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diff --git a/Turbomachines_by_A._V._Arasu/Ch7.ipynb b/Turbomachines_by_A._V._Arasu/Ch7.ipynb new file mode 100644 index 00000000..901a931e --- /dev/null +++ b/Turbomachines_by_A._V._Arasu/Ch7.ipynb @@ -0,0 +1,429 @@ +{ + "metadata": { + "name": "", + "signature": "sha256:f827c11afa624e3e81bfed710ad978d27a2bfba89c05ec909ef7162ba7b3cadb" + }, + "nbformat": 3, + "nbformat_minor": 0, + "worksheets": [ + { + "cells": [ + { + "cell_type": "heading", + "level": 1, + "metadata": {}, + "source": [ + "Chapter 7 - Dimensional and Modal Analysis" + ] + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Ex 7.5 Page 312" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "from __future__ import division\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", + "print '(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)\n" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "(1)Speed of prototype pump is 353.6 rpm\n", + "(2)Power developed by the prototype pump is 4143 kW\n", + "(3)Ratio of the flow rates of two pumps is 44.1942\n" + ] + } + ], + "prompt_number": 1 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Ex 7.6 Page 313" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "#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", + "print '(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)\n", + "# Answer in the textbook is wrong" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "(1)The head ratio of the model is 1.0\n", + "(2)The speed ratio of the model is 3.3\n", + "(3)The scale ratio of the model is 0.3\n" + ] + } + ], + "prompt_number": 2 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Ex 7.7 Page 315" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "#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", + "print '(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)" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "(a)Speed of the model is 1191.75 rpm\n", + "(b)Discharge of the model is 0.0234 m**3/s\n", + "(c)Power required by the model is 2.45 kW\n" + ] + } + ], + "prompt_number": 3 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Ex 7.8 Page 316" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "#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", + "print '(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)" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "(a)Impeller diameter of the pump-2 is 0.238 m\n", + "(b)Head developed by the pump-2 is 9.45 m\n" + ] + } + ], + "prompt_number": 4 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Ex 7.9 Page 316" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "#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", + "print '(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)" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "(a)Power developed by the prototype is 4163 kW\n", + "(b)Speed of the prototype is 135.76 rpm\n", + "(c)Specific speed of the prototype is 87.1\n", + "(d)Specific speed of the model is 87.1\n", + " Thus the specific speed of the model is equal to the prototype and thus it is verified\n" + ] + } + ], + "prompt_number": 5 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Ex 7.10 Page 317" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "from __future__ import division\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", + "print '(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)" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "(a)Speed of the model is 920.4 rpm\n", + "(b)Discharge from the model is 0.866 m**3/s\n", + "(c)Power of the model is 36.1 kW\n" + ] + } + ], + "prompt_number": 6 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Ex 7.11 Page 318" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "#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", + "print '(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)" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "(1)The final speed of the turbine is 77.46 rpm\n", + "(2)The final power developed by the turbine is 3067 kW\n" + ] + } + ], + "prompt_number": 7 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Ex 7.12 Page 319" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "#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", + "print '(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)" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "(a)The final speed of the turbine is 178.89 rpm\n", + "(b)The final discharge of the turbine is 8.05 m**3/s\n", + "(c)Power produced by the turbine initially is 1986.525 kW\n", + "(d)Power produced by the turbine finally is 1421.44 kW\n" + ] + } + ], + "prompt_number": 8 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Ex 7.13 Page 320" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "#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", + "print '(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)" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "(a)The unit speed of the turbine is 13.28\n", + "(b)The unit power of the turbine is 1.265\n", + "(c)The unit discharge of the turbine is 0.152\n", + "(d)The final discharge of the turbine is 1.92 m**3/s\n", + "(e)The final speed of the turbine is 168.00 rpm\n", + "(f)The final power of the turbine is 2560.0 kW\n", + "(g)The specific speed of the turbine is 14.94\n" + ] + } + ], + "prompt_number": 9 + } + ], + "metadata": {} + } + ] +}
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