", +"clear\n", +"//input data\n", +"Np=400//The speed of the prototype in rpm\n", +"Qp=1.7//The discharge of the prototype in m^3/s\n", +"Hp=36.5//The head of the prototype in m\n", +"Pp=720//The power input of the prototype in kW\n", +"Hm=9//The head of the model in m\n", +"DmDp=1/6//The scale of model to prototype \n", +"\n", +"//calculations\n", +"Nm=((Hm/Hp)^(1/2))*(1/DmDp)*Np//Speed of the model in rpm\n", +"Qm=((DmDp)^(3))*(Nm/Np)*(Qp)//Discharge of the model in m^3/s\n", +"Pm=((DmDp)^(5))*((Nm/Np)^(3))*Pp//Power required by the model in kW\n", +"\n", +"//output\n", +"printf('(a)Speed of the model is %3.2f rpm\n(b)Discharge of the model is %3.4f m^3/s\n(c)Power required by the model is %3.2f kW',Nm,Qm,Pm)" + ] + } +, +{ + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 7.8: IMPELLER_DIAMETER_OF_PUMP2.sce" + ] + }, + { +"cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], +"source": [ +"clc\n", +"clear\n", +"//input data\n", +"N1=1000//The running speed of the pump-1 in rpm\n", +"D1=0.3//The impeller diameter of pump-1 in m\n", +"Q1=0.02//The discharge of pump-1 in m^3/s\n", +"H1=15//The head developed by the pump-1 in m\n", +"N2=1000//The running speed of the pump-2 in rpm\n", +"Q2=0.01//The discharge of pump-2 in m^3/s\n", +"\n", +"//calculations\n", +"D2=(((Q2/Q1)*(N1/N2))^(1/3))*(D1)//Impeller diameter of the pump-2 in m\n", +"H2=(((D2/D1)*(N2/N1))^(2))*(H1)//Head developed by the pump-2 in m\n", +"\n", +"//output\n", +"printf('(a)Impeller diameter of the pump-2 is %3.3f m\n(b)Head developed by the pump-2 is %3.2f m',D2,H2)" + ] + } +, +{ + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 7.9: SPECIFIC_SPEEDS.sce" + ] + }, + { +"cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], +"source": [ +"clc\n", +"clear\n", +"//input data\n", +"DmDp=1/10//The model ratio to prototype \n", +"Pm=1.84//Power developed by the model in kW\n", +"Hm=5//Head developed by the model in m\n", +"Nm=480//Speed of the model in rpm\n", +"Hp=40//Head developed by the prototype in m\n", +"\n", +"//calculations\n", +"Np=((Hp/Hm)^(1/2))*(DmDp)*(Nm)//Speed of the prototype in rpm\n", +"Pp=((1/DmDp)^(5))*((Np/Nm)^(3))*Pm//Power developed by the prototype in kW\n", +"Nsp=((Np*((Pp)^(1/2)))/((Hp)^(5/4)))//Specific speed of the prototype\n", +"Nsm=((Nm*((Pm)^(1/2)))/((Hm)^(5/4)))//Specific speed of the prototype\n", +"\n", +"//output\n", +"printf('(a)Power developed by the prototype is %3i kW\n(b)Speed of the prototype is %3.2f rpm\n(c)Specific speed of the prototype is %3.1f\n(d)Specific speed of the model is %3.1f\n Thus the specific speed of the model is equal to the prototype and thus it is verified',Pp,Np,Nsp,Nsm)" + ] + } +], +"metadata": { + "kernelspec": { + "display_name": "Scilab", + "language": "scilab", + "name": "scilab" + }, + "language_info": { + "file_extension": ".sce", + "help_links": [ + { + "text": "MetaKernel Magics", + "url": "https://github.com/calysto/metakernel/blob/master/metakernel/magics/README.md" + } + ], + "mimetype": "text/x-octave", + "name": "scilab", + "version": "0.7.1" + } + }, + "nbformat": 4, + "nbformat_minor": 0 +} diff --git a/Turbomachines_by_A_V_Arasu/8-HYDRAULIC_PUMPS.ipynb b/Turbomachines_by_A_V_Arasu/8-HYDRAULIC_PUMPS.ipynb new file mode 100644 index 0000000..c5c9fd7 --- /dev/null +++ b/Turbomachines_by_A_V_Arasu/8-HYDRAULIC_PUMPS.ipynb @@ -0,0 +1,963 @@ +{ +"cells": [ + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "# Chapter 8: HYDRAULIC PUMPS" + ] + }, +{ + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 8.10: EXIT_BLADE_ANGLE.sce" + ] + }, + { +"cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], +"source": [ +"clc\n", +"clear\n", +"//input data\n", +"Ihl=3//Head loss in impeller in m\n", +"Cr2=4.64//Flow velocity through impeller at outlet in m/s\n", +"U2=30//Blade outlet speed in m/s\n", +"dPi=35.3//Difference in pressure gauge readings at impeller inlet and outlet in m of water\n", +"Pg=4.7//Pressure gain in the casing in m of water \n", +"n=0.385//Part of absolute kinetic energy converted into pressure gain\n", +"g=9.81//Acceleration due to gravity in m/s^2\n", +"d=1000//Density of water in kg/m^3\n", +"ss=0.85//Slip coefficient\n", +"\n", +"//calculations\n", +"Kei=Pg/n//Kinetic energy at impeller exit in m/s\n", +"C2=((Kei)*2*g)^(1/2)//Velocity at impeller exit in m/s\n", +"Cx22=(C2^2-Cr2^2)^(1/2)//Absolute whirl component at outlet with fliud slip in m/s\n", +"Cx2=Cx22/ss//Ideal absolute whirl velocity in m/s\n", +"b22=atand(Cr2/(U2-Cx2))//Blade angle at exit in degree\n", +"Wm=ss*U2*Cx2//Euler work input in J/kg\n", +"nm=dPi/(U2*Cx22/g)//Manometric efficiency\n", +"dP=(U2*Cx22/g)-(Ihl)-(C2^2/(2*g))//Pressure rise in impeller in m\n", +"\n", +"//output\n", +"printf('(a)\n Exit blade angle is %3.2f degree\n Euler work input is %3.2f J/kg\n(b)Manometric efficiency is %3.4f\n(c)Pressure rise in the impeller is %3.3f m',b22,Wm,nm,dP)" + ] + } +, +{ + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 8.11: VOLUME_FLOW_RATE_THROUGH_IMPELLER.sce" + ] + }, + { +"cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], +"source": [ +"clc\n", +"clear\n", +"//input data\n", +"r1=0.051//Eye radius of the impeller in m\n", +"D2=0.406//Outer diameter of the impeller in m\n", +"b11=(90-75)//Inlet blade angle measured from tangential flow direction in degree\n", +"b22=(90-83)//Outlet blade angle measured from tangential flow direction in degree\n", +"b=0.064//Blade depth in m\n", +"Cx1=0//Inlet whirl velocity in m/s\n", +"nh=0.89//Hydraulic efficiency \n", +"g=9.81//Acceleration due to gravity in m/s^2\n", +"d=1000//Density of water in kg/m^3\n", +"N=900//Rotating speed of impeller in rpm\n", +"\n", +"//calculations\n", +"w=(2*3.1415*N)/60//Angular velocity at inlet in rad/s\n", +"U1=(w*r1)//Inlet tangential impeller velocity in m/s\n", +"C1=U1*tand(b11)//Velocity at impeller inlet in m/s\n", +"A=2*3.1415*r1*b//Area of flow through the pump in m^2\n", +"Cr1=C1//Flow velocity through impeller at inlet in m/s\n", +"Q=A*Cr1//Volume flow through the pump in m^3/s\n", +"r2=D2/2//Outer radius of the impeller in m\n", +"Cr2=(r1*Cr1)/r2//Flow velocity through impeller at outlet in m/s\n", +"U2=w*r2//Outlet tangential impeller velocity in m/s\n", +"Wx2=Cr2/tand(b22)//Exit relative velocity in m/s\n", +"E=(U2/g)*(U2-Wx2)//Theoretical head developed in m\n", +"Hm=nh*E//Total stagnation head developed by the pump in m\n", +"dP021=Hm*d*g*10^-3//Total pressure head coefficient in kPa\n", +"Cx2=U2-(Cr2/tand(b22))//Absolute whirl velocity in m/s\n", +"C2=(Cr2^2+Cx2^2)^(1/2)//Velocity at impeller exit in m/s\n", +"dP21=(Hm-(((C2^2)-(C1^2))/(2*g)))*d*g*10^-3//The static pressure head in kPa\n", +"P=d*g*Q*Hm*10^-3//Power given to the fluid in kW\n", +"Ps=P/nh//Input power to impeller in kW\n", +"\n", +"//output\n", +"printf('(a)Volume flow rate through the impeller is %3.4f m^3/s\n(b)\n stagnation pressure rise across the impeller is %3.1f kPa\n Static pressure rise across the impeller is %3.1f kPa\n(c)Power given to fluid is %3.2f kW\n(d)Input power to impeller is %3.2f kW',Q,dP021,dP21,P,Ps)" + ] + } +, +{ + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 8.12: IMPELLER_DIAMETER.sce" + ] + }, + { +"cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], +"source": [ +"clc\n", +"clear\n", +"//input data\n", +"Q=0.04//Discharge of the pump design in m^3/s\n", +"Ns=0.075//Specific speed in rev\n", +"b22=(180-120)//Outlet angle with the normal in degree\n", +"H=35//Distance to which pumping of water is done in m\n", +"Dp=0.15//Diameter of suction and delivery pipes in m\n", +"L=40//Combined length of suction and