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diff --git a/Gas_Dynamics_and_Jet_Propulsion_by_P._Murugaperumal/ch2.ipynb b/Gas_Dynamics_and_Jet_Propulsion_by_P._Murugaperumal/ch2.ipynb new file mode 100755 index 00000000..12361fe9 --- /dev/null +++ b/Gas_Dynamics_and_Jet_Propulsion_by_P._Murugaperumal/ch2.ipynb @@ -0,0 +1,1509 @@ +{ + "metadata": { + "name": "", + "signature": "sha256:6875085981d30c40f21af9abe827ee04ccc837d7faa969a757e96f393b389713" + }, + "nbformat": 3, + "nbformat_minor": 0, + "worksheets": [ + { + "cells": [ + { + "cell_type": "heading", + "level": 1, + "metadata": {}, + "source": [ + "Chapter 2 : Flow Through Variable Area Ducts" + ] + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 2.1 page : 19" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "import math \n", + "\n", + "\t\t\t\t\n", + "#Input data\n", + "do1 = 1.12 \t\t\t\t#Density of air i reservoir in kg/m**3\n", + "ao1 = 500 \t\t\t\t#Velocity of sound in reservoir in m/s\n", + "d = 0.01 \t\t\t\t#Throat diameter in m \n", + "k = 1.4 \t\t\t\t#Adiabatic Consmath.tant \n", + "R = 287 \t\t\t\t#Specific gas consmath.tant in J/kg-K\n", + "\n", + "\t\t\t\t\n", + "#Calculation\n", + "To1 = ao1**2/(k*R) \t\t\t\t#Stagnation temperature in K\n", + "Po1 = do1*R*To1 \t\t\t\t#Stagnation pressure in Pa\n", + "p1 = 0.528 \t\t\t\t#Ratio of critical pressure to Stagnation pressure from gas tables @M = 1\n", + "Pt = (Po1*p1)*10**-5 \t\t\t\t#Throat pressure in bar\n", + "t1 = 0.834 \t\t\t\t#Ratio of critical temperature to Stagnation temperature from gas tables @M = 1\n", + "Tt = To1*t1 \t\t\t\t#critical temperature in K\n", + "d_t = (Pt*10**5)/(R*Tt) \t\t\t\t#Density of air at throat in kg/m**3\n", + "a_t = math.sqrt(k*R*Tt) \t\t\t\t#Sound velocity at throat in m/s \n", + "Ct = a_t \t\t\t\t#Air velocity t throat in m/s, Since M = 1\n", + "A_t = math.pi*d**2/4 \t\t\t\t#Throat area in m**2 \n", + "m = d_t*A_t*Ct \t\t\t\t#Maximum mass flow rate in kg/s\n", + "\n", + "\t\t\t\t\n", + "#Output\n", + "print 'A)Maximum mass flow rate is %3.5f kg/s \\\n", + "\\nB)Pressure and temperarature at the throat are %3.3f bar and %3.4f K'%(m,Pt,Tt)\n" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "A)Maximum mass flow rate is 0.02543 kg/s \n", + "B)Pressure and temperarature at the throat are 1.056 bar and 518.9149 K\n" + ] + } + ], + "prompt_number": 1 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 2.2 page : 20" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "import math \n", + "\n", + "\t\t\t\t\n", + "#Input data\n", + "P1 = 2. \t\t\t\t#Intial pressure in bar\n", + "C1 = 170. \t\t\t\t#Initial velocity of air in m/s\n", + "T1 = 473. \t\t\t\t#Intial temperature in K\n", + "A1 = 1000. \t\t\t\t#Inlet area in mm**2\n", + "P2 = 0.95 \t\t\t\t#Exit pressure in bar\n", + "k = 1.4 \t\t\t\t#Adiabatic Consmath.tant \n", + "R = 287. \t\t\t\t#Specific gas consmath.tant in J/kg-K\n", + "\n", + "\t\t\t\t\n", + "#Calculation\n", + "a_1 = math.sqrt(k*R*T1) \t\t\t\t#Velocity of sound at inlet in m/s\n", + "M1 = C1/a_1 \t\t\t\t#Inlet mach number\n", + "t1 = 0.970 \t\t\t\t#Ratio of inlet temperature to Stagnation temperature from gas tables @M = 1\n", + "To1 = T1/t1 \t\t\t\t#Stagnation temperature in K\n", + "p1 = 0.900 \t\t\t\t#Ratio of inlet pressure to Stagnation pressure from gas tables @M = 1\n", + "Po1 = P1/p1 \t\t\t\t#Stagnation pressure in bar\n", + "a1 = 1.623 \t\t\t\t#Ratio of inlet area to critical area from isentropic gas tables @M = 1\n", + "At = A1/a1 \t\t\t\t#critical area in mm**2\n", + "p2 = 0.528 \t\t\t\t#Pressure ratio at critical state from isentropic gas tables @M = 1\n", + "Pt = Po1*p2 \t\t\t\t#Throat pressure in bar\n", + "t2 = 0.834 \t\t\t\t#Temperature ratio at critical state from isentropic gas tables @M = 1\n", + "Tt = To1*t2 \t\t\t\t#Throat temperature in K\n", + "a_t = math.sqrt(k*R*Tt) \t\t\t\t#Velocity of sound at throat in m/s\n", + "C_t = a_t \t\t\t\t#Critical velocity of air in m/s\n", + "p3 = P2/Po1 \t\t\t\t#Pressure ratio at exit \n", + "M2 = 1.17 \t\t\t\t#Mach number at exit from isentropic gas tables @p3\n", + "t3 = 0.785 \t\t\t\t#Temperature ratio at exit from isentropic gas tables @M2\n", + "T2 = To1*t3 \t\t\t\t#Exit temperature in K\n", + "a3 = 1.022 \t\t\t\t#Area ratio at exit from isentropic gas tables @M2\n", + "A2 = At*a3 \t\t\t\t#Exit area in mm**2, wrong answer in textbook\n", + "C2 = M2*math.sqrt(k*R*T2) \t\t\t\t#Exit velocity in m/s\n", + "\n", + "\t\t\t\t\n", + "#Output\n", + "print 'A)Stagnation temperature and pressure are %3.2f K and %3.3f bar \\\n", + "\\nB)Sonic velocity and mach number at entry are %3.2f m/s and %3.2f \\\n", + "\\nC)Velocity, Mach number and flow area at outlet section are %3.2f m/s, %3.2f and %3.2f mm**2 \\\n", + "\\nD)Pressure, area at throat of the nozzle are %3.5f bar and %3.3f mm**2'%(To1,Po1,a_1,M1,C2,M2,A2,Pt,At)\n" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "A)Stagnation temperature and pressure are 487.63 K and 2.222 bar \n", + "B)Sonic velocity and mach number at entry are 435.95 m/s and 0.39 \n", + "C)Velocity, Mach number and flow area at outlet section are 458.85 m/s, 1.17 and 629.70 mm**2 \n", + "D)Pressure, area at throat of the nozzle are 1.17333 bar and 616.143 mm**2\n" + ] + } + ], + "prompt_number": 2 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 2.3 page: 21" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "import math \n", + "\n", + "\t\t\t\t\n", + "#Input data\n", + "Po1 = 10. \t\t\t\t#Stagnation pressure in bar\n", + "To1 = 798. \t\t\t\t#Stagnation temperature in K\n", + "Pt = 7.6 \t\t\t\t#Throat pressure in bar \n", + "m = 1.5 \t\t\t\t#Mass flow rate in kg/s\n", + "k = 1.4 \t\t\t\t#Adiabatic Consmath.tant\n", + "R = 287. \t\t\t\t#Specific gas consmath.tant in J/kg-K\n", + "Cp = 1005. \t\t\t\t#Specific heat capacity at consmath.tant pressure in J/kg-K \n", + " \n", + "\t\t\t\t\n", + "#Calculation\n", + "p1 = 0.528 \t\t\t\t#Ratio of critical pressure to Stagnation pressure from isentropic gas tables @M = 1,k = 1.4\n", + "Pc = p1*Po1 \t\t\t\t#Critical pressure in bar\n", + "P2 = Pt \t\t\t\t#Exit pressure in bar, Since Pc<P2\n", + "p2 = P2/Po1 \t\t\t\t#Pressure ratio\n", + "M2 = 0.64 \t\t\t\t#Exit mach number from isentropic gas tables @p2\n", + "t1 = 0.924 \t\t\t\t#Ratio of exit temperature to Stagnation temperature from isentropic gas tables @M2\n", + "T2 = t1*To1 \t\t\t\t#exit temperature in K\n", + "C2 = math.sqrt(k*R*T2)*M2 \t\t\t\t#Exit velocity in m/s\n", + "C_max = math.sqrt(2*Cp*To1) \t\t\t\t#Maximum possible velocity in m/s\n", + "d2 = (P2*10**5)/(R*T2) \t\t\t\t#Density at exit in kg/m**3\n", + "At = (m/(d2*C2))*10**6 \t\t\t\t#Throat area in mm**2\n", + "\n", + "\t\t\t\t\n", + "#Output\n", + "print 'A)At the nozzle throat/exit: \\\n", + "\\nPressure is %3.2f bar \\\n", + "\\nTemperature is %3.2f K \\\n", + "\\nVelocity is %3.2f m/s \\\n", + "\\nB)Maximum possible velocity is %3.2f m/s \\\n", + "\\nC)Type of the nozzle is a convergent nozzle and its throat area is %3.3f mm**2'%(P2,T2,C2,C_max,At)\n" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "A)At the nozzle throat/exit: \n", + "Pressure is 7.60 bar \n", + "Temperature is 737.35 K \n", + "Velocity is 348.36 m/s \n", + "B)Maximum possible velocity is 1266.48 m/s \n", + "C)Type of the nozzle is a convergent nozzle and its throat area is 1198.980 mm**2\n" + ] + } + ], + "prompt_number": 5 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 2.4 page : 22" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "import math \n", + "\n", + "\t\t\t\t\n", + "#Input data\n", + "Po1 = 3.344 \t\t\t\t#Stagnation pressure in bar\n", + "To1 = 900. \t\t\t\t#Stagnation temperature in K\n", + "P2 = 1.05 \t\t\t\t#Exit pressure in bar\n", + "k = 1.4 \t\t\t\t#Adiabatic Consmath.tant\n", + "R = 287. \t\t\t\t#Specific gas consmath.tant in J/kg-K\n", + "Cp = 1005. \t\t\t\t#Specific heat capacity at consmath.tant pressure in J/kg-K \n", + "\n", + "\t\t\t\t\n", + "#Calculation\n", + "p1 = P2/Po1 \t\t\t\t#Pressure ratio\n", + "M2 = 1.40 \t\t\t\t#Exit mach number from gas tables @p1,k = 1.4\n", + "t1 = 0.718 \t\t\t\t#Ratio of exit temperature to Stagnation temperature from isentropic gas tables @M2,k = 1.4\n", + "T2 = To1*t1 \t\t\t\t#exit temperature in K\n", + "C2 = math.sqrt(k*R*T2)*M2 \t\t\t\t#Exit velocity in m/s\n", + "d2 = (P2*10**5)/(R*T2) \t\t\t\t#Density at exit in kg/m**3\n", + "a1 = 1.115 \t\t\t\t#Ratio of exit area to critical area from isentropic gas tables @M2\n", + "M_2 = 0.6733 \t\t\t\t#Exit mach number when it acts as diffuser \n", + "t2 = 0.91633 \t\t\t\t#Ratio of exit temperature to Stagnation temperature from isentropic gas tables @M2\n", + "T_2 = t2*To1 \t\t\t\t#exit temperature in K\n", + "C_2 = math.sqrt(k*R*T_2)*M_2 \t\t\t\t#Exit velocity in m/s\n", + "p2 = 0.738 \t\t\t\t#Ratio of exit pressure to Stagnation pressure from isentropic gas tables @M2\n", + "P_2 = Po1*p2 \t\t\t\t#exit pressure in bar\n", + "d_2 = (P_2*10**5)/(R*T_2) \t\t\t\t#Density at exit in kg/m**3\n", + "\n", + "\t\t\t\t\n", + "#Output\n", + "print 'A)At exit: \\nTemperaure is %3i K \\\n", + "\\nVelocity is %3.2f m/s \\\n", + "\\nDensity is %3.3f kg/m**3 \\\n", + "\\nB)At diffuser: Temperaure is %3.3f K \\\n", + "\\nVelocity is %3.3f m/s \\\n", + "\\nDensity is %3.4f kg/m**3 \\\n", + "\\nPressure is %3.4f bar'%(T2,C2,d2,T_2,C_2,d_2,P_2)\n" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "A)At exit: \n", + "Temperaure is 646 K \n", + "Velocity is 713.37 m/s \n", + "Density is 0.566 kg/m**3 \n", + "B)At diffuser: Temperaure is 824.697 K \n", + "Velocity is 387.579 m/s \n", + "Density is 1.0427 kg/m**3 \n", + "Pressure is 2.4679 bar\n" + ] + } + ], + "prompt_number": 7 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 2.5 page : 23" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "import math \n", + "\n", + "\t\t\t\t\n", + "#Input data\n", + "Po1 = 8 \t\t\t\t#Stagnation pressure in bar\n", + "To1 = 273+15 \t\t\t\t#Stagnation temperature in K\n", + "At = 25 \t\t\t\t#Throat area in cm**2\n", + "A2 = 100 \t\t\t\t#Exit area in cm**2\n", + "k = 1.4 \t\t\t\t#Adiabatic Consmath.tant\n", + "R = 287 \t\t\t\t#Specific gas consmath.tant in J/kg-K\n", + "\n", + "\t\t\t\t\n", + "#Calculation\n", + "a1 = A2/At \t\t\t\t#Area ratio\n", + "M2 = 2.94 \t\t\t\t#Exit mach number from gas tables @a1,k = 1.4\n", + "p1 = 0.0298 \t\t\t\t#Ratio of exit pressure to Stagnation pressure from isentropic gas tables @M2,k = 1.4\n", + "P2 = Po1*p1 \t\t\t\t#exit pressure in bar\n", + "M_2 = 0.146 \t\t\t\t#Exit mach number when it acts as diffuser\n", + "p2 = 0.9847 \t\t\t\t#Ratio of exit pressure to Stagnation pressure from isentropic gas tables @M2\n", + "P_2 = Po1*p2 \t\t\t\t#exit pressure in bar\n", + "p3 = 0.528 \t\t\t\t#Ratio of critical pressure to Stagnation pressure from isentropic gas tables @M = 1,k = 1.4 \n", + "Pc = (Po1*p3) \t\t\t\t#Critical pressure in bar\n", + "t1 = 0.834 \t\t\t\t#Ratio of critical temperature to Stagnation temperature from isentropic gas tables @M = 1,k = 1.4 \n", + "Tt = To1*t1 \t\t\t\t#critical temperature in K\n", + "d_t = (Pc*10**5)/(R*Tt) \t\t\t\t#Density at critical state in kg/m**3\n", + "a_t = math.sqrt(k*R*Tt) \t\t\t\t#Velocity of sound at critical state in m/s\n", + "Ct = a_t \t\t\t\t#Velocity of air at critical state in m/s\n", + "m = d_t*At*Ct*10**-4 \t\t\t\t#Mass flow rate in kg/s\n", + "\n", + "\t\t\t\t\n", + "#Output\n", + "print 'A)Maximum mass flow rate is %3.3f kg/s \\\n", + "\\n\\\n", + "\\nB)As nozzle: \\\n", + "\\nPressure is %3.4f bar \\\n", + "\\nMach number is %3.2f \\\n", + "\\nAs diffuser: \\\n", + "\\nPressure is %3.4f bar \\\n", + "\\nMach number is %3.3f'%(m,P2,M2,P_2,M_2)\n" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "A)Maximum mass flow rate is 4.759 kg/s \n", + "\n", + "B)As nozzle: \n", + "Pressure is 0.2384 bar \n", + "Mach number is 2.94 \n", + "As diffuser: \n", + "Pressure is 7.8776 bar \n", + "Mach number is 0.146\n" + ] + } + ], + "prompt_number": 9 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 2.6 page : 24" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "import math \n", + "\n", + "\t\t\t\t\n", + "#Input data\n", + "D1 = 15 \t\t\t\t#Entry diameter in cm\n", + "D2 = 30 \t\t\t\t#Exit diamater in cm \n", + "P1 = 0.96 \t\t\t\t#Inlet pressure in bar\n", + "T1 = 340 \t\t\t\t#Inlet temperature in K\n", + "C1 = 185 \t\t\t\t#INlet velocity in m/s\n", + "k = 1.4 \t\t\t\t#Adiabatic Consmath.tant\n", + "R = 287 \t\t\t\t#Specific gas consmath.tant in J/kg-K\n", + "\n", + "\t\t\t\t\n", + "#Calculation\n", + "A1 = math.pi*D1**2/4 \t\t\t\t#Entry area in cm**2\n", + "A2 = math.pi*D2**2/4 \t\t\t\t#Exit area in cm**2\n", + "a_1 = math.sqrt(k*R*T1) \t\t\t\t#Sound velocity in m/s\n", + "M1 = C1/a_1 \t\t\t\t#Inlet mach number \n", + "p1 = 0.843 \t\t\t\t#Ratio of inlet pressure to Stagnation pressure from gas tables @M1,k = 1.4\n", + "Po1 = P1/p1 \t\t\t\t#Stagnation pressure in bar\n", + "t1 = 0.952 \t\t\t\t#Ratio of inlet temperature to Stagnation temperature from gas tables @M1,k = 1.4\n", + "To1 = T1/t1 \t\t\t\t#Stagnation temperature in K\n", + "a1 = 1.34 \t\t\t\t#Ratio of inlet area to critical area from isentropic gas tables @M1,k = 1.4\n", + "At = A1/a1 \t\t\t\t#critical area in cm**2\n", + "a2 = A2/At \t\t\t\t#Area ratio\n", + "M2 = 0.1088 \t\t\t\t#Exit mach number from gas tables @a2,k = 1.4\n", + "p2 = 0.992 \t\t\t\t#Ratio of exit pressure to Stagnation pressure from isentropic gas tables @M2,k = 1.4\n", + "P2 = Po1*p2 \t\t\t\t#exit pressure in bar\n", + "t2 = 0.9976 \t\t\t\t#Ratio of exit temperature to Stagnation temperature from isentropic gas tables @M2,k = 1.4\n", + "T2 = To1*t2 \t\t\t\t#exit temperature in K\n", + "C2 = math.sqrt(k*R*T2)*M2 \t\t\t\t#Exit velocity in m/s\n", + "F1 = P1*10**5*A1*10**-4*(1+(k*(M1**2))) \t\t\t\t#Force exerted at entry in kN\n", + "F2 = P2*10**5*A2*10**-4*(1+(k*(M2**2))) \t\t\t\t#Force exerted at exit in kN\n", + "F = (F2-F1)*10**-3 \t\t\t\t#Force exerted on the diffuser walls in kN, wrong answer in textbook \n", + "\n", + "\t\t\t\t\n", + "#Output\n", + "print 'A)Exit pressure is %3.3f bar \\\n", + "\\n\\\n", + "\\nB)Exit velocity is %3.2f m/s \\\n", + "\\n\\\n", + "\\nC)Force exerted on the diffuser walls is %3.3f kN'%(P2,C2,F)\n" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "A)Exit pressure is 1.130 bar \n", + "\n", + "B)Exit velocity is 41.17 m/s \n", + "\n", + "C)Force exerted on the diffuser walls is 5.826 kN\n" + ] + } + ], + "prompt_number": 10 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 2.7 page : 25" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "import math \n", + "\n", + "\t\t\t\t\n", + "#Input data\n", + "M1 = 3.6 \t\t\t\t#Inlet mach number \n", + "M2 = 2 \t\t\t\t#Exit mach number\n", + "m = 15 \t\t\t\t#Mass flow rate in kg/s\n", + "P1 = 1.05 \t\t\t\t#Inlet pressure in bar\n", + "T1 = 313 \t\t\t\t#Inlet temperature in K\n", + "k = 1.4 \t\t\t\t#Adiabatic Consmath.tant\n", + "R = 287 \t\t\t\t#Specific gas consmath.tant in J/kg-K\n", + "\n", + "\t\t\t\t\n", + "#Calculation\n", + "p1 = 11.38*10**-3 \t\t\t\t#Ratio of inlet pressure to Stagnation pressure from gas tables @M1,k = 1.4\n", + "Po = P1/p1 \t\t\t\t#Stagnation pressure in bar\n", + "t1 = 0.278 \t\t\t\t#Ratio of inlet temperature to Stagnation temperature from gas tables @M1,k = 1.4\n", + "To = T1/t1 \t\t\t\t#Stagnation temperature in K\n", + "C1 = math.sqrt(k*R*T1)*M1 \t\t\t\t#Inlet velocity in m/s\n", + "d1 = (P1*10**5)/(R*T1) \t\t\t\t#Density at inlet in kg/s, P1 in Pa\n", + "A1 = (m/(d1*C1))*10**4 \t\t\t\t#Inlet area in cm**2\n", + "p2 = 0.128 \t\t\t\t#Ratio of exit pressure to Stagnation pressure from isentropic gas tables @M2,k = 1.4\n", + "P2 = Po*p2 \t\t\t\t#exit pressure in bar\n", + "t2 = 0.555 \t\t\t\t#Ratio of exit temperature to Stagnation temperature from isentropic gas tables @M2,k = 1.4\n", + "T2 = To*t2 \t\t\t\t#exit temperature in K\n", + "C2 = math.sqrt(k*R*T2)*M2 \t\t\t\t#Exit velocity in m/s\n", + "d2 = (P2*10**5)/(R*T2) \t\t\t\t#Density at exit in kg/s\n", + "A2 = (m/(d2*C2))*10**4 \t\t\t\t#Exit area in cm**2\n", + "\n", + "\t\t\t\t\n", + "#Output \n", + "print 'A)At Inlet: \\\n", + "\\nArea is %3.1f cm**2 \\\n", + "\\nTotal pressure %3.2f bar \\\n", + "\\nTotal temperature is %3.1f K \\\n", + "\\nB)At Exit: \\\n", + "\\nArea is %3.1f cm**2 \\\n", + "\\nTotal pressure %3.2f bar \\\n", + "\\nTotal temperature is %3.2f K \\\n", + "\\nStatic temperature is %3.2f K \\\n", + "\\nStatic pressure is %3.2f bar'%(A1,Po,To,A2,Po,To,T2,P2)\n" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "A)At Inlet: \n", + "Area is 100.5 cm**2 \n", + "Total pressure 92.27 bar \n", + "Total temperature is 1125.9 K \n", + "B)At Exit: \n", + "Area is 22.7 cm**2 \n", + "Total pressure 92.27 bar \n", + "Total temperature is 1125.90 K \n", + "Static temperature is 624.87 K \n", + "Static pressure is 11.81 bar\n" + ] + } + ], + "prompt_number": 12 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 2.8 page :26" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "import math \n", + "\n", + "\t\t\t\t\n", + "#Input data\n", + "Po = 6.91 \t\t\t\t#Stagnation pressure in bar\n", + "To = 325+273 \t\t\t\t#Stagnation temperature in K\n", + "P2 = 0.98 \t\t\t\t#exit pressure in bar\n", + "m = 3600/3600 \t\t\t\t#Mass flow rate in kg/s\n", + "k = 1.4 \t\t\t\t#Adiabatic Consmath.tant\n", + "R = 287 \t\t\t\t#Specific gas consmath.tant in J/kg-K\n", + "Cp = 1005 \t\t\t\t#Specific heat capacity at consmath.tant pressure in J/kg-K \n", + "\n", + "\t\t\t\t\n", + "#Calculation\n", + "p1 = 0.528 \t\t\t\t#Ratio of critical pressure to Stagnation pressure from gas tables @M = 1\n", + "Pt = Po*p1 \t\t\t\t#critical pressure in bar\n", + "t1 = 0.834 \t\t\t\t#Ratio of critical temperature to Stagnation temperature from gas tables @M = 1\n", + "Tt = To*t1 \t\t\t\t#critical temperature in K\n", + "at = math.sqrt(k*R*Tt) \t\t\t\t#Sound velocity at throat in m/s \n", + "Ct = at \t\t\t\t#Air velocity t throat in m/s, Since M = 1\n", + "dt = (Pt*10**5)/(R*Tt) \t\t\t\t#Density of air at throat in kg/m**3, Pt in Pa\n", + "At = (m/(dt*Ct))*10**4 \t\t\t\t#Throat area in m**2 x10**-4 \n", + "p2 = P2/Po \t\t\t\t#Pressure ratio \n", + "M2 = 1.93 \t\t\t\t#Exit mach number from gas tables @p2,k = 1.4\n", + "t2 = 0.573 \t\t\t\t#Ratio of exit temperature to Stagnation temperature from isentropic gas tables @M2,k = 1.4\n", + "T2 = To*t2 \t\t\t\t#exit temperature in K\n", + "a2 = 1.593 \t\t\t\t#Ratio of exit area to critical area from isentropic gas tables @M2,k = 1.4\n", + "A2 = a2*At \t\t\t\t#Exit area in m**2, At in m**2 x10**-4\n", + "C_max = math.sqrt(2*Cp*To) \t\t\t\t#Maximum possible velocity in m/s\n", + "\n", + "\t\t\t\t\n", + "#Output\n", + "print 'A)At throat: \\\n", + "\\nArea is %3.2fx10**-4 m**2 \\\n", + "\\nPressure is %3.2f bar \\\n", + "\\nVelocity is %3.1f m/s \\\n", + "\\nB)At Exit: \\\n", + "\\nArea is %3.3fx10**-4 m**2 \\\n", + "\\nMach number is %3.2f \\\n", + "\\nC)Maximum possible velocity is %3.2f m/s'%(At,Pt,Ct,A2,M2,C_max)\n" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "A)At throat: \n", + "Area