{ "metadata": { "name": "", "signature": "sha256:e77c793709c88cc39a2de404e997a6f1eed32d352c214c1580d822fd7a5a83a2" }, "nbformat": 3, "nbformat_minor": 0, "worksheets": [ { "cells": [ { "cell_type": "heading", "level": 1, "metadata": {}, "source": [ "Chapter 17: COMPRESSIBLE FLOW" ] }, { "cell_type": "heading", "level": 2, "metadata": {}, "source": [ "Ex17.1:PG-710" ] }, { "cell_type": "code", "collapsed": false, "input": [ "#ques1\n", "#to determine isentropic stagnation pressure and temperature \n", "\n", "T=300;#Temperature of air in K\n", "P=150;#Pressure of air in kPa\n", "v=200;#velocity of air flow n m/s\n", "Cp=1.004;#specific heat at constant pressure in kJ/kg\n", "To=v**2/(2000*Cp)+T;#stagnation temperature in K\n", "k=1.4;#constant\n", "Po=P*(To/T)**(k/(k-1));#stagnation pressure in kPa\n", "print 'Stagnation Temperature is ',round(To,1),' K \\n'\n", "print 'Stagnation Pressure is ',round(Po,2),'kPa \\n'" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "Stagnation Temperature is 319.9 K \n", "\n", "Stagnation Pressure is 187.85 kPa \n", "\n" ] } ], "prompt_number": 5 }, { "cell_type": "heading", "level": 2, "metadata": {}, "source": [ "Ex17.2:PG-713" ] }, { "cell_type": "code", "collapsed": false, "input": [ "#ques2\n", "#to determine the force\n", "\n", "#initializing variables\n", "mdot=-1 # mass flow rate out of control volume in kg/s\n", "Vx=-1 # x component of velocity of control volume in m/s\n", "Vy=10 # y component of velocity of control volume in m/s\n", "\n", "Fx=mdot*Vx # Force in X direction\n", "\n", "Fy=mdot*Vy # Force in Y direction\n", "\n", "print \"the force the man exert on the wheelbarrow\",round(Fx),\"N\"\n", "print \"the force the floor exerts on the wheelbarrow\",round(Fy),\"N\"\n", "\n", "\n" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "the force the man exert on the wheelbarrow 1.0 N\n", "the force the floor exerts on the wheelbarrow -10.0 N\n" ] } ], "prompt_number": 6 }, { "cell_type": "heading", "level": 2, "metadata": {}, "source": [ "Ex17.3:PG-715" ] }, { "cell_type": "code", "collapsed": false, "input": [ "#ques3\n", "#determining the thrust acting on a control surface\n", "\n", "#i-inlet\n", "#e-exit\n", "#using momentum equation on control surface in x direction\n", "me=20.4;#mass exiting in kg\n", "mi=20;#mass entering in kg\n", "ve=450;#exit velocity in m/s\n", "vi=100;#inlet velocity in m/s\n", "Pi=95;#Pressure at inlet in kPa\n", "Pe=125;#Pressure at exit in kPa\n", "Po=100;#surrounding pressure in kPa\n", "Ai=0.2;#inlet area in m^2\n", "Ae=0.1;#exit area in m^2\n", "Rx=(me*ve-mi*vi)/1000-(Pi-Po)*Ai+(Pe-Po)*Ae;#thrust in x direction in kN\n", "\n", "print \"Thrust acting in x direction is \",round(Rx,2),\"kN\"" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "Thrust acting in x direction is 10.68 kN\n" ] } ], "prompt_number": 11 }, { "cell_type": "heading", "level": 2, "metadata": {}, "source": [ "Ex17.4:PG-717" ] }, { "cell_type": "code", "collapsed": false, "input": [ "#ques4\n", "#to determine increase in enthalpy\n", "#initializing variables\n", "#i-inlet\n", "#e-exit\n", "\n", "T=25+273 # temperature in kelvin\n", "v=0.001003 # specific volume of water in kg/m^3 at 25 *c from table B.1.1 \n", "ve=7;#exit velocity in m/s\n", "vi=30;#inlet velocity in m/s\n", "Pi=350;#Pressure at inlet in kPa\n", "Pe=600;#Pressure at exit in kPa\n", "\n", "#using momentum equation