delivery pipes in m\n", +"WD=1/10//Width to diameter ratio at outlet of impeller \n", +"f=0.005//Friction factor \n", +"g=9.81//Acceleration due to gravity in m/s^2\n", +"nh=0.76//Hydraulic effficiency neglecting the slip\n", +"n=0.06//Percentage occupied by blades on circumference area\n", +"\n", +"//calculations\n", +"A=(3.1415/4)*(Dp^2)//Area of flow in pipe in m^2\n", +"V=Q/A//Velocity in the pipes in m/s\n", +"OL=3*V^2/(2*g)//Other loses in the pipes in m\n", +"TL=(4*f*L*V^2/(2*g*Dp))+(OL)//Total loses in a pipe in m\n", +"TH=TL+H//Total required head in m\n", +"N=(Ns*((g*H)^(3/4)))/((Q)^(1/2))//The speed of the pump in rev/s\n", +"Ao=3.1415*WD*(1-n)//Flow area perpendicular to impeller outlet periphery in terms of D^2 in m^2 In this the area is calculated using only the circumferential area without blades\n", +"Cr2=Q/Ao//Flow velocity through impeller at outlet in m/s\n", +"U2=3.1415*N//Outlet tangential impeller velocity in m/s in terms of D\n", +"Cx2=(g*H)/(U2*nh)//Absolute whirl velocity in m/s\n", +"\n", +"//The following steps are for calculating the cubic root equation in D\n", +"//This is obtained by solving tand(b22)=(Cr2/(Cx2-U2)) all values are substituted in terms of D\n", +"//The final equation which is obtained is D^3-0.0495D+0.0008=0\n", +"//The above equation is solved using the following formulae\n", +"\n", +"a=0//Coefficient of D^2 in the above equation\n", +"b=-0.0511//Coefficient of D in the above equation\n", +"c=0.00083//Constant term in above equation\n", +"q=c+((2*(a^3))/27)-(a*b/3)//Constant in solving the cubic equation\n", +"p=((3*b)-(a^2))/3//Constant in solving the cubic equation\n", +"d=(p/2)^2+(q/3)^3//Constant in solving the cubic equation\n", +"u=((-q/2)+(d^(1/2)))^(1/3)//Constant in solving the cubic equation\n", +"v=((-q/2)-(d^(1/2)))^(1/3)//Constant in solving the cubic equation\n", +"D=(u+v)/2//Impeller diameter in m\n", +"\n", +"//output\n", +"printf('The pump impeller diameter is %3.3f m',D)" + ] + } +, +{ + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 8.13: SPECIFIC_SPEED.sce" + ] + }, + { +"cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], +"source": [ +"clc\n", +"clear\n", +"//input data\n", +"N=2875//Speed of the pump in rpm \n", +"Q=57.2/3600//Discharge of the pump in m^3/s\n", +"Hm=42.1//Total head developed by the pump in m\n", +"d=1000//Density of the water in kg/m^3\n", +"g=9.81//Acceleration due to gravity in m/s^2\n", +"n=0.76//Efficiency of the pump\n", +"\n", +"//calculations\n", +"Ns=(N*Q^(1/2))/(Hm^(3/4))//Specific speed of the pump \n", +"P=((d*g*Q*Hm)/n)*10^-3//Power input in kW\n", +"\n", +"//calculations\n", +"printf('(a)Specific speed of the pump is %3.f\n(b)Power input is %3.3f kW',Ns,P)" + ] + } +, +{ + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 8.14: MANOMETRIC_EFFICIENCY.sce" + ] + }, + { +"cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], +"source": [ +"clc\n", +"clear\n", +"//input data\n", +"D1=0.6//Inlet impeller diameter in m\n", +"D2=1.2//Outlet impeller diameter in m\n", +"Cr2=2.5//Radial flow velocity in m/s\n", +"N=200//Running speed of the pump in rpm\n", +"Q=1.88//Discharge of the pump in m^3/s\n", +"Hm=6//Head which the pump has to overcome in m\n", +"b22=26//Vane angle at exit at tangent to impeller in degree\n", +"d=1000//Density of the water in kg/m^3\n", +"g=9.81//Acceleration due to gravity in m/s^2\n", +"\n", +"//calculations\n", +"U2=(3.1415*D2*N)/60//Outlet tangential impeller velocity in m/s\n", +"Wx2=Cr2/tand(b22)//Exit relative velocity in m/s\n", +"Cx2=U2-Wx2//Absolute whirl velocity in m/s\n", +"nm=(Hm/(U2*Cx2/g))//Manometric efficiency \n", +"Nls=((2*g*Hm*60^2)/((3.1415^2)*((1.2^2)-(0.6^2))))^(1/2)//Least starting speed of the pump in rpm\n", +"\n", +"//output\n", +"printf('(1)Manometric efficiency is %3.3f\n(2)Least speed to start the pump is %3.2f rpm',nm,Nls)" + ] + } +, +{ + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 8.15: HYDRAULIC_OR_MANOMETRIC_EFFICIENCY.sce" + ] + }, + { +"cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], +"source": [ +"clc\n", +"clear\n", +"//input data\n", +"D2=1.25//External diameter of the impeller in m\n", +"D1=0.5//Internal diameter of the impeller in m\n", +"Q=2//Discharge of the pump in m^3/s\n", +"Hm=16//Head over which pump has to operate in m\n", +"N=300//Running speed of the pump in rpm\n", +"b22=30//Angle at which vanes are curved back in degree\n", +"Cr1=2.5//Flow velocity through impeller at inlet in m/s\n", +"Cr2=Cr1//Flow velocity through impeller at outlet in m/s\n", +"d=1000//Density of the water in kg/m^3\n", +"g=9.81//Acceleration due to gravity in m/s^2\n", +"\n", +"//calculations\n", +"U2=(3.1415*D2*N)/60//Outlet tangential impeller velocity in m/s\n", +"Wx2=Cr2/tand(b22)//Exit relative velocity in m/s\n", +"Cx2=U2-Wx2//Absolute whirl velocity in m/s\n", +"nm=(Hm*g)/(U2*Cx2)//Manometric or hydraulic efficiency\n", +"m=d*Q//Mass flow rate of water in kg/s\n", +"W=m*U2*Cx2*10^-3//Fluid power developed by the impeller in kW\n", +"Ps=W//Power required by the pump in kW neglecting mechanical loses\n", +"Nls=((2*g*Hm)/(((3.1415/60)^2)*(D2^2-D1^2)))^(1/2)//Minimum starting speed of the pump in rpm\n", +"\n", +"//output\n", +"printf('(a)Manometric or hydraulic efficiency is %3.3f \n(b)Power required by the pump is %3.2f kW\n(c)Minimum starting speed of the pump is %3.1f rpm',nm,Ps,Nls)" + ] + } +, +{ + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 8.16: HEAT_GENERATED_BY_PUMP.sce" + ] + }, + { +"cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], +"source": [ +"clc\n", +"clear\n", +"//input data\n", +"n=3//Number of stages \n", +"D2=0.4//Outlet impeller diameter in m\n", +"b2=0.02//Outlet impeller width in m\n", +"b22=45//Backward vanes angle at outlet in degree\n", +"dA=0.1//Reduction in circumferential area\n", +"nm=0.9//Manometric efficiency of the pump\n", +"Q=0.05//Discharge of the pump in m^3/s\n", +"N=1000//Running speed of the pump in rpm\n", +"n0=0.8//Overall efficiency of the pump\n", +"g=9.81//Acceleration due to gravity in m/s^2\n", +"d=1000//Density of water in kg/m^3\n", +"\n", +"//calculations\n", +"A2=(1-dA)*3.1415*D2*b2//Area of flow at outlet in m^2\n", +"Cr2=Q/A2//Flow velocity through impeller at outlet in m/s\n", +"U2=(3.1415*D2*N)/60//Outlet impeller tangential velocity in m/s\n", +"Wx2=Cr2//Exit relative velocity in m/s as tand(b22)=1\n", +"Cx2=U2-Wx2//Absolute whirl velocity in m/s\n", +"Hm=(nm*U2*Cx2)/g//Head over which pump has to operate in m\n", +"H=n*Hm//Total head generated by the pump in m\n", +"P=d*g*Q*Hm*n//Power output from the pump in W\n", +"Ps=P/n0*10^-3//Shaft power input in kW\n", +"\n", +"//output\n", +"printf('(1)The head generated by the pump is %3.2f m\n(2)Shaft power input is %3.3f kW',H,Ps)" + ] + } +, +{ + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 8.17: NUMBER_OF_PUMPS.sce" + ] + }, + { +"cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], +"source": [ +"clc\n", +"clear\n", +"//input data\n", +"H=156//Total head operated by the pumps in m\n", +"N=1000//Running speed of the pump in rpm\n", +"Ns=20//Specific speed of each pump \n", +"Q=0.150//Discharge of the pump in m^3/s\n", +"\n", +"//calculations\n", +"Hm=((N*(Q)^(1/2))/(Ns))^(4/3)//Head developed by each pump in m\n", +"n=H/Hm//Number of pumps\n", +"\n", +"//output\n", +"printf('The number of pumps are %3.f',n)" + ] + } +, +{ + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 8.18: IMPELLER_DIAMETER_AND_NUMBER_OF_STAGES.sce" + ] + }, + { +"cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], +"source": [ +"clc\n", +"clear\n", +"//input