is 8.76x10**-4 m**2 \n", + "Pressure is 3.65 bar \n", + "Velocity is 447.6 m/s \n", + "B)At Exit: \n", + "Area is 13.961x10**-4 m**2 \n", + "Mach number is 1.93 \n", + "C)Maximum possible velocity is 1096.35 m/s\n" + ] + } + ], + "prompt_number": 15 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 2.9 page : 27" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "import math \n", + "\n", + "\t\t\t\t\n", + "#Input data\n", + "P1 = 2.45 \t\t\t\t#Inlet pressure in bar\n", + "T1 = 26.5+273 \t\t\t\t#Inlet temperature in K\n", + "M1 = 1.4 \t\t\t\t#Inlet mach number \n", + "M2 = 2.5 \t\t\t\t#Exit mach number\n", + "k = 1.3 \t\t\t\t#Adiabatic Consmath.tant\n", + "R = 469 \t\t\t\t#Specific gas consmath.tant in J/kg-K\n", + "\n", + "\t\t\t\t\n", + "#Calculation\n", + "t1 = 0.773 \t\t\t\t#Ratio of inlet temperature to Stagnation temperature from gas tables @M1,k = 1.3\n", + "To = T1/t1 \t\t\t\t#Stagnation temperature in K\n", + "t2 = 0.516 \t\t\t\t#Ratio of exit temperature to Stagnation temperature from isentropic gas tables @M2,k = 1.3\n", + "T2 = To*t2 \t\t\t\t#exit temperature in K\n", + "C2 = math.sqrt(k*R*T2)*M2 \t\t\t\t#Exit velocity in m/s\n", + "a1 = math.sqrt(k*R*T1) \t\t\t\t#Sound velocity at inlet in m/s\n", + "G = (P1*10**5*a1*M1)/(R*T1) \t\t\t\t#)Flow rate per square meter of the inlet cross section in kg/s-m**2\n", + "\n", + "\t\t\t\t\n", + "#Output\n", + "print 'A)Stagnation temperature is %3.2f K \\\n", + "\\nB)At Exit: \\\n", + "\\nTemperature is %3.3f K \\\n", + "\\nVelocity is %3.2f m/s \\\n", + "\\nC)Flow rate per square meter of the inlet cross section is %3.2f kg/s-m**2'%(To,T2,C2,G)\n" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "A)Stagnation temperature is 387.45 K \n", + "B)At Exit: \n", + "Temperature is 199.925 K \n", + "Velocity is 872.83 m/s \n", + "C)Flow rate per square meter of the inlet cross section is 1043.47 kg/s-m**2\n" + ] + } + ], + "prompt_number": 17 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 2.10 page : 27" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "import math \n", + "\n", + "\t\t\t\t\n", + "#Input data\n", + "Po = 1000 \t\t\t\t#Stagnation pressure in kPa\n", + "To = 800 \t\t\t\t#Stagnation temperature in K\n", + "k = 1.4 \t\t\t\t#Adiabatic Consmath.tant \n", + "M2 = 2 \t\t\t\t#Exit mach number\n", + "At = 20 \t\t\t\t#Throat area in cm**2 \n", + "R = 287 \t\t\t\t#Specific gas consmath.tant in J/kg-K\n", + "\n", + "\t\t\t\t\n", + "#Calculation\n", + "t1 = 0.834 \t\t\t\t#Ratio of critical temperature to Stagnation temperature from isentropic gas tables @M = 1,k = 1.4 \n", + "Tt = To*t1 \t\t\t\t#critical temperature in K\n", + "at = math.sqrt(k*R*Tt) \t\t\t\t#Velocity of sound at critical state in m/s\n", + "Ct = at \t\t\t\t#Velocity of air at critical state in m/s, Since M = 1\n", + "p1 = 0.528 \t\t\t\t#Ratio of critical pressure to Stagnation pressure from isentropic gas tables @M = 1,k = 1.4 \n", + "Pt = Po*p1 \t\t\t\t#Critical pressure in bar\n", + "dt = (Pt*10**3)/(R*Tt) \t\t\t\t#Density at critical state in kg/m**3, Pt in Pa\n", + "m = dt*At*10**-4*Ct \t\t\t\t#Mass flow rate in kg/s, At in m**2\n", + "p2 = 0.128 \t\t\t\t#Ratio of exit pressure to Stagnation pressure from isentropic gas tables @M2,k = 1.4\n", + "P2 = Po*p2 \t\t\t\t#exit pressure in kPa\n", + "t2 = 0.555 \t\t\t\t#Ratio of exit temperature to Stagnation temperature from isentropic gas tables @M2,k = 1.4\n", + "T2 = To*t2 \t\t\t\t#exit temperature in K\n", + "a2 = 1.687 \t\t\t\t#Ratio of exit area to critical area from isentropic gas tables @M2,k = 1.4\n", + "A2 = At*a2 \t\t\t\t#Exit area in cm**2\n", + "C2 = math.sqrt(k*R*T2)*M2 \t\t\t\t#Exit velocity in m/s\n", + "d2 = P2*10**3/(R*T2) \t\t\t\t#Density at exit in kg/m**3, P2 in Pa\n", + "\n", + "\t\t\t\t\n", + "#Output\n", + "print 'A)At throat: \\\n", + "\\nTemperature is %3.1f K \\\n", + "\\nVelocity is %3.2f m/s \\\n", + "\\nPressure is %3i kPa \\\n", + "\\nB)At Exit: \\\n", + "\\nTemperature is %3i K \\\n", + "\\nPressure is %3i kPa \\\n", + "\\nArea is %3.2f m**2 \\\n", + "\\nMass flow rate is %3.4f kg/s'%(Tt,Ct,Pt,T2,P2,A2,m)\n" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "A)At throat: \n", + "Temperature is 667.2 K \n", + "Velocity is 517.77 m/s \n", + "Pressure is 528 kPa \n", + "B)At Exit: \n", + "Temperature is 444 K \n", + "Pressure is 128 kPa \n", + "Area is 33.74 m**2 \n", + "Mass flow rate is 2.8553 kg/s\n" + ] + } + ], + "prompt_number": 19 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 2.11 page : 28" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "import math \n", + "\n", + "\t\t\t\t\n", + "#Input data\n", + "M2 = 2 \t\t\t\t#Exit mach number\n", + "At = 1000 \t\t\t\t#Throat area in cm**2 \n", + "Po = 0.69 \t\t\t\t#Stagnation pressure in bar \n", + "To = 310 \t\t\t\t#Stagnation temperature in K\n", + "k = 1.4 \t\t\t\t#Adiabatic Consmath.tant \n", + "R = 287 \t\t\t\t#Specific gas consmath.tant in J/kg-K\n", + "Cp = 1.005 \t\t\t\t#Specific heat capacity at consmath.tant pressure in kJ/kg-K \n", + "\n", + "\t\t\t\t\n", + "#Calculation\n", + "t1 = 0.834 \t\t\t\t#Ratio of critical temperature to Stagnation temperature from isentropic gas tables @M = 1,k = 1.4\n", + "Tt = To*t1 \t\t\t\t#critical temperature in K\n", + "at = math.sqrt(k*R*Tt) \t\t\t\t#Velocity of sound at critical state in m/s\n", + "Ct = at \t\t\t\t#Velocity of air at critical state in m/s, Since M = 1\n", + "p1 = 0.528 \t\t\t\t#Ratio of critical pressure to Stagnation pressure from isentropic gas tables @M = 1,k = 1.4 \n", + "Pt = Po*p1 \t\t\t\t#Critical pressure in bar\n", + "dt = (Pt*10**5)/(R*Tt) \t\t\t\t#Density at critical state in kg/m**3, Pt in Pa\n", + "m = dt*At*10**-4*Ct \t\t\t\t#Mass flow rate in kg/s, At in m**2\n", + "p2 = 0.128 \t\t\t\t#Ratio of exit pressure to Stagnation pressure from isentropic gas tables @M2,k = 1.4\n", + "P2 = Po*p2 \t\t\t\t#exit pressure in bar\n", + "t2 = 0.555 \t\t\t\t#Ratio of exit temperature to Stagnation temperature from isentropic gas tables @M2,k = 1.4\n", + "T2 = To*t2 \t\t\t\t#exit temperature in K\n", + "C2 = math.sqrt(k*R*T2)*M2 \t\t\t\t#Exit velocity in m/s\n", + "d2 = (P2*10**5)/(R*T2) \t\t\t\t#Density at exit in kg/m**3, P2 in Pa\n", + "A2 = (m/(d2*C2))*10**4 \t\t\t\t#Exit area in cm**2\n", + "P = m*Cp*(To-T2) \t\t\t\t#Power required to drive the compressor in