on control surface \n", "Pes= (vi**2-ve**2)/(2*v*1000)+Pi # exit pressure for reversible diffuser\n", "delH=(vi**2-ve**2)/(2*1000.0) # change in enthalpy from first law in kJ/kg\n", "delU=delH-v*(Pe-Pi) # change in internal energy in kJ/kg\n", "delS=delU/T # change in entropy in kJ/kg.K\n", "print\"the exit pressure for reversible diffuser is \",round(Pes),\"kPa\"\n", "print\"the increase in enthalpy is \",round(delH,5),\"kJ/kg\"\n", "print\"the increase in internal energy is \",round(delU,5),\"kJ/kg\"\n", "print\"the increase in entropy is \",round(delS,6),\"kJ/kg.K\"\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "the exit pressure for reversible diffuser is 774.0 kPa\n", "the increase in enthalpy is 0.4255 kJ/kg\n", "the increase in internal energy is 0.17475 kJ/kg\n", "the increase in entropy is 0.000586 kJ/kg.K\n" ] } ], "prompt_number": 19 }, { "cell_type": "heading", "level": 2, "metadata": {}, "source": [ "Ex17.5:PG-720" ] }, { "cell_type": "code", "collapsed": false, "input": [ "#ques5\n", "#determining velocity of sound in air\n", "import math\n", "k=1.4;#constant\n", "R=0.287;#gas constant\n", "#at 300K\n", "T1=300;# temperature in kelvin\n", "c1=math.sqrt(k*R*T1*1000)\n", "print \"Speed of sound at 300 K is\",round(c1,1),\" m/s\" \n", "#at 1000K\n", "T2=1000;# temperature in kelvin\n", "c2=math.sqrt(k*R*T2*1000)\n", "print \"Speed of sound at 1000 K is\",round(c2,1),\" m/s\"" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "Speed of sound at 300 K is 347.2 m/s\n", "Speed of sound at 1000 K is 633.9 m/s\n" ] } ], "prompt_number": 24 }, { "cell_type": "heading", "level": 2, "metadata": {}, "source": [ "Ex17.6:PG-727" ] }, { "cell_type": "code", "collapsed": false, "input": [ "#ques6\n", "#determining mass flow rate through control volume\n", "import math\n", "k=1.4;#constant\n", "R=0.287;#gas constant\n", "To=360;#stagnation Temperature in K \n", "T=To*0.8333;#Temperature of air in K, 0.8333 stagnation ratio from table\n", "v=math.sqrt(k*R*T*1000);#velocity in m/s\n", "P=528;#stagnation pressure in kPa\n", "d=P/(R*T);#stagnation density in kg/m^3\n", "A=500*10**-6;#area in m^2\n", "ms=d*A*v;#mass flow rate in kg/s\n", "print\" Mass flow rate at the throat section is\",round(ms,4),\"kg/s\"\n", "#e-exit state\n", "Te=To*0.9381;#exit temperature in K, ratio from table\n", "ce=math.sqrt(k*R*Te*1000);#exit velocity of sound in m/s\n", "Me=0.573;#Mach number\n", "ve=Me*ce;\n", "Pe=800;#exit pressure in kPa\n", "de=Pe/R/Te;\n", "mse=de*A*ve;\n", "print\" Mass flow rate at the exit section is\",round(mse,4),\" kg/s\"" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ " Mass flow rate at the throat section is 1.0646 kg/s\n", " Mass flow rate at the exit section is 0.8711 kg/s\n" ] } ], "prompt_number": 30 }, { "cell_type": "heading", "level": 2, "metadata": {}, "source": [ "Ex17.7:PG-728" ] }, { "cell_type": "code", "collapsed": false, "input": [ "#ques7\n", "#determining exit properties in a control volume\n", "import math\n", "Po=1000;#stagnation pressure in kPa\n", "To=360;#stagnation temperature in K\n", "\n", "#when diverging section acting as nozzle\n", "\n", "Pe1=0.0939*Po;#exit pressure of air in kPa\n", "Te1=0.5089*To;#exit temperature in K\n", "k=1.4;#constant\n", "R=0.287;#gas constant for air\n", "ce=math.sqrt(k*R*Te1*1000);#velocity of sound in exit section in m/s\n", "Me=2.197;#mach number from