data\n", +"Q1=120//Discharge of each of the multi stage pump in parallel in first case in m^3/s\n", +"Q2=450//Discharge of the multi stage pump in second case in m^3/s\n", +"H1=16//Head of each stage in first case in m\n", +"D1=0.15//Diameter of impeller in first case in m\n", +"H=140//Total head developed by all pumps in second case in m\n", +"N1=1500//Running speed of the pump in rpm in first case\n", +"N2=1200//Running speed of the pump in rpm in second case\n", +"//calculations\n", +"H2=H1*((Q2/Q1)*((N2/N1)^2))^(4/6)//Head of each stage in second case in m\n", +"n=H/H2//Number of stages in second case \n", +"D2=D1*(((N1/N2)^(2))*(H2/H1))^(1/2)//Diameter of impeller in second case in m\n", +"\n", +"//output\n", +"printf('(a)number of stages required is %3.f\n(b)Diameter of impeller in the second case is %3.2f m',n,D2)" + ] + } +, +{ + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 8.19: CAVITATION_PARAMETER.sce" + ] + }, + { +"cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], +"source": [ +"clc\n", +"clear\n", +"//input data\n", +"H=36//Initial total head of the pump in m\n", +"Q1=0.05//Initial discharge of the pump in m^3/s\n", +"H2=3.5//Sum of static pressure and velocity head at inlet in m\n", +"P01=0.75//Atmospheric pressure initially in m of Hg\n", +"Pvap1=1.8*10^3//Vapour pressure of water initially in Pa\n", +"Pvap2=830//Vapour pressure of water finanlly in Pa\n", +"P02=0.62//Atmospheric pressure finally in m of Hg\n", +"g=9.81//Acceleration due to gravity in m/s^2\n", +"dW=1000//Density of water in kg/m^3\n", +"dHg=13.6//Density of mercury in kg/m^3\n", +"\n", +"//calculations\n", +"NPSH=H2-((Pvap1)/(dW*g))//Net positive suction head in m\n", +"s=NPSH/H//Cavitation parameter when pump dvelops same total head and discharge \n", +"dH1=(P01*dHg)-(s*H)-(Pvap1/(dW*g))//The height reduced in initial condition above supply in m\n", +"dH2=(P02*dHg)-(s*H)-(Pvap2/(dW*g))//The height reduced in final condition above supply in m\n", +"Z=dH1-dH2//The total height which the pump must be lowered at new location in m\n", +"\n", +"//output\n", +"printf('(a)The cavitation parameter is %3.4f\n(b)\n The height reduced in initial condition above supply is %3.1f m\n The height reduced in final condition above supply is %3.2f m\n The total height which the pump must be lowered at new location is %3.2f m',s,dH1,dH2,Z)" + ] + } +, +{ + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 8.1: TORQUE_DELIVERED.sce" + ] + }, + { +"cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], +"source": [ +"clc\n", +"clear\n", +"//input data\n", +"D=1.3//Diameter of the pump in m\n", +"Q=3.5/60//Discharge of water by pump in m^3/s\n", +"U2=10//Tip speed of pump in m/s\n", +"Cr2=1.6//Flow velocity of water in pump in m/s\n", +"b2=30//Outlet blade angle tangent to impeller periphery in degree\n", +"Cx1=0//Whirl velocity at inlet in m/s\n", +"U=10//Tip speed of pump in m/s\n", +"d=1000//Density of water in kg/m^3\n", +"g=9.81//Acceleration due to gravity in m/s^2\n", +"\n", +"//calculations\n", +"Wx2=Cr2/tand(b2)//Exit relative velocity in m/s\n", +"E=(U2/g)*(U2-(Wx2))//Euler head in m or W/(N/S)\n", +"m=d*Q//Mass flow rate of water in kg/s\n", +"W=E*m*g//Power delivered in W\n", +"r=D/2//Radius of the pump in m\n", +"T=W/(U/r)//Torque delivered in Nm\n", +"\n", +"//output\n", +"printf('Torque delivered by the impeller is %3.1f Nm',T)" + ] + } +, +{ + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 8.20: VANE_ANGLE_AT_ENTRY.sce" + ] + }, + { +"cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], +"source": [ +"clc\n", +"clear\n", +"//input data\n", +"Dt=1//Impeller outlet diameter in m\n", +"Dh=0.5//Diameter of the boss in m\n", +"Ns=38//Specific speed of the pump \n", +"Ca=2//Velocity of the flow in m/s\n", +"H=6//Head which the pump has to drive in m\n", +"\n", +"//calculations\n", +"A=(3.1415/4)*(Dt^2-Dh^2)//Area of flow in m^2\n", +"Q=A*Ca//Discharge of the pump in m^3/s\n", +"N=(Ns*H^(3/4))/(Q^(1/2))//Pump speed in rpm\n", +"U1=(3.1415*Dh*N)/60//Blade inlet speed in m/s\n", +"b1=atand(Ca/U1)//Vane angle at the entry of the pump when the flow is axial at inlet in degree\n", +"\n", +"//output\n", +"printf('(a)Pump speed is %3.3f rpm\n(b)Vane angle at the entry of the pump when the flow is axial at inlet is %3.2f degree',N,b1)" + ] + } +, +{ + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 8.21: PUMP_SPEED.sce" + ] + }, + { +"cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], +"source": [ +"clc\n", +"clear\n", +"//input data\n", +"Q=0.180//Discharge of the pump in m^3/s\n", +"H=2//Head developed by the pump in m\n", +"Ns=250//Specific speed of the pump \n", +"SR=2.4//Speed ratio of the pump\n", +"FR=0.5//Flow ratio of the pump\n", +"g=9.81//Acceleration due to gravity in m/s^2\n", +"\n", +"//calculations\n", +"N=(Ns*(H^(3/4)))/(Q^(1/2))//Pump speed in rpm\n", +"U=SR*(2*g*H)^(1/2)//Peripheral velocity in m/s\n", +"D=(60*U)/(3.1415*N)//Runner diameter of the pump in m\n", +"Ca=FR*(2*g*H)^(1/2)//Velocity of flow in m/s\n", +"Dh=((D^2)-(Q*4/(Ca*3.14)))^(1/2)//Boss diameter of the pump in m\n", +"\n", +"//output\n", +"printf('(a)Pump speed is %3.i rpm\n(b)Runner diameter of the pump is %3.2f m\n(c)Boss diameter of the pump is %3.2f m\n',N,D,Dh)" + ] + } +, +{ + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 8.22: JET_PUMP_EFFICIENCY.sce" + ] + }, + { +"cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], +"source": [ +"clc\n", +"clear\n", +"//input data\n", +"Hs=2.5//Height of the pipe above suction reservoir in m\n", +"H1=18//Height of the pipe below supply reservoir in m\n", +"H=2.7//Total height through which the pump lifts water in m\n", +"Q1=2.75//Discharge of water used from supply reservoir in l/s\n", +"Qt=7.51//Discharge of water totally delivered in l/s\n", +"\n", +"//calculations\n", +"Hd=H-Hs//Height of the pipe from discharge reservoir in m\n", +"Qs=Qt-Q1//Discharge of water in delivery reservoir in l/s\n", +"nj=(Qs/Q1)*((Hs+Hd)/(H1-Hd))//Jet pump efficiency \n", +"\n", +"//output\n", +"printf('The efficiency of the jet pump is %3.3f',nj)" + ] + } +, +{ + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 8.2: THEORETICAL_HEAD.sce" + ] + }, + { +"cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], +"source": [ +"clc\n", +"clear\n", +"//input data\n", +"b2=30//Impeller blade angle to the tangent at impeller outlet in degree\n", +"d=0.02//Blade depth in m\n", +"D=0.25//Blade diameter in m\n", +"N=1450//Pump rotation speed in rpm\n", +"Q=0.028//FLow rate of the pump in m^3/s\n", +"sf=0.77//Slip factor \n", +"g=9.81//Acceleration due to gravity in m/s^2\n", +"\n", +"//calculations\n", +"A=3.1415*d*D//Flow area in m^2\n", +"Cr2=Q/A//Flow velocity in m/s\n", +"Wx2=Cr2/tand(b2)//Exit relative velocity in m/s\n", +"U2=(3.14*D*N)/60//Tip speed of pump in m/s\n", +"Cx2=U2-Wx2//Absolute whirl component at exit in m/s\n", +"E=(U2*Cx2)/g//Euler head with no whirl at inlet in m\n", +"Cx21=sf*Cx2//Actual value of component of absolute value in tangential direction in m/s\n", +"Es=sf*E//Theoretical head with slip in m\n", +"Z=(3.145*sind(b2))/((1-sf)*(1-((Cr2/U2)*cotd(b2))))//Number of blades required based on stodola slip factor\n", +"\n", +"//output\n", +"printf('(a)Theoretical head with slip is %3.2f m\n(b)Number of blades required is %3.f',Es,Z)" + ] + } +, +{ + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 8.3: DISCHARGE.sce" + ] + }, + { +"cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], +"source": [ +"clc\n", +"clear\n", +"//input data\n", +"D2=0.4//Outer diameter of impeller in m\n", +"b2=0.05//Outlet width of impeller