kW\n", + "\n", + "\t\t\t\t\n", + "#Output\n", + "print 'A)At throat: \\\n", + "\\nTemperature is %3.2f K \\\n", + "\\nVelocity is %3.2f m/s \\\n", + "\\nPressure is %3.3f bar \\\n", + "\\nAt Test section: Temperature is %3.2f K \\\n", + "\\nVelocity is %3.3f m/s \\\n", + "\\nPressure is %3.3f bar \\\n", + "\\nB)Area of cross section at test section is %3i cm**2 \\\n", + "\\nC)Mass flow rate is %3.3f kg/s \\\n", + "\\nD)Power required to drive the compressor is %3.2f kW'%(Tt,Ct,Pt,T2,C2,P2,A2,m,P)\n", + "\n", + "# note : rounding off error." + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "A)At throat: \n", + "Temperature is 258.54 K \n", + "Velocity is 322.31 m/s \n", + "Pressure is 0.364 bar \n", + "At Test section: Temperature is 172.05 K \n", + "Velocity is 525.851 m/s \n", + "Pressure is 0.088 bar \n", + "B)Area of cross section at test section is 1682 cm**2 \n", + "C)Mass flow rate is 15.825 kg/s \n", + "D)Power required to drive the compressor is 2193.97 kW\n" + ] + } + ], + "prompt_number": 22 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 2.12 page : 30" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "import math \n", + "\n", + "\n", + "#Input data\n", + "Po = 10. \t\t\t\t#Stagnation pressure in bar \n", + "To = 100.+273 \t\t\t\t#Stagnation temperature in K\n", + "m = 15. \t\t\t\t#mass flow rate in kg/s\n", + "P2s = 1. \t\t\t\t#Back pressure in isentropic state in bar\n", + "eff = 0.95 \t\t\t\t#efficiency of diverging nozzle\n", + "k = 1.4 \t\t\t\t#Adiabatic Consmath.tant \n", + "R = 287. \t\t\t\t#Specific gas consmath.tant in J/kg-K\n", + "Cp = 1005. \t\t\t\t#Specific heat capacity at consmath.tant pressure in J/kg-K \n", + "\n", + "\n", + "#Calculation\n", + "#case I: isentropic\n", + "t1 = 0.834 \t\t\t\t#Ratio of critical temperature to Stagnation temperature from isentropic gas tables @M = 1,k = 1.4\n", + "Tt = To*t1 \t\t\t\t#critical temperature in K\n", + "at = math.sqrt(k*R*Tt) \t\t\t\t#Velocity of sound at critical state in m/s\n", + "Ct = at \t\t\t\t#Velocity of air at critical state in m/s, Since M = 1\n", + "p1 = 0.528 \t\t\t\t#Ratio of critical pressure to Stagnation pressure from isentropic gas tables @M = 1,k = 1.4 \n", + "Pt = Po*p1 \t\t\t\t#Critical pressure in bar\n", + "dt = (Pt*10**5)/(R*Tt) \t\t\t\t#Density at critical state in kg/m**3, Pt in Pa\n", + "At = (m/(dt*Ct))*10**4 \t\t\t\t#Throat area in cm**2 \n", + "p2 = P2s/Po \t\t\t\t#Pressure ratio\n", + "M2s = 2.15 \t\t\t\t#Exit mach number from gas tables (isentropic state) @p2,k = 1.4\n", + "t2 = 0.519 \t\t\t\t#Ratio of exit temperature to Stagnation temperature from isentropic gas tables @M2s,k = 1.4\n", + "T2s = t2*To \t\t\t\t#exit temperature in K\n", + "a2s = math.sqrt(k*R*T2s) \t\t\t\t#Velocity of sound at exit in m/s\n", + "C2s = M2s*a2s \t\t\t\t#Exit air velocity in m/s\n", + "d2s = (P2s*10**5)/(R*T2s) \t\t\t\t#Density at exit in kg/m**3, P2 in Pa\n", + "A2s = (m/(d2s*C2s))*10**4 \t\t\t\t#Exit area in cm**2\n", + "#case II: isentropic upto throat\n", + "T2 = To-(eff*(To-T2s)) \t\t\t\t#Exit tempareture in K\n", + "C2 = math.sqrt(2*Cp*(To-T2)) \t\t\t\t#Exit air velocity in m/s\n", + "P2 = P2s \t\t\t\t#Exit pressure in bar, Since it is diffuser\n", + "d2 = (P2*10**5)/(R*T2) \t\t\t\t#Density at exit in kg/m**3, P2 in Pa\n", + "A2 = (m/(d2*C2))*10**4 \t\t\t\t#Exit area in cm**2\n", + "\n", + "\n", + "#Output\n", + "print 'A)The nozzle cross section at throat in both cases is %3.2f cm**2 \\\n", + "\\nB)The nozzle cross section at exit in case I is %3.3f cm**2 and in case II is %3.2f cm**2'%(At,A2s,A2)\n", + "\n", + "# note : rounding off error." + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "A)The nozzle cross section at throat in both cases is 71.74 cm**2 \n", + "B)The nozzle cross section at exit in case I is 138.985 cm**2 and in case II is 148.98 cm**2\n" + ] + } + ], + "prompt_number": 25 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 2.13 page : 31" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "import math \n", + "\n", + "\t\t\t\t\n", + "#Input data\n", + "Po = 600. \t\t\t\t#Stagnation pressure in kPa\n", + "To = 40.+273 \t\t\t\t#Stagnation temperature in K\n", + "P2 = 100. \t\t\t\t#exit pressure in kPa\n", + "k = 1.4 \t\t\t\t#Adiabatic Consmath.tant \n", + "R = 287. \t\t\t\t#Specific gas consmath.tant in J/kg-K\n", + "\n", + "\t\t\t\t\n", + "#Calculation\n", + "p1 = P2/Po \t\t\t\t#pressure ratio \n", + "M2 = 1.82 \t\t\t\t#Exit mach number from gas tables @p2,k = 1.4\n", + "ar = 1.461 \t\t\t\t#Ratio of nozzle exit area to nozzle throat area from gas tables @M2\n", + "t1 = 0.602 \t\t\t\t#Ratio of exit temperature to Stagnation temperature from isentropic gas tables @M2,k = 1.4\n", + "T2 = To*t1 \t\t\t\t#exit temperature in K\n", + "C2 = math.sqrt(k*R*T2)*M2 \t\t\t\t#Exit air velocity in m/s\n", + "p2 = 3.698 \t\t\t\t#Ratio of static pressures after shock to before shock from normal shock gas tables @M2 \n", + "Py = p2*P2 \t\t\t\t#The back pressure at which normal shock acts at the exit plane of the nozzle in kPa\n", + "\n", + "\t\t\t\t\n", + "#Output\n", + "print 'A)Ratio of nozzle exit area to nozzle throat area is %3.3f \\\n", + "\\nB)The discharge velocity from nozzle is %3.2f m/s \\\n", + "\\nC)The back pressure at which normal shock acts at the exit plane of the nozzle is %3.1f kPa'%(ar,C2,Py)\n" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "A)Ratio of nozzle exit area to nozzle throat area is 1.461 \n", + "B)The discharge velocity from nozzle is 500.78 m/s \n", + "C)The back pressure at which normal shock acts at the exit plane of the nozzle is 369.8 kPa\n" + ] + } + ], + "prompt_number": 27 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 2.14 page : 32" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "import math \n", + "\n", + "\t\t\t\t\n", + "#Input data\n", + "ar = 2. \t\t\t\t#Ratio of nozzle exit area to nozzle throat area\n", + "Po = 700. \t\t\t\t#Stagnation pressure in kPa\n", + "P2 = 400. \t\t\t\t#exit pressure in kPa\n", + "\n", + "\t\t\t\t\n", + "#Calculation\n", + "p1 = 0.528 \t\t\t\t#Ratio of critical pressure to Stagnation pressure from gas tables @M = 1\n", + "Pt = Po*p1 \t\t\t\t#critical pressure in bar\n", + "p2 = P2/Po \t\t\t\t#Pressure ratio\n", + "M2 = 0.93 \t\t\t\t#Exit mach number from gas tables @p2,k = 1.4\n", + "\n", + "\t\t\t\t\n", + "#Output\n", + "print 'Since pressure