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diff --git a/Fluid_Mechanics-Fundamentals_&_Applications/Chapter12_1.ipynb b/Fluid_Mechanics-Fundamentals_&_Applications/Chapter12_1.ipynb new file mode 100755 index 00000000..e505af37 --- /dev/null +++ b/Fluid_Mechanics-Fundamentals_&_Applications/Chapter12_1.ipynb @@ -0,0 +1,853 @@ +{ + "metadata": { + "name": "", + "signature": "sha256:277bc4cb4b4cbb4032c88d8fd8301e41a2fcfc6cb9b7c57adbca5a396d6c0dce" + }, + "nbformat": 3, + "nbformat_minor": 0, + "worksheets": [ + { + "cells": [ + { + "cell_type": "heading", + "level": 1, + "metadata": {}, + "source": [ + "Chapter 12:Compressible Flow" + ] + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 12.12-1, Page No:638" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "import math\n", + "\n", + "#Variable Decleration\n", + "V_1=250 #Velocity in m/s\n", + "c_p=1.005 #Constant Pressure specific heat in kJ/kg.K\n", + "k=1.4 #Specific heat ratio \n", + "T1=255.7 #\n", + "C=10**-3 #COnversion factor\n", + "P1=54.05 #Atmospheric Pressure in kPa\n", + "SPR=8 #Stagnation pressure ratio \n", + "\n", + "#Calculations\n", + "#Part(a)\n", + "T_01=T1+((V_1**2/(2*c_p))*C) #Stagnation temperature in K\n", + "\n", + "P_01=P1*((T_01/T1)**(k/(k-1))) #Stagnation Pressure in kPa\n", + "\n", + "#Part(b)\n", + "T_02=T_01*((SPR)**((k-1)/k)) #Stagnation Temperature at compressor exit in K\n", + "\n", + "Win=c_p*(T_02-T_01) #Work per unit mass of air in kJ/kg\n", + "\n", + "#Result\n", + "print \"The stagnation pressure is\",round(P_01,2),\"kPa\"\n", + "print \"The required compressor work per unit mass is\",round(Win,1),\"kJ/kg\"\n" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "The stagnation pressure is 80.77 kPa\n", + "The required compressor work per unit mass is 233.9 kJ/kg\n" + ] + } + ], + "prompt_number": 1 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 12.12-2, Page No:639" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "import math\n", + "\n", + "#Variable Decleration\n", + "cp=0.846 #Specific Heat in kJ/kg.K\n", + "k=1.289 #Specific heat ratio\n", + "R=0.1889 #gas constant for Carbon dioxide in kJ/kg.K\n", + "T_0=473 #Temperature in K\n", + "P0=1.4*10**3 #Pressure in kPa\n", + "P=1.2*10**3 #Pressure in kPa\n", + "m_dot=3 #Mass flow rate in kg/s\n", + "\n", + "#Calcualtions\n", + "x=((k-1)/k)\n", + "b=float(P/P0)\n", + "T=T_0*((b)**x) #Temperature where pressure is P in K\n", + "V=(2*cp*(T0-T)*10**3)**0.5 #Velocity in m/s\n", + "\n", + "#Using The Ideal Gas relation\n", + "rho=P/(R*T) #Density of the fluid in kg/m^3\n", + "\n", + "#Using the mass flow rate relation\n", + "A=m_dot/(rho*V) #Area in m^2\n", + "\n", + "c=(k*R*T*10**3)**0.5 #speed of sound in m/s\n", + "\n", + "#Mach Number\n", + "Ma=V/c #Mach's Number\n", + "\n", + "#Result\n", + "print \"Similarly we can compute data for other pressures as well\"\n", + "print \"The denisty of air is\",round(rho,5),\"kg/m^3\"\n", + "print \"The area is\",A,\"m^2\"\n", + "print \"The speed of sound is\",round(c,2),\"m/s\"\n", + "print \"The Mach Number is\",round(Ma,3)\n" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "Similarly we can compute data for other pressures as well\n", + "The denisty of air is 13.90266 kg/m^3\n", + "The area is 0.00130869674184 m^2\n", + "The speed of sound is 333.56 m/s\n", + "The Mach NUmber is 0.494\n" + ] + } + ], + "prompt_number": 29 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 12.12-3,Page No:645" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "import math\n", + "\n", + "#Variable Decleration\n", + "k=1.289 #Specific Heat Ratio\n", + "To=473 #Stagnation temperature in K\n", + "Po=1400 #Stagnation pressure in kPa\n", + "\n", + "#Calculations\n", + "#Notation has been changed for simplicity of computation\n", + "T_ratio=2/(k+1) #ratio of T star to To\n", + "P_ratio=(2/(k+1))**(k/(k-1)) #Ratio of P star to Po\n", + "\n", + "T_star=T_ratio*To #Critical Temperature in K\n", + "P_star=P_ratio*Po #Critical Pressure in kPa\n", + "\n", + "#Result\n", + "print \"the critical temperature and pressrue are\",round(T_star),\"K and\",round(P_star),\"kPa\"" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "the critical temperature and pressrue are 413.0 K and 767.0 kPa\n" + ] + } + ], + "prompt_number": 30 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 12.12-4, Page No:648" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "import math\n", + "\n", + "#Variable decleration\n", + "Vi=150 #Velocity at the inlet in m/s\n", + "cp=1.005 #Specific heat in kJ/Kg.K\n", + "k=1.4 #Specific heat ratio\n", + "Ti=873 #Temperature at the inlet in K\n", + "Pi=1 #Pressure at the inlet in Mpa\n", + "Pb1=0.7 #Back pressure in part a in Mpa\n", + "Pb2=0.4 #Back pressure in part b in Mpa\n", + "R=0.287 #Gas Constant in kPa.m^3/kg.K\n", + "At=50*10**-4 #Area in m^2\n", + "\n", + "#Values taken from the table\n", + "P_ratio=0.67 #Presure ratio\n", + "T_ratio=0.892 #Temperature ratio\n", + "Mat=0.778 #Mach Number \n", + "\n", + "#Calculations\n", + "Toi=Ti+((Vi**2/(2*cp))*10**-3) #Stagnation Temperature in K\n", + "\n", + "Poi=Pi*((Toi/Ti)**(k/(k-1))) #Stagnation Presure in mPa\n", + "\n", + "#Stagnation pressure and temperature values remain constant throughout\n", + "\n", + "#Part(A)\n", + "#Notation will be changed to avoid computational complexicity\n", + "BPR1=Pb1/Poi #Back Pressure ratio\n", + "\n", + "Tt=T_ratio*Toi #Temperature in K\n", + "rhot=(Pb1*10**3)/(R*Tt) #Density in kg/m^3\n", + "Vt=Mat*((k*R*Tt*10**3)**0.5) #Velocity in m/s\n", + "m_dot1=rhot*At*Vt #Mass flow rate in kg/s\n", + "\n", + "#Part(B)\n", + "#Notation will be changed\n", + "BPR2=Pb2/Poi #Back pressure ratio\n", + "\n", + "m_dot2=(At*Poi*10**3)*((k/(Toi*R))**0.5)*((2/(k+1))**((k+1)/(2*(k-1))))*1000**0.5 #mass flow rate in kg/s\n", + "\n", + "#Result\n", + "print \"The mass flow rate at the nozzle is\",round(m_dot1,2),\"kg/s\"\n", + "print \"The mass flow rate through the nozzleis calculated to be\",round(m_dot2,2),\"kg/s\"" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "The mass flow rate at the nozzle is 6.77 