in m\n", +"N=800//Running speed of pump in rpm\n", +"Hm=16//Working head of pump in m\n", +"b22=40//Vane angle at outlet in degree\n", +"nm=0.75//Manometric efficiency \n", +"g=9.81//Acceleration due to gravity in m/s^2\n", +"\n", +"//calculations\n", +"U2=(3.1415*D2*N)/60//Impeller tip speed in m/s\n", +"Cx2=(g*Hm)/(U2*nm)//Absolute whirl component at exit in m/s\n", +"Wx2=U2-Cx2//Exit relative velocity in m/s\n", +"Cr2=Wx2*tand(b22)//Flow velocity of water in pump in m/s\n", +"A=3.14*D2*b2//Area of flow in m^2\n", +"Q=A*Cr2//Discharge of the pump in m^3/s\n", +"\n", +"//output\n", +"printf('The discharge of the pump is %3.4f m^3/s',Q)" + ] + } +, +{ + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 8.4: VANE_INLET_ANGLE.sce" + ] + }, + { +"cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], +"source": [ +"clc\n", +"clear\n", +"//input data\n", +"D2D1=2//The ratio of outer and inner diameter \n", +"N=1200//The running speed of pump in rpm\n", +"Hm=75//Total head producing work in m\n", +"Cr1=3//Flow velocity through impeller at inlet in m/s\n", +"Cr2=Cr1//Flow velocity through impeller at outlet in m/s\n", +"b22=30//Vanes set back angle at outlet in degree\n", +"D2=0.6//Outlet diameter of impeller in m\n", +"d=1000//Density of water in kg/m^3\n", +"b2=0.05//Width of impeller at outlet in m\n", +"g=9.81//Acceleartion due to gravity in m/s^2\n", +"\n", +"//calculations\n", +"D1=D2/D2D1//Inlet diameter of impeller in m\n", +"U1=(3.1415*D1*N)/60//Impeller tip speed at inlet in m/s\n", +"b11=atand(Cr1/U1)//Vane angle at inlet in degree\n", +"U2=(3.1415*D2*N)/60//Impeller tip speed at exit in m/s\n", +"A=3.1415*D2*b2//Area of flow in m^2\n", +"Q=A*Cr2//Discharge of the pump in m^/s\n", +"m=d*Q//Mass flow rate of water in kg/s\n", +"Wx2=Cr2/tand(b22)//Exit relative velocity in m/s\n", +"Cx2=U2-Wx2//Absolute whirl component at exit in m/s\n", +"W=m*U2*Cx2*10^-3//Work done per second in kW\n", +"nm=Hm/((U2*Cx2)/g)//Manometric efficiency \n", +"\n", +"//output\n", +"printf('(a)Vane angle at inlet is %3.3f degree\n(b)Work done per second is %3.2f kW\n(c)Manometric efficiency is %3.4f',b11,W,nm)" + ] + } +, +{ + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 8.5: ANGLES_AND_EFFICIENCIES.sce" + ] + }, + { +"cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], +"source": [ +"clc\n", +"clear\n", +"//input data\n", +"Q=75//Discharge from the pump in l/s\n", +"D1=0.1//Inlet diameter of the pump in m\n", +"D2=0.29//Outlet diameter of the pump in m \n", +"Hm=30//Total head producing work in m\n", +"N=1750//Speed of the pump in rpm\n", +"b1=0.025//Width of impeller at inlet per side in m\n", +"b2=0.023//Width of impeller at outlet in total in m\n", +"a11=90//The angle made by the entering fluid to impeller in degree\n", +"b22=27//Vanes set back angle at outlet in degree\n", +"Qloss=2.25//Leakage loss in l/s\n", +"ml=1.04//Mechanical loss in kW\n", +"cf=0.87//Contraction factor due to vane thickness \n", +"n0=0.55//Overall efficiency\n", +"d=1000//Density of water in kg/m^3\n", +"g=9.81//Acceleration due to gravity in m/s^2\n", +"\n", +"//calculations\n", +"U1=(3.1415*D1*N)/60//Blade inlet speed in m/s\n", +"A1=3.1415*D1*b1*cf*10^3//Area of flow at inlet in m^2\n", +"Qt=Q+Qloss//Total quantity of water handled by pump in l/s\n", +"Qts=Qt/2//Total quantity of water handled by pump per side in l/s\n", +"Cr1=(Qts*10^-3)/(A1*10^-3)//Flow velocity through impeller at inlet in m/s\n", +"b11=atand(Cr1/U1)//Inlet vane angle in degree\n", +"A2=3.1415*D2*(b2/2)*cf*10^3//Area of flow at outlet in m^2 here b2 is calculated per side\n", +"Cr2=Qts/A2//Velocity of flow at outlet in m/s\n", +"U2=(3.1415*D2*N)/60//Peripheral speed at outlet in m/s\n", +"Wx2=Cr2/tand(b22)//Exit relative velocity in m/s\n", +"Cx2=U2-Wx2//Absolute whirl component at exit in m/s\n", +"a22=atand(Cr2/Cx2)//The absolute water angle at outlet in degree\n", +"C2=Cr2/sind(a22)//Absolute velocity of water at exit in m/s\n", +"nh=Hm/((U2*Cx2)/g)//Manometric efficiency \n", +"nv=Q/Qt//Volumetric efficiency \n", +"SP=(d*g*(Q*10^-3/2)*Hm)/n0*10^-3//Shaft power in kW\n", +"nm=(SP-ml)/SP//Mechanical efficiency \n", +"\n", +"//output\n", +"printf('(a)Inlet vane angle is %3.2f degree\n(b)The absolute water angle is %3.2f degree\n(c)Absolute velocity of water at exit is %3.2f m/s\n(d)Manometric efficiency is %3.3f\n(e)Volumetric efficiency is %3.4f\n(f)Mechanical efficiency is %3.3f',b11,a22,C2,nh,nv,nm)" + ] + } +, +{ + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 8.6: MANOMETRIC_HEAD_AND_OVERALL_EFFICIENCY.sce" + ] + }, + { +"cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], +"source": [ +"clc\n", +"clear\n", +"//input data\n", +"Hi=0.25//Vaccum gauge reading in m of Hg vaccum\n", +"P0=1.5//Pressure gauge reading in bar\n", +"Z01=0.5//Effective height between gauges in m\n", +"P=22//Power of electric motor in kW\n", +"Di=0.15//Inlet diameter in m\n", +"Do=0.15//Outlet diameter in m\n", +"Q=0.1//Discharge of pump in m^3/s\n", +"dHg=13600//Density of mercury in kg/m^3\n", +"dw=1000//Density of water in kg/m^3\n", +"g=9.81//Acceleration due to gravity in m/s^2\n", +"\n", +"//calculations\n", +"Pi=dHg*g*Hi//Inlet pressure in N/m^2 vaccum\n", +"Po=P0*10^5//Outlet pressure in N/m^2\n", +"V0=Q/((3.1415*Do^2)/4)//Velocity of water in delivery pipe in m/s\n", +"Vi=V0//vleocity of water in suction pipe in m/s\n", +"Hm=((Po+Pi)/(dw*g))+((V0^2-Vi^2)/(2*g))+(Z01)//Manometric head in m\n", +"n0=(dw*g*Q*Hm)/(P*10^3)//Overall efficiency \n", +"\n", +"//output\n", +"printf('(a)Manometric head is %3.2f m\n(b)Overall efficiency is %3.3f',Hm,n0)" + ] + } +, +{ + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 8.7: IMPELLER_DIAMETER.sce" + ] + }, + { +"cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], +"source": [ +"clc\n", +"clear\n", +"//input data\n", +"Hm=20//Head against which work is produced in pump in m\n", +"b22=45//Vanes set back angle at outlet in degree\n", +"N=600//Rotating speed of pump in rpm\n", +"Cr1=2//Flow velocity through impeller at inlet in m/s\n", +"Cr2=Cr1//Flow velocity through impeller at outlet in m/s\n", +"g=9.81//acceleration due to gravity in m/s^2\n", +"\n", +"//calculations\n", +"Wx2=Cr2/tand(b22)//Exit relative velocity in m/s\n", +"U2=(4+(16+(4*3*792.8))^(1/2))/(2*3)// Blade outlet speed in m/s\n", +" //The above equation is obtained by solving \n", +" //Cx2=U2-Wx2 //Absolute whirl component at exit in m/s\n", +" //C2=(Cx2^2+Cr2^2)^(1/2) //Absolute velocity of water at exit in m/s\n", +" //Hm=(U2*Cx2/g)-((C2^2)/(4*g)) //Total head producing work in m\n", +" //3*(U2^2)-(4*U2)-792.8=0 \n", +"D2=(60*U2)/(3.1415*N)//Impeller diameter in m\n", +"\n", +"//output\n", +"printf('The impeller diameter is %3.4f m',D2)" + ] + } +, +{ + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 8.8: POWER_REQUIRED.sce" + ] + }, + { +"cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], +"source": [ +"clc\n", +"clear\n", +"//input data\n", +"n0=0.7//Overall efficiency\n", +"Q=0.025//Discharge of water by the pump in m^3/s\n", +"H=20//Height of supplied by the pump in m\n", +"D=0.1//Diameter of the pump in m\n", +"L=100//Length of the pipe in m\n", +"f=0.012//Friction coefficient \n", +"g=9.81//Acceleration due to gravity in m/s^2\n", +"d=1000//Density of water in kg/m^3\n", +"\n", +"//calculations\n", +"V0=Q/((3.1415/4)*D^2)//Velocity of water in the pipe in m/s\n", +"hf0=(4*f*L*V0^2)/(2*g*D)//Loss of head due to friction in pipe in m\n", +"Hm=H+hf0+(V0^2/(2*g))//Manometric head in m\n", +"P=(d*g*Q*Hm)/(n0)*10^-3//Power required to drive the pump in kW\n", +"\n", +"//output\n", +"printf('Power