decreases from %3i kPa to %3.1f kPa from inlet to throat, \\\n", + "\\nit acts as nozzle Since exit pressure %3i kPa is above critical pressure %3.1f kPa, \\\n", + "\\nit acts as diffuser with M = %3.2f Hence the duct acts as Venturi'%(Po,Pt,P2,Pt,M2)\n" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "Since pressure decreases from 700 kPa to 369.6 kPa from inlet to throat, \n", + "it acts as nozzle Since exit pressure 400 kPa is above critical pressure 369.6 kPa, \n", + "it acts as diffuser with M = 0.93 Hence the duct acts as Venturi\n" + ] + } + ], + "prompt_number": 29 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 2.15 page : 33" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "import math \n", + "\n", + "\t\t\t\t\n", + "#Input data\n", + "A1 = 0.15 \t\t\t\t#Inlet area in m**2\n", + "C1 = 240 \t\t\t\t#Inlet velocity in m/s \n", + "T1 = 300 \t\t\t\t#Inlet temperature in K\n", + "P1 = 0.7 \t\t\t\t#Inlet pressure in bar\n", + "C2 = 120 \t\t\t\t#Exit velocity in m/s\n", + "k = 1.4 \t\t\t\t#Adiabatic Consmath.tant\n", + "R = 287 \t\t\t\t#Specific gas consmath.tant in J/kg-K\n", + "Cp = 1005 \t\t\t\t#Specific heat capacity at consmath.tant pressure in J/kg-K \n", + "\n", + "\t\t\t\t\n", + "#Calculations\n", + "a1 = math.sqrt(k*R*T1) \t\t\t\t#Velocity of sound at inlet in m/s\n", + "M1 = C1/a1 \t\t\t\t#Inlet mach number \n", + "d1 = (P1*10**5)/(R*T1) \t\t\t\t#Density at inlet in kg/s, P1 in Pa\n", + "m = d1*A1*C1 \t\t\t\t#Mass flow rate in kg/s\n", + "t1 = 0.913 \t\t\t\t#Ratio of inlet temperature to Stagnation temperature from gas tables @M1,k = 1.4\n", + "To = T1/t1 \t\t\t\t#Stagnation temperature in K\n", + "p1 = 0.727 \t\t\t\t#Ratio of inlet pressure to Stagnation pressure from gas tables @M1,k = 1.4\n", + "Po = P1/p1 \t\t\t\t#Stagnation pressure in bar\n", + "T2 = To-(C2**2/(2*Cp)) \t\t\t\t#Exit temperature in K\n", + "t2 = T2/To \t\t\t\t#Temperature ratio \n", + "M2 = 0.33 \t\t\t\t#Exit mach number from gas tables @t2,k = 1.4\n", + "p2 = 0.927 \t\t\t\t#Ratio of exit pressure to Stagnation pressure from isentropic gas tables @M2,k = 1.4\n", + "P2 = Po*p2 \t\t\t\t#exit pressure in bar\n", + "d2 = (P2*10**5)/(R*T2) \t\t\t\t#Density at exit in kg/s, P2 in Pa\n", + "A2 = (m/(d2*C2)) \t\t\t\t#Exit area in m**2\n", + "ds = 0 \t\t\t\t#Entropy change in kJ/kg-K, math.since process is isentropic\n", + "\n", + "\t\t\t\t\n", + "#Output\n", + "print 'A)Mass flow rate is %3.3f kg/s \\\n", + "\\nB)Stagnation pressure at exit is %3.4f bar \\\n", + "\\nC)Stagnation Temperature at exit is %3.3f K \\\n", + "\\nD)Static exit pressure is %3.3f bar \\\n", + "\\nE)Entropy change is %3i kJ/kg-K \\\n", + "\\nF)Exit area is %3.3f m**2'%(m,Po,To,P2,ds,A2)\n" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "A)Mass flow rate is 29.268 kg/s \n", + "B)Stagnation pressure at exit is 0.9629 bar \n", + "C)Stagnation Temperature at exit is 328.587 K \n", + "D)Static exit pressure is 0.893 bar \n", + "E)Entropy change is 0 kJ/kg-K \n", + "F)Exit area is 0.252 m**2\n" + ] + } + ], + "prompt_number": 33 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 2.16 page : 34" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "import math \n", + "\n", + "\t\t\t\t\n", + "#Input data\n", + "A2 = 645. \t\t\t\t#Exit area in mm**2\n", + "M2 = 2. \t\t\t\t#Exit mach number\n", + "P2 = 1. \t\t\t\t#exit pressure in bar\n", + "T2 = 185. \t\t\t\t#Exit temperature in K\n", + "k = 1.4 \t\t\t\t#Adiabatic Consmath.tant\n", + "R = 287. \t\t\t\t#Specific gas consmath.tant in J/kg-K\n", + "\n", + "\t\t\t\t\n", + "#Calculation\n", + "t1 = 0.555 \t\t\t\t#Ratio of exit temperature to Stagnation temperature from gas tables @M2,k = 1.4\n", + "To = T2/t1 \t\t\t\t#Stagnation temperature in K\n", + "p1 = 0.128 \t\t\t\t#Ratio of exit pressure to Stagnation pressure from isentropic gas tables @M2,k = 1.4\n", + "Po = P2/p1 \t\t\t\t#Stagnation pressure in bar\n", + "a1 = 1.687 \t\t\t\t#Ratio of exit area to critical area from isentropic gas tables @M2,k = 1.4\n", + "At = A2/a1 \t\t\t\t#Critical area in mm**2\n", + "d2 = (P2*10**5)/(R*T2) \t\t\t\t#Density at exit in kg/s, P2 in Pa\n", + "C2 = math.sqrt(k*R*T2)*M2 \t\t\t\t#Exit air velocity in m/s\n", + "m = d2*A2*C2*10**-6 \t\t\t\t#Mass flow rate in kg/s, A2 in m**2\n", + "\n", + "\t\t\t\t\n", + "#Output\n", + "print 'A)Throat area is %3.2f mm**2 \\\n", + "\\nB)Reservoir pressure is %3.4f bar \\\n", + "\\nC)Reservoir temperature is %3.2f K \\\n", + "\\nD)Mass flow rate is %3.4f kg/s'%(At,Po,To,m)\n" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "A)Throat area is 382.34 mm**2 \n", + "B)Reservoir pressure is 7.8125 bar \n", + "C)Reservoir temperature is 333.33 K \n", + "D)Mass flow rate is 0.6624 kg/s\n" + ] + } + ], + "prompt_number": 35 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 2.17 page : 34" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "import math \n", + "\n", + "\t\t\t\t\n", + "#Input data\n", + "Po = 20. \t\t\t\t#Stagnation pressure in kPa\n", + "To = 1000. \t\t\t\t#Stagnation temperature in K\n", + "P2 = 3. \t\t\t\t#exit pressure in bar\n", + "A2 = 100. \t\t\t\t#Exit area in cm**2\n", + "k = 1.4 \t\t\t\t#Adiabatic Consmath.tant\n", + "R = 287. \t\t\t\t#Specific gas consmath.tant in J/kg-K\n", + "Cp = 1005. \t\t\t\t#Specific heat capacity at consmath.tant pressure in J/kg-K \n", + "\n", + "\t\t\t\t\n", + "#Calculations\n", + "p1 = P2/Po \t\t\t\t#Pressure ratio\n", + "M2 = 1.9 \t\t\t\t#Exit mach number from gas tables @p1,k = 1.4\n", + "t1 = 0.581 \t\t\t\t#Ratio of exit temperature to Stagnation temperature from isentropic gas tables @M2,k = 1.4 \n", + "T2 = To*t1 \t\t\t\t#exit temperature in K\n", + "C2 = M2*math.sqrt(k*R*T2) \t\t\t\t#Exit velocity in m/s\n", + "a1 = 1.555 \t\t\t\t#Ratio of exit area to critical area from isentropic gas tables @M2,k = 1.4\n", + "At = A2/a1 \t\t\t\t#critical area in cm**2\n", + "p1 = 0.528 \t\t\t\t#Ratio of critical pressure to Stagnation pressure from gas tables @M = 1\n", + "Pt = Po*p1 \t\t\t\t#critical pressure in bar\n", + "t1 = 0.834 \t\t\t\t#Ratio of critical temperature to Stagnation temperature from gas tables @M = 1\n", + "Tt = To*t1 \t\t\t\t#critical temperature in K\n", + "at = math.sqrt(k*R*Tt) \t\t\t\t#Sound velocity at throat in m/s \n", + "Ct = at \t\t\t\t#Air velocity t throat in m/s, Since M = 1\n", + "dt = (Pt*10**5)/(R*Tt) \t\t\t\t#Density