kg/s\n", + "The mass flow rate through the nozzleis calculated to be 7.11 kg/s\n" + ] + } + ], + "prompt_number": 53 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 12.12-5, Page No:650" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "import math\n", + "\n", + "#Variable Decleration\n", + "Pgauge=220 #Gauge Pressure in the tire in kPa\n", + "Patm=94 #Atmospheric Pressure in kPa\n", + "R=0.287 #Gas Constant in kPa.m^3/kg.K\n", + "k=1.4 #Specific heat ratio\n", + "T=298 #Temperature in K\n", + "D=0.004 #Diamter in m\n", + "\n", + "#Calculations\n", + "P=Pgauge+Patm #Absolute Pressure in the tre in kPa\n", + "\n", + "#Critical Presure in the tire from table\n", + "Pstar=round(0.5283*P) #Critical Presure in kPa\n", + "\n", + "#Flow is choked\n", + "rho0=P/(R*T) #Denisty of the fluid in kg/m^3\n", + "rho_star=rho0*((2/(k+1))**(1/(k-1))) #Critical Density in kg/m^3\n", + "T_star=(2/(k+1))*T #Critical Temperature in K\n", + "\n", + "V=(k*R*T_star*1000)**0.5 #Velocity in m/s\n", + "m_dot=rho_star*((pi*D**2)/4)*V #mass flow rate in kg/s\n", + "\n", + "#Result\n", + "print \"The initial mass flow rate is\",round(m_dot,5),\"kg/s\"\n" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "The initial mass flow rate is 0.00924 kg/s\n" + ] + } + ], + "prompt_number": 63 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 12.12-6, Page No:653" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "import math\n", + "\n", + "#Variable Decleration\n", + "k=1.4 #Specific Heat ratio\n", + "R=0.287 #Gas Constant in kJ/kg.K\n", + "Ma=2 #Mach Number\n", + "A=20*10**-4 #Throat Area in m^2\n", + "P0=1000 #Pressure in kPa\n", + "T0=800 #Temperature in K\n", + "\n", + "#Calculations\n", + "rho0=P0/(R*T0) #Density of the fluid in kg/m^3\n", + "\n", + "#Part(a) When Ma=1\n", + "#Notation has been changed\n", + "#Taking values from the table\n", + "P_ratio=0.5283 #Pressure ratio\n", + "T_ratio=0.8333 #Temperature Ratio\n", + "rho_ratio=0.6339 #Density Ratio\n", + "\n", + "#Thus\n", + "P_star=P_ratio*P0 #Critical Pressure in kPa\n", + "T_star=T_ratio*T0 #Critical Temperature in K\n", + "rho_star=rho_ratio*rho0 #Critical Denisty in kg/m^3\n", + "\n", + "V_star=(k*R*T_star*1000)**0.5 #Critical Velocity in m/s\n", + "\n", + "#Part(b) When Ma=2\n", + "P_ratio2=0.1278 #Pressure ratio in part b\n", + "T_ratio2=0.5556 #Temperature ratio in part b\n", + "rho_ratio2=0.23 #Density ratio in part b\n", + "Ma_star=1.633 #Critical Mach Number\n", + "A_ratio=1.6875 #Area ratio in part b\n", + "\n", + "#Thus\n", + "Pe=P_ratio2*P0 #Pressure at the exit plane in kPa\n", + "Te=T_ratio2*T0 #Temperature at the exit plane in K\n", + "rho_e=rho_ratio2*rho0 #Density at the exit plane in kg/m^3\n", + "Ae=A_ratio*A #Area at the exit plane in m^2\n", + "Ve=Ma_star*V_star #Velocity at the exit plane in m/s\n", + "\n", + "#Part(c)\n", + "m_dot=rho_star*A*V_star #Mass flow rate in kg/s\n", + "\n", + "\n", + "#Result\n", + "print \"The throat conditions are as follows\"\n", + "print \"P*=\",round(P_star),\"kPa\",\"T*=\",round(T_star,1),\"K\",\"rho*=\",round(rho_star,3),\"kg/m^3\"\n", + "print \"The exit plane conditions are as follows\"\n", + "print \"Pe=\",round(Pe),\"kPa\",\"Te=\",round(Te,1),\"K\",\"rho_e=\",round(rho_e,3),\"kg/m^3\"\n", + "print \"Ae=\",Ae,\"m^2\"\n", + "print \"The mass flow rate is\",round(m_dot,2),\"kg/s\"" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "The throat conditions are as follows\n", + "P*= 528.0 kPa T*= 666.6 K rho*= 2.761 kg/m^3\n", + "The exit plane conditions are as follows\n", + "Pe= 128.0 kPa Te= 444.5 K rho_e= 1.002 kg/m^3\n", + "Ae= 0.003375 m^2\n", + "The mass flow rate is 2.86 kg/s\n" + ] + } + ], + "prompt_number": 69 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 12.12-8, Page No:659" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "import math\n", + "\n", + "#NOTE:The variable names have been changed\n", + "\n", + "#Variable Decleration\n", + "k=1.4 #Specific Heat ratio\n", + "R=0.287 #gas Constant in kJ/kg.K\n", + "cp=1.005 #Specfic heat at constant pressure in kJ/kg.K\n", + "#Table Values\n", + "P01=1 #pressure in MPa\n", + "P1=0.1278 #Pressure in MPa\n", + "T1=444.5 #Temperature in K\n", + "rho1=1.002 #Denisty in kg/m^3\n", + "Ma1=2 #Mach Number \n", + "Ma2=0.5774 #Mach Number \n", + "Po_ratio=0.7209 #Presure ratio\n", + "P_ratio=4.5 #Pressure ratio\n", + "T_ratio=1.6875 #Temperature Ratio\n", + "rho_ratio=2.6667 #Density Ratio\n", + "A=20*10**-4 #Area in m^2\n", + "\n", + "#Calculations\n", + "#Part(a)\n", + "\n", + "P02=Po_ratio*P01 #Stagnation Pressure after the shockwave in MPa\n", + "P2=P1*P_ratio #Static Pressure after the shockwave in MPa\n", + "T2=T_ratio*T1 #Temperature after the shockwave in K\n", + "rho2=rho_ratio*rho1 #Denisty after the shockwave in kg/m^3\n", + "\n", + "#Part(b)\n", + "e_change=cp*(np.log(T2/T1))-(R*np.log(P2/P1)) #Entropy change across the shock in kJ/kg.K\n", + "\n", + "#Part(c)\n", + "V2=Ma2*(k*R*T2*1000)**0.5 #Velocity in m/s\n", + "\n", + "#Part(d)\n", + "#Same as example 12-6 above\n", + "m_dot=2.86 #Mass Flow rate in kg/s\n", + "\n", + "#Result\n", + "print \"The Following are the values\"\n", + "print \"Stagnation Pressure\",round(P02,3),\"MPa\"\n", + "print \"Static Pressure\",round(P2,3),\"MPa\"\n", + "print \"Static Temperature\",round(T2,1),\"K\"\n", + "print \"Static Denisty\",round(rho2,2),\"kg/m^3\"\n", + "print \"The entropy change is\",round(e_change,5),\"kJ/kg.K\"\n", + "print \"The exit velocity is\",round(V2),\"m/s\"\n", + "print \"The mass flow rate is\",round(m_dot,3),\"kg/s\"" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "The Following are the values\n", + "Stagnation Pressure 0.721 MPa\n", + "Static Pressure 0.575 MPa\n", + "Static Temperature 750.1 K\n", + "Static Denisty 2.67 kg/m^3\n", + "The entropy change is 0.09419 kJ/kg.K\n", + "The exit velocity is 317.0 m/s\n", + "The mass flow rate is 2.86 kg/s\n" + ] + } + ], + "prompt_number": 77 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 12.12-9, Page No:667" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "import math\n", + "\n", + "#Variable