required to drive the pump is %3.2f kW',P)" + ] + } +, +{ + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 8.9: RISE_IN_PRESSURE_IN_THE_IMPELLER.sce" + ] + }, + { +"cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], +"source": [ +"clc\n", +"clear\n", +"//input data\n", +"Q=0.015//Discharge of water in pump in m^3/s\n", +"D1=0.2//Internal diameter of the impeller in m\n", +"D2=0.4//External diameter of the impeller in m\n", +"b1=0.016//Width of impeller at inlet in m\n", +"b2=0.008//Width of impeller at outlet in m\n", +"N=1200//Running speed of the pump in rpm\n", +"b22=30//Impeller vane angle at outlet in degree\n", +"g=9.81//Acceleration due to gravity in m/s^2\n", +"d=1000//Density of water in kg/m^3\n", +"\n", +"//calculations\n", +"printf('From velocity triangles the following values have been deduced')\n", +"a11=90//The absolute water angle at inlet in degree\n", +"Cx1=0//Absolute whirl component at inlet in m/s\n", +"A1=3.1415*D1*b1//Area of flow at inlet in m^2\n", +"Cr1=Q/A1//Flow velocity through impeller at inlet in m/s\n", +"C1=Cr1//Absolute velocity at inlet in m/s\n", +"A2=3.1415*D2*b2//Area of flow at outlet in m^2\n", +"Cr2=Q/A2//Flow velocity through impeller at outlet in m/s\n", +"U2=(3.1415*D2*N)/60//Blade outlet speed in m/s\n", +"Cx2=U2-(Cr2/tand(b22))//Absolute whirl component at outlet in m/s\n", +"C2=(Cx2^2+Cr2^2)^(1/2)//Velocity at impeller exit in m/s\n", +"Ihl=((Cx2*U2)/g)-((C2^2)/(2*g))+((C1^2)/(2*g))//Pressure rise in impeller in m\n", +"\n", +"//output\n", +"printf('\n\nThe rise in pressure in the impeller is %3.3f m',Ihl)" + ] + } +], +"metadata": { + "kernelspec": { + "display_name": "Scilab", + "language": "scilab", + "name": "scilab" + }, + "language_info": { + "file_extension": ".sce", + "help_links": [ + { + "text": "MetaKernel Magics", + "url": "https://github.com/calysto/metakernel/blob/master/metakernel/magics/README.md" + } + ], + "mimetype": "text/x-octave", + "name": "scilab", + "version": "0.7.1" + } + }, + "nbformat": 4, + "nbformat_minor": 0 +} diff --git a/Turbomachines_by_A_V_Arasu/9-HYDRAULIC_TURBINES.ipynb b/Turbomachines_by_A_V_Arasu/9-HYDRAULIC_TURBINES.ipynb new file mode 100644 index 0000000..0993022 --- /dev/null +++ b/Turbomachines_by_A_V_Arasu/9-HYDRAULIC_TURBINES.ipynb @@ -0,0 +1,896 @@ +{ +"cells": [ + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "# Chapter 9: HYDRAULIC TURBINES" + ] + }, +{ + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 9.10: ABSOLUTE_VELOCITY_OF_WATER_AT_ENTRY.sce" + ] + }, + { +"cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], +"source": [ +"clc\n", +"clear\n", +"//input data\n", +"D=1.4//Diameter of the turbine in m\n", +"N=430//Speed of the turbine in rpm\n", +"Cr1=9.5//Flow velocity without shock at runner in m/s\n", +"C2=7//Absolute velocity at the exit without whirl in /s\n", +"dSPH=62//Difference between the sum of static and potential heads at entrance to runner and at exit from runner in m\n", +"W=12250//Power given to runner in kW\n", +"Q=12//Flow rate of water from the turbine in m^3/s\n", +"H=115//Net head from the turbine in m\n", +"g=9.81//Acceleration due to gravity in m/s^2\n", +"dw=1000//Density of water in kg/m^3\n", +"\n", +"//calculations\n", +"U1=(3.1415*D*N)/60//Runner tip speed in m/s\n", +"Cx1=(W*10^3)/(dw*Q*U1)//Absolute inlet velocity in m/s as flow is radial at outlet Cx2=0 in m/s as Cx2=0 as zero whirl at outlet\n", +"a1=atand(Cr1/Cx1)//Guide vane angle in degree\n", +"C1=(Cr1^2+Cx1^2)^(1/2)//Inlet velocity in m/s\n", +"b1=atand(Cr1/(Cx1-U1))//Runner blade entry angle in degree\n", +"dHr=dSPH+(((C1^2)-(C2^2))/(2*g))-(U1*Cx1/g)//Loss of head in the runner in m\n", +"\n", +"//output\n", +"printf('(a)\n (1)Guide vane angle at inlet is %3.1f degree\n (2)Inlet absolute velocity of water at entry to runner is %3.1f m/s\n(b)Runner blade entry angle is %3.1f degree\n(c)Total Loss of head in the runner is %3.2f m',a1,C1,b1,dHr)" + ] + } +, +{ + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 9.11: RUNNER_BLADE_ANGLES.sce" + ] + }, + { +"cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], +"source": [ +"clc\n", +"clear\n", +"//input data\n", +"D1=0.9//External diameter of the turbine in m\n", +"D2=0.45//Internal diameter of the turbine in m\n", +"N=200//Speed of turbine running in rpm\n", +"b1=0.2//Width of turbine at inlet in m\n", +"Cr1=1.8//Velocity of flow through runner at inlet in m/s\n", +"Cr2=Cr1//Velocity of flow through runner at outlet in m/s\n", +"a11=10//Guide blade angle to the tangent of the wheel in degree\n", +"a22=90//Discharge angle at outlet of turbine in degree\n", +"g=9.81//Acceleration due to gravity in m/s^2\n", +"dw=1000//Density of water in kg/m^3\n", +"\n", +"//calculations\n", +"C1=Cr1/sind(a11)//Absolute velocity of water at inlet of runner in m/s\n", +"Cx1=Cr1/tand(a11)//Velocity of whirl at inlet in m/s\n", +"U1=(3.1415*D1*N)/60//Runner tip speed at inlet in m/s\n", +"Wx1=Cx1-U1//Inlet whirl velocity component in m/s\n", +"W1=(Wx1^2+Cr1^2)^(1/2)//Relative velocity at inlet in m/s\n", +"b11=atand(Cr1/Wx1)//Runner blade entry angle in degree\n", +"U2=(3.1415*D2*N)/60//Runner tip speed at exit in m/s\n", +"b22=atand(Cr2/U2)//Runner blade exit angle in degree\n", +"b2=D1*b1/D2//Width of runner at outlet in m\n", +"Q=3.1415*D1*b1*Cr1//Discharge of water in turbine in m^3/s\n", +"m=dw*Q//Mass of water flowing through runner per second in kg/s\n", +"V2=Cr2//Velocity of water at exit in m/s \n", +"H=(U1*Cx1/g)+(V2^2/(2*g))//Head at the turbine inlet in m\n", +"W=m*U1*Cx1*10^-3//Power developed in kW\n", +"nH=(U1*Cx1/(g*H))//Hydraulic efficiency\n", +"\n", +"//output\n", +"printf('(a)Absolute velocity of water at inlet of runner is %3.3f m/s\n(b)Velocity of whirl at inlet is %3.3f m/s\n(c)Relative velocity at inlet is %3.3f m/s\n(d)\n Runner blade entry angle is %3.2f degree\n Runner blade exit angle is %3.2f degree\n(e)Width of runner at outlet is %3.1f m\n(f)Mass of water flowing through runner per second is %3.f kg/s\n(g)Head at the turbine inlet is %3.3f m\n(h)Power developed is %3.3f kW\n(i)Hydraulic efficiency is %3.4f',C1,Cx1,W1,b11,b22,b2,m,H,W,nH)" + ] + } +, +{ + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 9.12: DESIGN_OF_INWARD_FLOW_FRANCIS_TURBINE.sce" + ] + }, + { +"cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], +"source": [ +"clc\n", +"clear\n", +"//input data\n", +"P=330//Power output from the turbine is kW\n", +"H=70//Head of operating turbine in m\n", +"N=750//Speed of the turbine in rpm\n", +"nH=0.94//Hydraulic efficiency\n", +"n0=0.85//Overall efficiency\n", +"FR=0.15//Flow ratio \n", +"BR=0.1//Breadth ratio\n", +"D1D2=2//Ratio inner and outer diameter of runner\n", +"g=9.81//Acceleration due to gravity in m/s^2\n", +"dw=1000//Density of water in kg/m^3\n", +"\n", +"//calculations\n", +"Cr1=FR*(2*g*H)^(1/2)//Flow velocity at inlet in m/s\n", +"Q=(P*10^3)/(dw*g*H*n0)//Discharge at outlet in m^3/s\n", +"D1=(Q/(nH*3.1415*BR*Cr1))^(1/2)//Runner inlet diameter in m\n", +"b1=BR*D1//Height of the runner vanes at inlet in m\n", +"U1=(3.1415*D1*N)/60//Runner tip speed at inlet in m/s\n", +"Cx1=(nH*g*H)/(U1)//Velocity of whirl at inlet in m/s\n", +"a11=atand(Cr1/Cx1)//Guide blade angle in degree\n", +"b11=atand(Cr1/(Cx1-U1))//Runner vane angle at inlet in degree\n", +"D2=D1/D1D2//Runner outlet diameter in m\n", +"U2=(3.1415*D2*N)/60//Runner tip speed at outlet in m/s\n", +"Cr2=Cr1//Flow velocity at outlet in m/s\n", +"b22=atand(Cr2/U2)//Runner vane angle at outlet in degree\n", +"b2=D1*b1/D2//Width at outlet in m\n", +"\n", +"//output\n", +"printf('(a)Flow