of air at throat in kg/m**3, Pt in Pa\n", + "m = dt*At*10**-4*Ct \t\t\t\t#Mass flow rate in kg/s, At in m**2\n", + "C_max = math.sqrt(2*Cp*To) \t\t\t\t#Maximum possible velocity in m/s\n", + "cr = C2/C_max \t\t\t\t#Ratio of velocities\n", + "\n", + "\t\t\t\t\n", + "#Output\n", + "print 'A)At Throat: \\\n", + "\\nArea is %3.2f cm**2 \\\n", + "\\nPressure is %3.2f bar \\\n", + "\\nTemperature is %3i K \\\n", + "\\nB)Exit velocity is %3.4f times C_max in m/s \\\n", + "\\nC)Mass flow rate is %3.2f kg/s'%(At,Pt,Tt,cr,m)\n" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "A)At Throat: \n", + "Area is 64.31 cm**2 \n", + "Pressure is 10.56 bar \n", + "Temperature is 834 K \n", + "B)Exit velocity is 0.6475 times C_max in m/s \n", + "C)Mass flow rate is 16.42 kg/s\n" + ] + } + ], + "prompt_number": 37 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 2.18 page : 35" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "import math \n", + "\n", + "\t\t\t\t\n", + "#Input data\n", + "Po = 7. \t\t\t\t#Stagnation pressure in bar\n", + "To = 100.+273 \t\t\t\t#Stagnation temperature in K\n", + "At = 12. \t\t\t\t#Critical area in cm**2\n", + "A2 = 25.166 \t\t\t\t#Exit area in cm**2\n", + "k = 1.4 \t\t\t\t#Adiabatic Consmath.tant\n", + "R = 287. \t\t\t\t#Specific gas consmath.tant in J/kg-K\n", + "\n", + "\t\t\t\t\n", + "#Calculation\n", + "a1 = A2/At \t\t\t\t#Ratio of areas\n", + "\t\t\t\t#subsonic\n", + "M2 = 0.29 \t\t\t\t#Exit mach number from gas tables @a1,k = 1.4\n", + "p1 = 0.943 \t\t\t\t#Ratio of exit pressure to Stagnation pressure from isentropic gas tables @M2,k = 1.4\n", + "P2 = Po*p1 \t\t\t\t#exit pressure in bar\n", + "t1 = 0.983 \t\t\t\t#Ratio of exit temperature to Stagnation temperature from gas tables @M2,k = 1.4\n", + "T2 = To*t1 \t\t\t\t#Exit temperature in K\n", + "C2 = M2*math.sqrt(k*R*T2) \t\t\t\t#Exit air velocity in m/s\n", + "\t\t\t\t#supersonic\n", + "M_2 = 2.25 \t\t\t\t#Exit mach number from gas tables @a1,k = 1.4\n", + "p2 = 0.0865 \t\t\t\t#Ratio of exit pressure to Stagnation pressure from isentropic gas tables @M2,k = 1.4\n", + "P_2 = Po*p2 \t\t\t\t#exit pressure in bar\n", + "t2 = 0.497 \t\t\t\t#Ratio of exit temperature to Stagnation temperature from gas tables @M2,k = 1.4\n", + "T_2 = To*t2 \t\t\t\t#Exit temperature in K\n", + "C_2 = M_2*math.sqrt(k*R*T_2) \t\t\t\t#Exit air velocity in m/s\n", + "d2 = (P2*10**5)/(R*T2) \t\t\t\t#Density at exit in kg/s, P2 in Pa\n", + "m = d2*A2*10**-4*C2 \t\t\t\t#Mass flow rate in kg/s, A2 in m**2\n", + "\n", + "\t\t\t\t\n", + "#Output\n", + "print 'A)Maximum mass flow rate is %3.3f kg/s \\\n", + "\\nB)Subsonic exit condition: \\\n", + "\\nTemperature is %3.3f K \\\n", + "\\nVelocity is %3.2f m/s \\\n", + "\\nPressure is %3.3f bar \\\n", + "\\nMach number is %3.2f \\\n", + "\\nSupersonic exit condition: \\\n", + "\\nTemperature is %3.3f K \\\n", + "\\nVelocity is %3.2f m/s \\\n", + "\\nPressure is %3.4f bar \\\n", + "\\nMach number is %3.2f'%(m,T2,C2,P2,M2,T_2,C_2,P_2,M_2)\n" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "A)Maximum mass flow rate is 1.757 kg/s \n", + "B)Subsonic exit condition: \n", + "Temperature is 366.659 K \n", + "Velocity is 111.31 m/s \n", + "Pressure is 6.601 bar \n", + "Mach number is 0.29 \n", + "Supersonic exit condition: \n", + "Temperature is 185.381 K \n", + "Velocity is 614.07 m/s \n", + "Pressure is 0.6055 bar \n", + "Mach number is 2.25\n" + ] + } + ], + "prompt_number": 39 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 2.19 page : 36" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "import math \n", + "\n", + "\t\t\t\t\n", + "#Input data\n", + "T1 = 335. \t\t\t\t#Inlet temperature in K\n", + "P1 = 655. \t\t\t\t#Inlet pressure in kPa\n", + "C1 = 150. \t\t\t\t#Inlet velocity in m/s\n", + "P2 = 138. \t\t\t\t#Exit pressure in kPa\n", + "T2 = 222. \t\t\t\t#Exit temperature in K\n", + "m = 9. \t\t\t\t#Mass flow rate in kg/s\n", + "Mol = 32. \t\t\t\t#Molar mass of oxygen in kg/mol\n", + "Ri = 8314. \t\t\t\t#Ideal gas consmath.tant in J/kg-k\n", + "k = 1.4 \t\t\t\t#Adiabatic Consmath.tant\n", + "Cp = 915. \t\t\t\t#Specific heat capacity at consmath.tant pressure in J/kg-K \n", + "\n", + "\t\t\t\t\n", + "#Calculation\n", + "R = Ri/Mol \t\t\t\t#Specific gas consmath.tant in J/kg-K\n", + "a1 = math.sqrt(k*R*T1) \t\t\t\t#Sound velocity at inlet in m/s \n", + "M1 = C1/a1 \t\t\t\t#Inlet mach number\n", + "t1 = 0.964 \t\t\t\t#Ratio of inlet temperature to Stagnation temperature from gas tables @M1,k = 1.4\n", + "To1 = T1/t1 \t\t\t\t#Stagnation temperature at inlet in K\n", + "p1 = 0.881 \t\t\t\t#Ratio of inlet pressure to Stagnation pressure at entry from gas tables @M1,k = 1.4 \n", + "Po1 = P1/p1 \t\t\t\t#Stagnation pressure at entry in kPa\n", + "t2 = 0.834 \t\t\t\t#Ratio of critical temperature to Stagnation temperature from gas tables @M = 1\n", + "Tt = To1*t2 \t\t\t\t#critical temperature in K\n", + "C2 = math.sqrt(C1**2+(2*Cp*(T1-T2))) \t\t\t\t#Exit velocity in m/s, \n", + "a2 = math.sqrt(k*R*T2) \t\t\t\t#Sound velocity at exit in m/s \n", + "M2 = C2/a2 \t\t\t\t#Exit mach number \n", + "p2 = 0.208 \t\t\t\t#Ratio of exit pressure to Stagnation pressure at exit from isentropic gas tables @M2,k = 1.4\n", + "Po2 = P2/p2 \t\t\t\t#Stagnation pressure at exit in kPa\n", + "SPC = (Po1-Po2) \t\t\t\t#Change in the stagnation pressure between inlet and exit in kPa\n", + "ds = R*math.log(Po1/Po2) \t\t\t\t#Change in entropy in J/kg-K\n", + "T2s = T1*((P2/P1)**((k-1)/k)) \t\t\t\t#Exit temperature at isentropic state in K\n", + "eff = ((T1-T2)/(T1-T2s))*100 \t\t\t\t#Nozzle efficiency in percent\n", + "\n", + "\t\t\t\t\n", + "#Output\n", + "print 'A)Exit mach number is %3.2f \\\n", + "\\nB)Change in the stagnation pressure between inlet and exit is %3.2f kPa \\\n", + "\\nC)Change in entropy is %3.3f J/kg-K \\\n", + "\\nD)Static temperature at throat is %3.1f K \\\n", + "\\nE)Nozzle efficiency is %3.2f percent'%(M2,SPC,ds,Tt,eff)\n", + "\n", + "# note : rounding off error." + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "A)Exit mach number is 1.69 \n", + "B)Change in the stagnation pressure between inlet and exit is 80.01 kPa \n", + "C)Change in entropy is 29.583 J/kg-K \n", + "D)Static temperature at throat is 289.8 K \n", + "E)Nozzle efficiency is 93.92 percent\n" + ] + } + ], + "prompt_number": 42 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 