Decleration\n", + "u=19 #angle of Mach lines in Degrees\n", + "\n", + "#Calculations\n", + "Ma1=1/(sin((u*pi)/180)) #Mach Number \n", + "\n", + "#Result\n", + "print \"The Mach Number is\",round(Ma1,2)" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "The Mach Number is 3.07\n" + ] + } + ], + "prompt_number": 81 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 12.12-10, Page No:667" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "import math\n", + "\n", + "#NOTE:Some Variable names have been changed\n", + "\n", + "#Variable Decleration\n", + "Ma1=2 #Mach Number\n", + "k=1.4 #Specific heat ratio\n", + "theta=10 #Deflection in degrees\n", + "beta_weak=39.3 #Oblique shock angle in degrees\n", + "beta_strong=83.7 #Oblique shock angle in degrees\n", + "P1=75 #Pressure in kPa\n", + "Ma2_n_w=0.8032 #Mach Number on Downstream side\n", + "Ma2_n_s=0.5794 #Mach Number on Downstream Side \n", + "\n", + "#Calculations\n", + "\n", + "#Weak shock\n", + "Ma1_n_w=Ma1*sin((beta_weak*pi)/180) #Mach Number\n", + "\n", + "#Strong Shock\n", + "Ma1_n_s=Ma1*sin((beta_strong*pi)/180) #Mach Number\n", + "\n", + "#Pressure Calculations\n", + "\n", + "#Weak Shock\n", + "P2_w=((2*k*(Ma1_n_w**2)-k+1)/(k+1))*P1 #Pressure in kPa\n", + "\n", + "#Strong Shock\n", + "P2_s=((2*k*(Ma1_n_s**2)-k+1)/(k+1))*P1 #Pressure in kPa\n", + "\n", + "Ma2_w=Ma2_n_w/sin(((beta_weak-theta)*pi)/180) #Mach NUmber on the downstream side\n", + "\n", + "Ma2_s=Ma2_n_s/sin(((beta_strong-theta)*pi)/180) #Mach NUmber on the downstream side\n", + "\n", + "#Result\n", + "print \"The Mach number on the downstream side of the oblique shock are\"\n", + "print \"Ma in weak shock\",round(Ma2_w,3),\"Ma in strong shock\",round(Ma2_s,3)" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "The Mach number on the downstream side of the oblique shock are\n", + "Ma in weak shock 1.641 Ma in strong shock 0.604\n" + ] + } + ], + "prompt_number": 85 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 12.12-11, Page no:668" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "import math\n", + "\n", + "#Variable Decleration\n", + "Ma1=2 #Mach Number \n", + "P1=230 #Pressure in kPa\n", + "k=1.4 #Specific Heat ratio\n", + "theta=10 #Degrees\n", + "Ma2=2.38 #Mach Number \n", + "\n", + "#Calculations\n", + "#Simplfying the calculation\n", + "a=((k+1)/(k-1))**0.5\n", + "b=((Ma1**2)-1)**0.5\n", + "c=((k-1)/(k+1))**0.5\n", + "d=arctan(b)*180*pi**-1\n", + "e=arctan(c*b)*180*pi**-1\n", + "\n", + "vMa1=a*e-d #Upstream Prandtl-Meyer Function in degrees\n", + "vMa2=theta+vMa1 #Degrees\n", + "\n", + "#Pressure Calculations\n", + "#Simplifying Calculations\n", + "a1=(k-1)*0.5\n", + "b1=k/(k-1)\n", + "f=(1+a1*Ma2**2)**(-b1)\n", + "g=(1+a1*Ma1**2)**(-b1)\n", + "P2=P1*(f/g) #Pressure in kPa\n", + "\n", + "#Result\n", + "print \"The Mach Number on the Downstream Side is\",round(Ma2,2)\n", + "print \"The Pressure at the downstream side is\",round(P2),\"kPa\"\n", + "#The answer in the textbook has not been rounded and hence differes " + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "The Mach Number on the Downstream Side is 2.38\n", + "The Pressure at the downstream side is 127.0 kPa\n" + ] + } + ], + "prompt_number": 128 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 12.12-14, Page No:677" + ] + }, + { + "cell_type": "code", + "collapsed": true, + "input": [ + "import math\n", + "\n", + "#Variable Decleration\n", + "k=1.4 #Specific Heat Ratio\n", + "cp=1.005 #Specific Heat in kJ/kg.K\n", + "R=0.287 #Gas COnstant in kJ/kg.K\n", + "P1=480 #Pressure in kPa\n", + "T1=550 #Temperature in K\n", + "D=0.15 #Diameter in m\n", + "AF=40 #Air-Fuel mass ratio\n", + "HV=42000 #Heating Value in kJ/kg\n", + "V=80 #Velocity in m/s\n", + "\n", + "#Values from Tables\n", + "T_ratio=0.1291 #Temperature ratio\n", + "T_ratio1=0.1541 #Temperature Ratio\n", + "P_ratio1=2.3065 #Pressure ratio\n", + "V_ratio1=0.0668 #Velocity Ratio\n", + "T_ratio2=0.4389 #Temperature Ratio\n", + "P_ratio2=2.1086 #Pressure Ratio\n", + "V_ratio2=0.2082 #Velocity ratio\n", + "\n", + "#Calculations\n", + "rho1=P1/(R*T1) #Density in kg/m^3\n", + "A1=(pi*D**2)/4 #Area in m^2\n", + "m_dot_air=rho1*A1*V #Mass flow rate of air in kg/s\n", + "m_dot_fuel=m_dot_air/AF #Mass flow rate of the fuel in kg/s\n", + "Q_dot=m_dot_fuel*HV #Heat in kW\n", + "q=Q_dot/m_dot_air #HEat Transfer rate in kJ/kg\n", + "\n", + "#Stagnation Temperature and Mach Number at INLET\n", + "T01=T1+(V**2/(2*cp))*10**-3 #Stagnation Temperature in K\n", + "c1=(k*R*T1*1000)**0.5 #Speed in m/s\n", + "Ma1=V/c1 #Mach Number\n", + "\n", + "#EXIT stagnation Temperature and Mach Number\n", + "T02=T01+(q/cp) #Stagnation Temperature in K\n", + "\n", + "T0_star=T01/T_ratio #Critical Temperature in K\n", + "\n", + "#Value for Ma2 is taken form the table corresponding to the Temperature ratio given below\n", + "T_rat=T02/T0_star #Temperature Ratio\n", + "Ma2=0.314 #Mach Number\n", + "\n", + "#Exit Values\n", + "T2=T1*(T_ratio2/T_ratio1) #Temperature in K\n", + "P2=P1*(P_ratio2/P_ratio1) #Pressure in kPa\n", + "V2=V*(V_ratio2/V_ratio1) #Velocity in m/s\n", + "\n", + "#Result\n", + "print \"The Temperature at the exit is\",round(T2),\"K\"\n", + "print \"The pressure at the exit is\",round(P2),\"kPa\"\n", + "print \"The velocity at the exit is\",round(V2),\"m/s\"\n", + "#The answer for temperature in tetbook is incorrect\n" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "The Temperature at the exit is 1566.0 K\n", + "The pressure at the exit is 439.0 kPa\n", + "The velocity at the exit is 249.0 m/s\n" + ] + } + ], + "prompt_number": 3 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 12.12-15, Page No:685" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "import math\n", + "\n", + "#Varialble Decleration\n", + "k=1.4 #Specific Heat ratio\n", + "cp=1.005 #Specific Heat in kJ/kg.K\n", + "R=0.287 #Gas Constant in kJ/kg.K\n", + "v=1.58*10**-5 #Kinematic Viscosity in m^2/s\n", + "P1=150 #Pressure in kPa\n", + "T1=300 #Temperature in K\n", + "Ma1=0.4 #Mach Number\n", + "D=0.03 #Diameter in m\n", + "f=0.0148 #Friction