velocity at inlet is %3.2f m/s\n(b)Discharge at outlet is %3.3f m^3/s\n(c)Runner inlet diameter is %3.3f m\n(d)Height of the runner vanes at inlet is %3.4f m\n(e)Guide blade angle is %3.2f degree\n(f) Runner vane angle at inlet is %3.2f degree\n Runner vane angle at outlet is %3.2f degree\n(g)Runner outlet diameter is %3.4f m\n(h)Width at outlet is %3.4f m\n(i)Runner tip speed at inlet is %3.2f m/s\n(j)Velocity of whirl at inlet is %3.f m/s',Cr1,Q,D1,b1,a11,b11,b22,D2,b2,U1,Cx1)" + ] + } +, +{ + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 9.13: SPEED_OF_THE_WHEEL.sce" + ] + }, + { +"cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], +"source": [ +"clc\n", +"clear\n", +"//input data\n", +"H=30//Working head of the turbine in m\n", +"D1=1.2//Inlet wheel diameter in m\n", +"D2=0.6//Outlet wheel diameter in m\n", +"b11=90//Vane angle at entrance in degree\n", +"a11=15//Guide blade angle in degree\n", +"Cx2=0//Velocity of whirl at inlet in m/s\n", +"g=9.81//Acceleration due to gravity in m/s^2\n", +"dw=1000//Density of water in kg/m^3\n", +"\n", +"//calculations\n", +"U11=1/tand(a11)//Runner tip speed at inlet in m/s in terms of Cr1\n", +"Cr1=(H/((U11^2/g)+(1/(2*g))))^(1/2)//Flow velocity at inlet in m/s\n", +"Cr2=Cr1//Flow velocity at outlet in m/s\n", +"U1=Cr1*U11//Runner tip speed at inlet in m/s \n", +"N=(60*U1)/(3.1415*D1)//Speed of the wheel in rpm\n", +"U2=(3.1415*D2*N)/60//Runner tip speed at inlet in m/s \n", +"b22=atand(Cr2/U2)//Vane angle at exit in degree\n", +"\n", +"//output\n", +"printf('(a)Speed of the wheel is %3.2f rpm\n(b)Vane angle at exit is %3.2f degree',N,b22)" + ] + } +, +{ + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 9.14: HYDRAULIC_EFFICIENCY.sce" + ] + }, + { +"cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], +"source": [ +"clc\n", +"clear\n", +"//input data\n", +"D1=0.6//Internal runner diameter in m\n", +"D2=1.2//External runner diameter in m\n", +"a11=15//Guide blade angle in degree\n", +"Cr1=4//Flow velocity at inlet in m/s\n", +"Cr2=Cr1//Flow velocity at outlet in m/s\n", +"N=200//Speed of the turbine in rpm\n", +"H=10//Head of the turbine in m\n", +"a22=90//Discharge angle at outlet in degree\n", +"g=9.81//Acceleration due to gravity in m/s^2\n", +"dw=1000//Density of water in kg/m^3\n", +"\n", +"//calculations\n", +"U1=(3.1415*D1*N)/60//Runner tip speed at inlet in m/s \n", +"U2=(3.1415*D2*N)/60//Runner tip speed at outlet in m/s \n", +"Cx1=Cr1/tand(a11)//Velocity of whirl at inlet in m/s\n", +"Wx1=Cx1-U1//Inlet whirl velocity component in m/s\n", +"b11=atand(Cr1/Wx1)//Vane angle at entrance in degree\n", +"b22=atand(Cr2/U2)//Vane angle at exit in degree\n", +"Wm=U1*Cx1//Work one per unit mass flow rate in W/(kg/s) as Cx2=0 in m/s\n", +"nH=(U1*Cx1/(g*H))//Hydraulic efficiency \n", +"\n", +"//output\n", +"printf('(a)\n Inlet vane angle is %3.2f degree\n Outlet vane angle is %3.2f degree\n(b)Work done by the water on the runner per kg of water is %3.2f W/(kg/s)\n(c)Hydraulic efficiency is %3.4f',b11,b22,Wm,nH)" + ] + } +, +{ + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 9.15: INLET_AND_OUTLET_BLADE_ANGLES.sce" + ] + }, + { +"cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], +"source": [ +"clc\n", +"clear\n", +"//input data\n", +"H=23//Net head across the turbine in m\n", +"N=150//Speed of the turbine in rpm\n", +"P=23//Power developed by the turbine in MW\n", +"D=4.75//Blade tip diameter in m\n", +"d=2//Blade hub diameter in m\n", +"nH=0.93//Hydraulic efficiency\n", +"n0=0.85//Overall efficiency\n", +"g=9.81//Acceleration due to gravity in m/s^2\n", +"dw=1000//Density of water in kg/m^3\n", +"\n", +"//calculations\n", +"dm=(D+d)/2//Mean diameter of the turbine in m\n", +"Pa=(P*10^6)/n0//Power available in MW\n", +"Q=(Pa/(dw*g*H))//Flow rate in the turbine in m^3/s\n", +"Um=(3.1415*dm*N)/60//Rotor speed at mean diameter in m/s\n", +"Pr=Pa*nH*10^-6//Power given to runner in MW\n", +"Cx1=Pr*10^6/(dw*Q*Um)//Velocity of whirl at inlet in m/s as Cx2=0 in m/s\n", +"Ca=Q/((3.1415/4)*(D^2-d^2))//Axial velocity in m/s\n", +"b11=180-(atand(Ca/(Um-Cx1)))//Inlet blade angle in degree\n", +"Wx2=Um//Outlet whirl velocity component in m/s\n", +"b22=atand(Ca/Wx2)//Outlet blade angle in degree\n", +"\n", +"//output\n", +"printf('(a)The inlet blade angle at mean radius is %3.1f degree\n(b)The outlet blade angle at mean radius is %3.1f degree',b11,b22)" + ] + } +, +{ + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 9.16: DIAMETER_OF_RUNNER_AND_SPECIFIC_SPEED_OF_TURBINE.sce" + ] + }, + { +"cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], +"source": [ +"clc\n", +"clear\n", +"//input data\n", +"P=9100//Power developed by the turbine in kW\n", +"H=5.6//Net head available at the turbine in m\n", +"SR=2.09//Speed ratio\n", +"FR=0.68//Flow ratio\n", +"n0=0.86//Overall effiiciency of the turbine\n", +"g=9.81//Acceleration due to gravity in m/s^2\n", +"dw=1000//Density of water in kg/m^3\n", +"DbD=1/3//Ratio of diameter of the boss to diameter of the runner\n", +"\n", +"//calculations\n", +"U1=SR*(2*g*H)^(1/2)//Runner tip speed at inlet in m/s\n", +"Cr1=FR*(2*g*H)^(1/2)//Flow velocity at inlet in m/s\n", +"Q=(P*10^3)/(n0*dw*g*H)//Discharge through the turbine in m^3/s\n", +"D=(Q*4/(3.1415*Cr1*((1^2)-(DbD^2))))^(1/2)//Diameter of the runner in m\n", +"N=(U1*60)/(3.1415*D)//Speed of the the turbine in rpm\n", +"Ns=(N*(P)^(1/2))/(H)^(5/4)//Specific speed \n", +"disp(Q)\n", +"//output\n", +"printf('(a)Diameter of the runner of the turbine is %3.2f m\n(b)Speed of the turbine is %3.1f rpm\n(c)The specific speed is %3.2f',D,N,Ns)" + ] + } +, +{ + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 9.17: RUNNER_INLET_AND_OUTLET_VANE_ANGLES.sce" + ] + }, + { +"cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], +"source": [ +"clc\n", +"clear\n", +"//input data\n", +"H=20//Head developed over the turbine in m\n", +"P=11800//Power developed by turbine in kW\n", +"D=3.5//Outer diameter of the runner in m\n", +"Db=1.75//Hub diameter in m\n", +"a11=35//Guide blade angle in degree \n", +"nH=0.88//Hydraulic efficiency \n", +"n0=0.84//Overall efficiency\n", +"Cx2=0//Velocity of whirl at outlet in m/s\n", +"g=9.81//Acceleration due to gravity in m/s^2\n", +"dw=1000//Density of water in kg/m^3\n", +"\n", +"//calculations\n", +"Q=(P*10^3)/(n0*g*H*dw)//Discharge of turbine in m^3/s\n", +"Cr1=Q/((3.1415/4)*(D^2-Db^2))//Flow velocity at inlet in m/s\n", +"Cx1=Cr1/tand(a11)//Velocity of whirl at inlet in m/s\n", +"U1=(nH*H*g)/(Cx1)//Runner tip speed at inlet in m/s\n", +"Wx1=U1-Cx1//Inlet whirl velocity component in m/s\n", +"b11=180-(atand(Cr1/-Wx1))//Runner inlet angle in degree\n", +"Cr2=Cr1//Flow velocity at outlet in m/s for a kaplan turbine\n", +"U2=U1//Runner tip speed at outlet in m/s for a kaplan turbine\n", +"b22=atand(Cr2/U2)//Runner outlet angle in degree \n", +"N=(U1*60)/(3.1415*D)//The speed of the turbine in rpm\n", +"\n", +"//output\n", +"printf('(1)\n (a)The runner inlet angle is %3.2f degree\n (b)The runner outlet angle is %3.1f degree\n(2)The speed of the turbine is %3.2f rpm',b11,b22,N)" + ] + } +, +{ + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 9.18: DISCHARGE_POWER_AND_HYDRAULIC_EFFICIENCY.sce" + ] + }, + { +"cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], +"source": [ +"clc\n", +"clear\n", +"//input data\n", +"N=50//Speed of the turbine in rpm\n", +"d=6//Runner diameter of the turbine in m\n", +"Ae=20//Effective area of flow in m^2\n", +"b11=150//The angle of the runner blades at inlet in degree\n", +"b22=20//The angle of the runner blade at outlet in