table\n", "ve1=Me*ce;#velocity of air at exit section in m/s\n", "print \"When diverging section act as a nozzle :-\"\n", "print \"Exit pressure is\",round(Pe1,4),\" kPa\"\n", "print \"Exit Temperature\",round(Te1,1),\" K\"\n", "print \"Exit velocity is\",round(ve1,1),\" m/s \"\n", "\n", "#when diverging section act as diffuser\n", "\n", "Me=0.308;\n", "Pe2=0.0936*Po;#exit pressure of air in kPa\n", "Te2=0.9812*To;#exit temperature in K\n", "ce=math.sqrt(k*R*Te2*1000);#velocity of sound in exit section in m/s\n", "ve2=Me*ce;\n", "print \"When diverging section act as a diffuser :-\"\n", "print \"Exit pressure is\",round(Pe2,1),\" kPa\"\n", "print \"Exit Temperature\",round(Te2,2),\" K\"\n", "print \"Exit velocity is\",round(ve2,),\" m/s \"\n", "\n", "# The value of Exit pressure when diverging section acts as diffuser is wrong\n", "\n" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "When diverging section act as a nozzle :-\n", "Exit pressure is 93.9 kPa\n", "Exit Temperature 183.2 K\n", "Exit velocity is 596.1 m/s \n", "When diverging section act as a diffuser :-\n", "Exit pressure is 93.6 kPa\n", "Exit Temperature 353.23 K\n", "Exit velocity is 116.0 m/s \n" ] } ], "prompt_number": 39 }, { "cell_type": "heading", "level": 2, "metadata": {}, "source": [ "Ex17.8:PG-731" ] }, { "cell_type": "code", "collapsed": false, "input": [ "#ques8\n", "#Determine the static pressure and temperature of supersonic nozzle\n", "#x-inlet\n", "#y-exit\n", "# using the data from previous example\n", "Mx=2.197 # Mach number at x\n", "Px=93.9 # IN kPa\n", "Tx=183.2 # IN K\n", "P0x=1000 # IN kPa\n", "T0x = 360 # in K\n", "My=0.547 # Mach number at y From Table A.13\n", "Py = 5.46*Px # From Table A.13\n", "Ty = 1.854 * Tx # From Table A.13\n", "P0y= 0.630 * P0x # From Table A.13\n", "print \"Exit pressure after shock is\",round(Py,1),\" kPa\"\n", "print \"Exit Temperature after shock is\",round(Ty,1),\" K\"\n", "print \"Exit stagnation pressure after shock is\",round(P0y,1),\" kPa\"\n" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "Exit pressure after shock is 512.7 kPa\n", "Exit Temperature after shock is 339.7 K\n", "Exit stagnation pressure after shock is 630.0 kPa\n" ] } ], "prompt_number": 2 }, { "cell_type": "heading", "level": 2, "metadata": {}, "source": [ "Ex17.9:PG-733" ] }, { "cell_type": "code", "collapsed": false, "input": [ "#ques9\n", "#determining exit plane properties in control volume\n", "\n", "#x-inlet\n", "#y-exit\n", "Mx=1.5;#mach number for inlet\n", "My=0.7011;#mach number for exit\n", "Px=272.4;#inlet pressure in kPa\n", "Tx=248.3;#inlet temperature in K\n", "Tox=360 # stagnation temperature in Kelvin\n", "Pox=1000.0;#stagnation pressure for inlet\n", "Py=2.4583*Px;# Pressure at 1.5 mach in kPa\n", "Ty=1.320*Tx;# temperature at 1.5 mach in K\n", "Poy=0.9298*Pox;# pressure at 1.5 mach in kPa\n", "\n", "Toy=Tox # constant\n", "Me=0.339 # from table with A/A*=1.860 and M < 1\n", "Pe=0.9222*Py;#Exit Pressure in kPa\n", "Te=0.9771*Toy;#Exit temperature in K\n", "Poe=0.9222*Poy;#Exit pressure in kPa\n", "\n", "print \"Exit Mach no.=\",Me\n", "print \"Exit temperature =\",round(Te,2),\"K \"\n", "print \"Exit pressure =\",round(Poe,1),\"kPa\"" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "Exit Mach no.= 0.339\n", "Exit temperature = 351.76 K \n", "Exit pressure = 857.5 kPa\n" ] } ], "prompt_number": 50 } ], "metadata": {} } ] }