factor\n", + "#Values from tables\n", + "P_ratio1=1.5901 \n", + "T_ratio1=1.1628\n", + "P_ratio2=2.6958\n", + "V_ratio=0.4313\n", + "fL1_D=2.3085\n", + "\n", + "#Calculations\n", + "c1=(k*R*T1*1000)**0.5 #Inlet Velocity in m/s\n", + "V1=Ma1*c1 #Velocity in m/s\n", + "Re1=(V1*D)/v #Reynolds Number\n", + "\n", + "L1_star=(fL1_D*D)/f #Duct Length in m\n", + "T_star=T1/T_ratio1 #Temperature in K\n", + "P_star=P1/P_ratio2 #Pressure in kPa\n", + "V_star=V1/V_ratio #Velocity in m/s\n", + "\n", + "fraction=1-(1/P_ratio1) #Fraction of the inlet stagnation pressure lost \n", + "\n", + "#Result\n", + "print \"The duct length is\",round(L1_star,2),\"m\"\n", + "print \"The Temperature is\",round(T_star),\"K\"\n", + "print \"The Pressure is\",round(P_star,1),\"kPa\"\n", + "print \"The Velocity is\",round(V_star),\"m/s\"\n", + "print round(fraction,3),\"Fraction of the total stagnation pressure is lost in the duct\"\n" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "The duct length is 4.68 m\n", + "The Temperature is 258.0 K\n", + "The Pressure is 55.6 kPa\n", + "The Velocity is 322.0 m/s\n", + "0.371 Fraction of the total stagnation pressure is lost in the duct\n" + ] + } + ], + "prompt_number": 5 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 12.12-16,Page No:686" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "import math\n", + "\n", + "#Variable Decleration\n", + "k=1.4 #Specific Heat ratio\n", + "cp=1.005 #Specific Heat in kJ/kg.K\n", + "R=0.287 #Gas Constant in kJ/kg.K\n", + "V1=85 #Velocity in m/s\n", + "P1=220 #Pressure in kPa\n", + "T1=450 #Temperature in K\n", + "f=0.023 #Friction factor \n", + "L=27 #Length in m\n", + "D=0.05 #Diameter in m\n", + "\n", + "#Value from table\n", + "fl_D=14.5333\n", + "\n", + "#Calculations\n", + "c1=(k*R*T1*1000)**0.5 #Velocity in m/s\n", + "Ma1=V1/c1 #Mach Number\n", + "\n", + "#Notation has been changed\n", + "fL_D1=(f*L)/D #Function\n", + "fL_D2=fl_D-fL_D1 #Function\n", + "\n", + "#Mach NUmber corresponding to this value is 0.42\n", + "Ma2=0.420 #Mach Number\n", + "\n", + "rho1=P1/(R*T1) #Density of the fluid in kg/m^3\n", + "A1=(pi*D**2)/4 #Area in m^2\n", + "m_air=rho1*V1*A1 #Mass flow rate in kg/s\n", + "\n", + "#Discussion Calculations\n", + "L_max1=(fl_D*D)/f #MAx Duct length in m\n", + "L_max2=(fL_D2*D)/f #Max Duct length in m\n", + "\n", + "#Result\n", + "print \"The Mach Number is\",round(Ma2,3)\n", + "print \"The mass flow rate is\",round(m_air,3),\"kg/s\"\n", + "print \"The max length at inlet is\",round(L_max1,1),\"m\"\n", + "print \"The max length at exit is\",round(L_max2,1),\"m\"\n" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "The Mach Number is 0.42\n", + "The mass flow rate is 0.284 kg/s\n", + "The max length at inlet is 31.6 m\n", + "The max length at exit is 4.6 m\n" + ] + } + ], + "prompt_number": 16 + }, + { + "cell_type": "code", + "collapsed": false, + "input": [], + "language": "python", + "metadata": {}, + "outputs": [] + } + ], + "metadata": {} + } + ] +}
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