degree\n", +"g=9.81//Acceleration due to gravity in m/s^2\n", +"dw=1000//Density of water in kg/m^3\n", +"\n", +"//calculations\n", +"U1=(3.141*d*N)/60//Runner tip speed at inlet in m/s\n", +"U2=U1//Runner tip speed at outlet in m/s\n", +"Cr2=U2*tand(b22)//Flow velocity at outlet in m/s\n", +"Cr1=Cr2//Flow velocity at inlet in m/s\n", +"Q=Ae*Cr1//Discharge by the turbine in m^3/s\n", +"Cx1=U1-(Cr1/(tand(180-b11)))//Velocity of whirl at inlet in m/s\n", +"P=dw*g*Q*(U1*Cx1/g)*10^-3//Theoretical Power developed in kW\n", +"C2=Cr2//Absolute outlet velocity in m/s\n", +"H=(U1*Cx1/g)+(C2^2/(2*g))//Net head across the turbine in m\n", +"nH=(U1*Cx1/g)/(H)//Hydraulic efficiency\n", +"\n", +"//output\n", +"printf('(a)Discharge of the turbine is %3.1f m^3/s\n(b)Theoretical Power developed is %3.2f kW\n(c)Hydraulic efficiency is %3.4f',Q,P,nH)" + ] + } +, +{ + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 9.19: BLADE_ANGLES_AND_EFFICIENCIES.sce" + ] + }, + { +"cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], +"source": [ +"clc\n", +"clear\n", +"//input data\n", +"D=8//Outer diameter of the turbine in m\n", +"Db=3//Inner diameter of the turbine in m\n", +"P=30000//Power developed by the turbine in kW\n", +"nH=0.95//Hydraulic efficiency\n", +"N=80//Speed of the turbine in rpm\n", +"H=12//Head operated by the turbine in m\n", +"Q=300//Discharge through the runner in m^3/s\n", +"g=9.81//Acceleration due to gravity in m/s^2\n", +"dw=1000//Density of water in kg/m^3\n", +"\n", +"//calculations\n", +"U1=(3.1415*D*N)/60//Runner tip speed at inlet in m/s\n", +"U2=U1//Runner tip speed at outlet in m/s as flow is axial\n", +"Cr1=Q/((3.1415/4)*(D^2-Db^2))//Flow velocity at inlet in m/s\n", +"Cr2=Cr1//Flow velocity at outlet in m/s as flow is axial\n", +"b22=atand(Cr2/U2)//The angle of the runner blade at outlet in degree\n", +"Cx1=(nH*g*H)/U1//Velocity of whirl at inlet in m/s\n", +"b11=180-(atand(Cr1/(U1-Cx1)))//The angle of the runner blade at inlet in degree\n", +"nM=(P*10^3)/(dw*g*Q*(Cx1*U1/g))//Mechanical efficiency\n", +"n0=nM*nH//Overall efficiency\n", +"\n", +"//output\n", +"printf('(a)Blade angle at\n inlet is %3.2f degree\n outlet is %3.2f degree\n(b)Mechanical efficiency is %3.3f\n(c)Overall efficiency is %3.3f',b11,b22,nM,n0)" + ] + } +, +{ + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 9.1: DIMENSIONLESS_POWER_SPECIFIC_SPEED.sce" + ] + }, + { +"cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], +"source": [ +"clc\n", +"clear\n", +"//input data\n", +"H=91.5//Head of the pelton wheel at inlet in m\n", +"Q=0.04//Discharge of the pelton wheel in m^3/s\n", +"N=720//Rotating speed of the wheel in rpm\n", +"Cv=0.98//Velocity coefficient of the nozzle \n", +"n0=0.8//Efficiency of the wheel\n", +"UC1=0.46//Ratio of bucket speed to jet speed\n", +"g=9.81//Acceleration due to gravity in m/s^2\n", +"dw=1000//Density of water in kg/m^3\n", +"\n", +"//calculations\n", +"P=dw*g*H*Q*n0*10^-3//Power developed in kw\n", +"C1=Cv*(2*g*H)^(1/2)//Jet speed in m/s\n", +"U=UC1*C1//Wheel speed in m/s\n", +"w=(2*3.1415*N)/60//Angular velocity of the wheel in rad/s\n", +"D=(2*U)/w//Diameter of the wheel in m\n", +"A=Q/C1//Jet area in m^2\n", +"d=((4*A)/3.1415)^(1/2)//Jet diameter in m\n", +"Dd=D/d//Wheel to jet diameter ratio at centre line of the buckets\n", +"Nsp=((1/(g*H))^(5/4))*(((P*10^3)/dw)^(1/2))*(N/60)*2*3.1415//Dimensionless power specific speed in rad\n", +"\n", +"//output\n", +"printf('(a)Wheel-to-jet diameter ratio at the centre line of the buckets is %3.1f \n(b)\n The jet speed of the wheel is %3.2f m/s\n Wheel speed is %3.1f m/s\n(c)Dimensionless power specific speed is %3.3f rad',Dd,C1,U,Nsp)" + ] + } +, +{ + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 9.20: RUNNER_DIAMETER_AND_SPEED.sce" + ] + }, + { +"cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], +"source": [ +"clc\n", +"clear\n", +"//input data\n", +"P=11500//Rated power of the turbine in kW\n", +"H=4.3//Average head of the turbine in m\n", +"n0=0.91//Overall efficiency of the turbine \n", +"DbD=0.3//Ratio of Diameters of runner boss and runner\n", +"SR=2//Speed ratio\n", +"FR=0.65//Flow ratio\n", +"g=9.81//Acceleration due to gravity in m/s^2\n", +"dw=1000//Density of water in kg/m^3\n", +"\n", +"//calculations\n", +"U=SR*(2*g*H)^(1/2)//Runner tip speed in m/s\n", +"Cr=FR*(2*g*H)^(1/2)//Flow velocity in m/s\n", +"Q=(P*10^3)/(n0*dw*g*H)//Discharge of the turbine in m^3/s\n", +"D=((4*Q)/(Cr*3.1415*(1^2-DbD^2)))^(1/2)//Runner diameter in \n", +"N=(60*U)/(3.1415*D)//Speed of the turbine in rpm \n", +"\n", +"//output\n", +"printf('(a)Runner diameter of the turbine is %3.2f m\n(b)Operating speed of the turbine is %3.1f rpm',D,N)" + ] + } +, +{ + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 9.2: DISCHARGE_OF_TURBINE.sce" + ] + }, + { +"cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], +"source": [ +"clc\n", +"clear\n", +"//input data\n", +"H=500//Head over which pelton wheel works in m\n", +"P=13000//Power which pelton wheel produces in kW\n", +"N=430//Speed of operation of pelton wheel in rpm\n", +"n0=0.85//Efficiency of the wheel \n", +"g=9.81//Acceleration due to gravity in m/s^2\n", +"dw=1000//Density of water in kg/m^3\n", +"Cv=0.98//Veloity coefficient\n", +"UC=0.46//Speed ratio\n", +"\n", +"//calculations\n", +"Q=(P*10^3)/(dw*g*H*n0)//Discharge of the turbine in m^3/s\n", +"C=Cv*(2*g*H)^(1/2)//Jet speed in m/s\n", +"U=UC*C//Wheel speed in m/s\n", +"D=(U*60)/(3.1415*N)//Wheel diameter in m\n", +"d=((Q/C)*(4/3.1415))^(1/2)//Diameter of the nozzle in m\n", +"\n", +"//output\n", +"printf('(a)Discharge of the turbine is %3.2f m^3/s\n(b)Diameter of the wheel is %3.2f m\n(c)Diameter of the nozzle is %3.3f m',Q,D,d)" + ] + } +, +{ + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 9.3: POWER_AVAILABLE_AT_THE_NOZZLE.sce" + ] + }, + { +"cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], +"source": [ +"clc\n", +"clear\n", +"//input data\n", +"D=0.8//Mean diameter of the bucket in m\n", +"N=1000//Running speed of the wheel in rpm\n", +"H=400//Net head on the pelton wheel in m\n", +"Q=0.150//Discharge through the nozzle in m^3/s\n", +"g=9.81//Acceleration due to gravity in m/s^2\n", +"UC1=0.46//Ratio of bucket speed to jet speed\n", +"dw=1000//Density of water in kg/m^3\n", +"a=15//Side clearance angle in degree\n", +"\n", +"//calculations\n", +"m=dw*Q//Mass flow rate through the nozzle in kg/s\n", +"U=(3.1415*D*N)/60//Wheel speed in m/s\n", +"C1=U/UC1//Jet speed in m/s\n", +"P=(1/2)*m*C1^2*(10^-3)//Power available at the nozzle in kW\n", +"W1=C1-U//Relative inlet fluid velocity in m/s\n", +"W2=W1//Relative exit fluid velocity in m/s assuming no loss of relative velocity\n", +"Wx2=W2*cosd(a)//Exit whirl velocity component in m/s\n", +"Cx2=Wx2-U//Absolute exit whirl velocity in m/s\n", +"Cx1=C1//Absolute inlet whirl velocity in m/s\n", +"Wm=U*(Cx1+Cx2)//Work done per unit mass flow rate in W/(kg/s)\n", +"nH=(Wm/g)/((C1^2/2)/g)//Hydrualic effciency \n", +"\n", +"//output\n", +"printf('(a)Power available at the nozzle is %3.3f kW\n(b)Hydraulic efficiency is %3.3f',P,nH)" + ] + } +, +{ + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 9.4: OVERALL_EFFICIENCY.sce" + ] + }, + { +"cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], +"source": [ +"clc\n", +"clear\n", +"//input data\n", +"n=2//Number of jets \n", +"SP=20000*0.736//Shaft power of the wheel in kW\n", +"D=0.15//Diameter of each jet in m\n", +"H=500//Net head on the turbine in m\n", +"Cv=1.0//Velocity coefficient\n", +"g=9.81//Acceleration due to gravity in m/s^2\n", +"d=1000//Density of water in