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+{
+ "metadata": {
+ "name": "",
+ "signature": "sha256:9350c41424c136ffdcb61a367641cc78b39d6999ad3a13b8f61c623099d55d5b"
+ },
+ "nbformat": 3,
+ "nbformat_minor": 0,
+ "worksheets": [
+ {
+ "cells": [
+ {
+ "cell_type": "heading",
+ "level": 1,
+ "metadata": {},
+ "source": [
+ "Chapter 6: The Ideal Gas"
+ ]
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 6.1, page no. 101"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "\n",
+ "import scipy.integrate\n",
+ "\n",
+ "#intialization of variables\n",
+ "T1 = 40+460.0 #temperature(R)\n",
+ "T2 = 340+460.0 #temperature(R)\n",
+ "\n",
+ "#calculation\n",
+ "def Cv(T):\n",
+ "\tcv = 0.162+0.00046*T\n",
+ "\treturn cv\n",
+ "\t\n",
+ "du = scipy.integrate.quadrature(Cv, T1, T2)[0]\n",
+ "\n",
+ "#result\n",
+ "print \"Change in specific internal energy = %.1f B/lbm\" %du"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "Change in specific internal energy = 138.3 B/lbm\n"
+ ]
+ }
+ ],
+ "prompt_number": 1
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 6.2, page no. 103"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "\n",
+ "#initialization\n",
+ "\n",
+ "cp = 0.24 #B/lbm F\n",
+ "R = 53.3 #ft-lb/lbm F\n",
+ "\n",
+ "#calculation\n",
+ "cv = cp-R/778.0\n",
+ "\n",
+ "#result\n",
+ "print \"Specific heat at constant volume = %.3f B/lbm F\" %cv"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "Specific heat at constant volume = 0.171 B/lbm F\n"
+ ]
+ }
+ ],
+ "prompt_number": 2
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 6.3, page no. 104"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "\n",
+ "import scipy.integrate\n",
+ "\n",
+ "#initialization\n",
+ "T1 = 1400+460.0 #temperature(R)\n",
+ "T2 = 1200+460.0 #temperature(R)\n",
+ "\n",
+ "#calculation\n",
+ "def Cp(T):\n",
+ "\tcp = 0.317- 1.2*100/T + 4*10**4/T**2\n",
+ "\treturn cp\n",
+ "\n",
+ "dh = scipy.integrate.quadrature(Cp, T1, T2)[0]\n",
+ "\n",
+ "#result\n",
+ "print \"Change in stagnation enthalpy = %.1f B/lbm\" %dh"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "Change in stagnation enthalpy = -52.3 B/lbm\n"
+ ]
+ }
+ ],
+ "prompt_number": 3
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 6.4, page no. 106"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "\n",
+ "import scipy.integrate\n",
+ "\n",
+ "#initialization\n",
+ "T1 = 100+460.0 #temperature(R)\n",
+ "T2 = 300+460.0 #temperature(R)\n",
+ "P1 = 15.0 #pressure(lb/in^2)\n",
+ "P2 = 30.0 #pressure(lb/in^2)\n",
+ "Cp = 0.3 #constant pressure(B/lbm F)\n",
+ "R = 40.0 #gas constant(ft-lb/lbm R)\n",
+ "\n",
+ "#calculation\n",
+ "def fun(f):\n",
+ "\ts=Cp/f\n",
+ "\treturn s\n",
+ "def fun1(f):\n",
+ "\ts2=R/(f*778)\n",
+ "\treturn s2\n",
+ "\n",
+ "ds1 = scipy.integrate.quadrature(fun, T1, T2)[0]\n",
+ "ds2 = scipy.integrate.quadrature(fun1, P1, P2)[0]\n",
+ "ds = ds1 - ds2\n",
+ "\n",
+ "#result\n",
+ "print \"Change in entropy = %.4f B/lbm R\" %ds"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "Change in entropy = 0.0560 B/lbm R\n"
+ ]
+ }
+ ],
+ "prompt_number": 4