2.20 page : 37" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "import math \n", + "\n", + "\t\t\t\t\n", + "#Input data\n", + "C1 = 200. \t\t\t\t#Inlet velocity in m/s\n", + "Po1 = 400. \t\t\t\t#Stagnation pressure at entry in kPa\n", + "To1 = 500. \t\t\t\t#Stagnation temperature at inlet in K\n", + "C2 = 100. \t\t\t\t#Exit velocity in m/s\n", + "eff = 0.9 \t\t\t\t#Nozzle efficiency \n", + "k = 1.4 \t\t\t\t#Adiabatic Consmath.tant\n", + "Cp = 1005. \t\t\t\t#Specific heat capacity at consmath.tant pressure in J/kg-K \n", + "\n", + "\t\t\t\t\n", + "#Calculation\n", + "T1 = To1-(C1**2/(2*Cp)) \t\t\t\t#Inlet temperature in K\n", + "t1 = T1/To1 \t\t\t\t#Temperature ratio \n", + "P1 = Po1*t1**(k/(k-1)) \t\t\t\t#Inlet pressure in kPa\n", + "To2s = (eff*(To1-T1))+T1 \t\t\t\t#Exit Stagnation temperature at isentropic state in K\n", + "To2 = To2s \t\t\t\t#Exit Stagnation temperature in K, Since adiabatic \n", + "T2 = To2-(C2**2/(2*Cp)) \t\t\t\t#Exit temperature in K\n", + "t2 = To2s/T1 \t\t\t\t#Temperature ratio \n", + "Po2 = P1*t2**(k/(k-1)) \t\t\t\t#Stagnation pressure at exit in kPa\n", + "t3 = T2/To2 \t\t\t\t#Temperature ratio \n", + "P2 = Po2*t3**(k/(k-1)) \t\t\t\t#Exit pressure in kPa\n", + "Cpr = (P2-P1)/(Po1-P1) \t\t\t\t#Pressure raise coefficient\n", + "ar = (P1*T2*C1)/(P2*T1*C2) \t\t\t\t#Ratio of exit to inlet area\n", + "\n", + "\t\t\t\t\n", + "#Output\n", + "print 'A)Pressure raise coefficient is %3.3f \\\n", + "\\nB)Ratio of exit to inlet area is %3.3f'%(Cpr,ar)\n" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "A)Pressure raise coefficient is 0.638 \n", + "B)Ratio of exit to inlet area is 1.871\n" + ] + } + ], + "prompt_number": 44 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 2.21 page : 38" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "import math \n", + "\n", + "\t\t\t\t\n", + "#Input data\n", + "Po1 = 4.9 \t\t\t\t#Stagnation pressure at entry in bar\n", + "P2 = 1.4 \t\t\t\t#Exit pressure in bar\n", + "To = 810 \t\t\t\t#Stagnation temperature in K\n", + "m = 1 \t\t\t\t#Mass flow rate in kg/s\n", + "eff = 0.9 \t\t\t\t#Nozzle efficiency \n", + "k = 1.4 \t\t\t\t#Adiabatic Consmath.tant\n", + "R = 287 \t\t\t\t#Specific gas consmath.tant in J/kg-K\n", + "Cp = 1005 \t\t\t\t#Specific heat capacity at consmath.tant pressure in J/kg-K \n", + "\n", + "\t\t\t\t\n", + "#Calculations\n", + "t1 = 0.834 \t\t\t\t#Ratio of critical temperature to Stagnation temperature from gas tables @M = 1\n", + "Tt = To*t1 \t\t\t\t#critical temperature in K\n", + "at = math.sqrt(k*R*Tt) \t\t\t\t#Sound velocity at critical state in m/s \n", + "Ct = at \t\t\t\t#Air velocity t throat in m/s, Since M = 1\n", + "p1 = 0.528 \t\t\t\t#Ratio of critical pressure to Stagnation pressure from gas tables @M = 1\n", + "Pt = Po1*p1 \t\t\t\t#critical pressure in bar\n", + "dt = (Pt*10**5)/(R*Tt) \t\t\t\t#Density of air at throat in kg/m**3, Pt in Pa\n", + "At = (m/(dt*Ct))*10**4 \t\t\t\t#Throat area in cm**2 \n", + "p2 = P2/Po1 \t\t\t\t#Pressure ratio\n", + "T2s = To*p2**((k-1)/k) \t\t\t\t#Exit temperature in K (at isentropic state)\n", + "T2 = To-(eff*(To-T2s)) \t\t\t\t#Exit temperature in K\n", + "d2 = (P2*10**5)/(R*T2) \t\t\t\t#Density at exit in kg/m**3, P2 in Pa\n", + "C2 = math.sqrt(2*Cp*(To-T2)) \t\t\t\t#Exit air velocity in m/s\n", + "A2 = (m/(d2*C2))*10**4 \t\t\t\t#Exit area in cm**2\n", + "a2 = math.sqrt(k*R*T2) \t\t\t\t#Sound velocity at exit in m/s \n", + "M2 = C2/a2 \t\t\t\t#Exit mach number\n", + "p3 = 0.332 \t\t\t\t#Static to stagnation pressure ratio at exit from isentropic gas tables @M2,k = 1.4 \n", + "Po2 = P2/p3 \t\t\t\t#stagnation pressure in bar\n", + "TPL = Po1-Po2 \t\t\t\t#Loss in total pressure is %3.3f bar\n", + "ds = R*math.log(Po1/Po2) \t\t\t\t#Increase in entropy in kJ/kg-K\n", + "\n", + "\t\t\t\t\n", + "#Output\n", + "print 'A)Throat and exit area are %3.2f cm**2 and %3.3f cm**2 \\\n", + "\\nB)Exit mach number is %3.2f \\\n", + "\\nC)Loss in total pressure is %3.3f bar \\\n", + "\\nD)Increase in entropy is %3.2f kJ/kg-K'%(At,A2,M2,TPL,ds)\n" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "A)Throat and exit area are 14.38 cm**2 and 18.236 cm**2 \n", + "B)Exit mach number is 1.36 \n", + "C)Loss in total pressure is 0.683 bar \n", + "D)Increase in entropy is 43.09 kJ/kg-K\n" + ] + } + ], + "prompt_number": 46 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 2.22 page : 40" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "import math \n", + "\n", + "\t\t\t\t\n", + "#Input data\n", + "Po = 3.5 \t\t\t\t#Stagnation pressure in bar\n", + "To = 425.+273 \t\t\t\t#Stagnation temperature in K\n", + "P2 = 0.97 \t\t\t\t#Exit pressure in bar\n", + "m = 18. \t\t\t\t#Mass flow rate in kg/s\n", + "Kd = 0.99 \t\t\t\t#Coefficient of discharge\n", + "eff = 0.94 \t\t\t\t#Nozzle efficiency \n", + "k = 1.33 \t\t\t\t#Adiabatic Consmath.tant\n", + "Cp = 1110. \t\t\t\t#Specific heat capacity at consmath.tant pressure in J/kg-K \n", + "\n", + "\t\t\t\t\n", + "#Calculations \n", + "Pt = Po*(2/(k+1))**(k/(k-1)) \t\t\t\t#critical pressure in bar\n", + "Tt = To*(2/(k+1)) \t\t\t\t#critical temperature in K\n", + "R = Cp/(k/(k-1)) \t\t\t\t#Specific gas consmath.tant in J/kg-K\n", + "m_s = m/Kd \t\t\t\t#Isentropic mass\n", + "at = math.sqrt(k*R*Tt) \t\t\t\t#Sound velocity at throat in m/s\n", + "Ct = at \t\t\t\t#Air velocity t throat in m/s, Since M = 1\n", + "dt = (Pt*10**5)/(R*Tt) \t\t\t\t#Density of air at throat in kg/m**3, Pt in Pa\n", + "At = (m_s/(dt*Ct))*10**4 \t\t\t\t#Throat area in cm**2 \n", + "p2 = P2/Po \t\t\t\t#Pressure ratio\n", + "T2s = To*p2**(1/(k/(k-1))) \t\t\t\t#Exit temperature in K (at isentropic state)\n", + "T2 = To-(eff*(To-T2s)) \t\t\t\t#Exit temperature in K\n", + "d2 = (P2*10**5)/(R*T2) \t\t\t\t#Density at exit in kg/m**3, P2 in Pa\n", + "C2 = math.sqrt(2*Cp*(To-T2)) \t\t\t\t#Exit air velocity in m/s\n", + "A2 = (m_s/(d2*C2))*10**4 \t\t\t\t#Exit area in cm**2\n", + "\n", + "\t\t\t\t\n", + "#Output\n", + "print 'Throat area and Exit area of nozzle are %3.1f cm**2 and %3.1f cm**2'%(At,A2)\n", + "\n", + "# note : rounding off error." + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "Throat area and Exit area of nozzle are 338.6 cm**2 and 425.2 cm**2\n" + ] + } + ], + "prompt_number": 49 + } + ], + "metadata": {} + } + ] +}
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