kg/m^3\n", +"\n", +"//calculations\n", +"C1=Cv*(2*g*H)^(1/2)//Velocity of each jet in m/s\n", +"A=(3.1415/4)*D^2//Area of each jet in m^2\n", +"Qj=A*C1//Discharge of each jet in m^3/s\n", +"Q=2*Qj//Total discharge in m^3/s\n", +"P=d*g*Q*H*10^-3//Power at turbine inlet in kW\n", +"no=SP/P//Overall efficiency\n", +"\n", +"//output\n", +"printf('The overall efficiency of the turbine is %3.3f',no)" + ] + } +, +{ + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 9.5: THEORETICAL_HYDRAULIC_EFFICIENCY.sce" + ] + }, + { +"cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], +"source": [ +"clc\n", +"clear\n", +"//input data\n", +"a=170//Jet deflection angle in degree\n", +"K=1-0.12//Percentage of effective relative velocity after considering friction\n", +"UC1=0.47//Ratio of bucket speed to jet speed\n", +"GH=600//Gross head on the wheel in m\n", +"P=1250//Actual power developed by the wheel in kW\n", +"Hl=48//Head loss in nozzle due to pipe friction in m\n", +"D=0.9//Bucket circle diameter of the wheel in m\n", +"ATnH=0.9//The ratio between actual and calculated hydraulic efficiency\n", +"g=9.81//Acceleration due to gravity in m/s^2\n", +"dw=1000//Density of water in kg/m^3\n", +"Cv=0.98//Velocity coefficient\n", +"\n", +"//calculations\n", +"H=GH-Hl//Net head after loses at entry to nozzle in m\n", +"C1=Cv*(2*g*H)^(1/2)//Jet speed in m/s\n", +"U=UC1*C1//Wheel bucket speed in m/s\n", +"N=(U*60)/(3.1415*D)//Wheel rotational speed in rpm\n", +"Wm=U*((C1-U)*(1-(K*cosd(a))))//Work done per unit mass flow rate in W/(kg/s)\n", +"Tnh=Wm/(C1^2/2)//Theoretical hydraulic efficiency \n", +"Anh=ATnH*Tnh//Actual hydrualic effficiency\n", +"m2=(P*10^3)/(Anh*(1/2)*C1^2)//Mass flow rate for both the nozzles in kg/s\n", +"m=m2/2//Mass flow rate of each nozzle in kg/s\n", +"d=((4*m)/(dw*C1*3.1415))^(1/2)//Nozzle diameter in m\n", +"\n", +"//output\n", +"printf('(a)theoretical hydraulic efficiency is %3.2f \n(b)Wheel rotational speed is %3.f rpm\n(c)diameter of the nozzle is %3.4f m',Tnh,N,d)" + ] + } +, +{ + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 9.6: DIAMETER_OF_THE_WHEEL.sce" + ] + }, + { +"cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], +"source": [ +"clc\n", +"clear\n", +"//input data\n", +"H=60//Head on the pelton wheel in m\n", +"N=200//Speed of the pelton wheel in rpm\n", +"P=100//Power developed by the pelton wheel in kW\n", +"Cv=0.98//Velocity coefficient\n", +"UC1=0.45//Speed ratio \n", +"n0=0.85//Overall efficiency of the wheel\n", +"g=9.81//Acceleration due to gravity in m/s^2\n", +"dw=1000//Density of water in kg/m^3\n", +"\n", +"//calculations\n", +"C1=Cv*(2*g*H)^(1/2)//Velocity of the jet in m/s\n", +"U=UC1*(2*g*H)^(1/2)//Velocity of the buckets in m/s\n", +"D=(60*U)/(3.1415*N)//Diameter of the wheel in m\n", +"Q=(P*10^3)/(dw*g*H*n0)//Discharge of the wheel in m^3/s\n", +"d=((4*Q)/(3.1415*C1))^(1/2)//Diameter of the jet in m\n", +"Z=15+(D/(2*d))+1//Number of buckets rounding off to nearest decimal as the final answer has a decimal value less than 0.5\n", +"w=5*d//Width of the buckets in m\n", +"de=1.2*d//Depth of the buckets in m\n", +"\n", +"//output\n", +"printf('(a)Diameter of the wheel is %3.2f m\n(b)Diameter of the jet is %3.3f m\n(c)Number of buckets is %3.f\n(d)Size of the buckets is \n width of the bucket is %3.3f m\n Depth of the bucket is %3.3f m',D,d,Z,w,de)" + ] + } +, +{ + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 9.7: DIAMETER_OF_WHEEL_AND_POWER_DEVELOPED.sce" + ] + }, + { +"cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], +"source": [ +"clc\n", +"clear\n", +"//input data\n", +"N=300//Running speed of the wheel in rpm\n", +"H=150//OPerating head of the wheel in m\n", +"dD=1/12//Ratio of nozzle diameter to wheel diameter\n", +"Cv=0.98//Velocity coefficient\n", +"UC1=0.46//Speed ratio\n", +"g=9.81//Acceleration due to gravity in m/s^2\n", +"dw=1000//Density of water in kg/m^3\n", +"n0=0.84//Overall efficiency\n", +"\n", +"//calculations\n", +"C1=Cv*(2*g*H)^(1/2)//Velocity of jet in m/s\n", +"U=UC1*(2*g*H)^(1/2)//Velocity of the wheel in m/s\n", +"D=(60*U)/(3.14*N)//Diameter of the wheel in m\n", +"d=D*dD//Diameter of the jet in m\n", +"Q=(3.1415/4)*(d^2)*C1//Quantity of water required in m^3/s\n", +"Pa=dw*g*Q*H//Power available at the nozzle in kW\n", +"P=n0*Pa*10^-3//Power developed in kW\n", +"disp(U)\n", +"//output\n", +"printf('(a)Diameter of the wheel is %3.2f m\n(b)Diameter of the jet is %3.3f m\n(c)Quantity of water required is %3.3f m^3/s\n(d)Power developed is %3.1f kW',D,d,Q,P)" + ] + } +, +{ + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 9.8: HYDRAULIC_EFFICIENCY.sce" + ] + }, + { +"cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], +"source": [ +"clc\n", +"clear\n", +"//input data\n", +"N=1260//Rotational speed of the francis turbine in rpm\n", +"H=124//The net head in m\n", +"Q=0.5//Volume flow rate of the turbine in m^3/s\n", +"r1=0.6//Radius of the runner in m\n", +"b1=0.03//Height of the runner vanes at inlet in m\n", +"b11=72//Angle of inlet guide vanes in radial direction in degree\n", +"g=9.81//Acceleration due to gravity in m/s^2\n", +"dw=1000//Density of water in kg/m^3\n", +"Cx2=0//Absolute exit whirl velocity in m/s as flow is radial at outlet\n", +"\n", +"//calculations\n", +"m=dw*Q//Mass flow rate in kg/s\n", +"T1=-m*r1//Torque by the turbine in Nm in terms of Cx1\n", +"A=2*3.1415*r1*b1//Area at inlet in m^2\n", +"Cr1=Q/A//Inlet flow velocity in m/s\n", +"Cx1=Cr1*tand(b11)//Absolute inlet whirl velocity in m/s\n", +"T=-T1*Cx1//Torque by water on the runner in Nm\n", +"w=(2*3.1415*N)/60//Angular velocity of the turbine in rad/s\n", +"W=T*w*10^-3//Power exerted in kW\n", +"nH=W*10^3/(dw*g*Q*H)//Hydraulic efficiency \n", +"\n", +"//output\n", +"printf('(a)Torque by water on the runner is %3.f Nm\n(b)Power exerted is %3i kW\n(c)Hydraulic efficiency is %3.3f',T,W,nH)" + ] + } +, +{ + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 9.9: INLET_GUIDE_VANE_ANGLE.sce" + ] + }, + { +"cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], +"source": [ +"clc\n", +"clear\n", +"//input data\n", +"n0=0.74//Overall efficiency\n", +"H=5.5//Net head across the turbine in m\n", +"P=125//Required Power output in kW\n", +"N=230//Speed of the runner in rpm\n", +"nH=(1-0.18)//Hydraulic efficiency\n", +"g=9.81//Acceleration due to gravity in m/s^2\n", +"dw=1000//Density of water in kg/m^3\n", +"U1=0.97*(2*g*H)^(1/2)//Runner tangential velocity in m/s\n", +"Cr1=0.4*(2*g*H)^(1/2)//Flow velocity in m/s\n", +"\n", +"//calculations\n", +"Cx1=(nH*g*H)/U1//Absolute inlet whirl velocity in m/s as flow is radial at outlet Cx2=0 in m/s\n", +"a11=atand(Cr1/Cx1)//Inlet guide vane angle in degree\n", +"b11=180+atand(Cr1/(Cx1-U1))//Angle of inlet guide vanes in radial direction in degree\n", +"D1=(U1*60)/(3.1415*N)//Runner inlet diameter in m\n", +"Q=(P*10^3)/(n0*dw*g*H)//Flow rate in m^3/s\n", +"b1=Q/(3.1415*D1*Cr1)//Height of runner in m\n", +"\n", +"//output\n", +"printf('(a)Inlet guide vane angle is %3.1f degree\n(b)Angle of inlet guide vanes in radial direction is %3.1f degree\n(c)Runner inlet diameter is %3.3f m\n(d)Height of runner is %3.3f m',a11,b11,D1,b1)" + ] + } +], +"metadata": { + "kernelspec": { + "display_name": "Scilab", + "language": "scilab", + "name": "scilab" + }, + "language_info": { + "file_extension": ".sce", + "help_links": [ + { + "text": "MetaKernel Magics", + "url": "https://github.com/calysto/metakernel/blob/master/metakernel/magics/README.md" + } + ], + "mimetype": "text/x-octave", + "name": "scilab", + "version": "0.7.1" + } + }, + "nbformat": 4, + "nbformat_minor": 0 +} |