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 6.5, page no. 108"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "\n",
+ "#initialization\n",
+ "\n",
+ "T1 = 40+460.0 #temperature(R)\n",
+ "T2 = 340+460.0 #temperature(R)\n",
+ "P1 = 15.0 #pressure(lb/in^2)\n",
+ "cp = 0.24\n",
+ "cv = 0.171\n",
+ "\n",
+ "#calculation\n",
+ "gamma=cp/cv\n",
+ "P2=P1 *((T2/T1)**(gamma/(gamma-1)))\n",
+ "\n",
+ "#result\n",
+ "print \"Final pressure = %.1f lb/in^2\" %P2"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "Final pressure = 76.9 lb/in^2\n"
+ ]
+ }
+ ],
+ "prompt_number": 7
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 6.6, page no. 110"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "\n",
+ "import math\n",
+ "\n",
+ "#initialization\n",
+ "P1 = 16.0 #lb/in^2\n",
+ "P2 = 14.0 #lb/in^2\n",
+ "Tt = 83+460.0 #R\n",
+ "gamma = 1.4\n",
+ "cp = 0.24 #B/lbm F\n",
+ "\n",
+ "#calculation\n",
+ "T = Tt *(P2/P1)**((gamma-1)/gamma)\n",
+ "dh = cp*(Tt-T)\n",
+ "V = math.sqrt(2*32.2*778*dh)\n",
+ "\n",
+ "#result\n",
+ "print \"Actual temperature in the flow = %d R\" %T\n",
+ "print \"Flow velocity = %d ft/sec\" %V\n",
+ "\n",
+ "#difference in answeres is due to internal rounding off in Python"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "Actual temperature in the flow = 522 R\n",
+ "Flow velocity = 494 ft/sec\n"
+ ]
+ }
+ ],
+ "prompt_number": 7
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 6.7, page no. 111"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "\n",
+ "import math\n",
+ "import scipy.integrate\n",
+ "\n",
+ "#initialization\n",
+ "T1 = 400.0+460.0 #R\n",
+ "P1 = 100.0 #lb/in^2\n",
+ "P2 = 20.0 #lb/in^2\n",
+ "T2 = 140.0+460.0 #R\n",
+ "Cp = 50.0\n",
+ "\n",
+ "#calculation\n",
+ "Pratio = P1/P2\n",
+ "Tratio = T1/T2\n",
+ "C = math.log(Tratio)/math.log(Pratio)\n",
+ "n=1/(1-C)\n",
+ "v1=Cp*T1/(144*P1)\n",
+ "v2=Cp*T2/(144*P2)\n",
+ "w=144*P1*v1**n\n",
+ "def fun(v):\n",
+ "\tp=w/v**n\n",
+ "\treturn p\n",
+ "\n",
+ "Work = scipy.integrate.quadrature(fun, v1, v2)[0]\n",
+ "\n",
+ "#result\n",
+ "print \"Work done = %f ft-lb/lbm\" %Work"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "Work done = 45118.149895 ft-lb/lbm\n"
+ ]
+ }
+ ],
+ "prompt_number": 9
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 6.8, page no. 113"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "\n",
+ "import math\n",
+ "\n",
+ "#initialization\n",
+ "P1 = 15.0 #lb/in^2\n",
+ "P2 = 20.0 #lb/in^2\n",
+ "T1 = 40+460 #R\n",
+ "T2 = 540+460 #R\n",
+ "\n",
+ "#calculation\n",
+ "#From table 6 at the two temperatures\"\n",
+ "phi1 = 0.58233\n",
+ "phi2 = 0.75042\n",
+ "ds = phi2-phi1-53.3*math.log(P2/P1)/778.0\n",
+ "\n",
+ "#result\n",
+ "print \"Entropy change = %.5f B/lbm R\" %ds"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "Entropy change = 0.14838 B/lbm R\n"
+ ]
+ }
+ ],
+ "prompt_number": 10
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 6.9, page no. 115"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "\n",
+ "#part a\n",
+ "\n",
+ "P2 = 1460.0 #pressure 2\n",
+ "P1 = 1900.0 #pressure 1\n",
+ "V2 = 1900.0 #volume 1\n",
+ "V1 = 1460.0 #volume 2\n",
+ "\n",
+ "pratio = (P2/P1)**3.5\n",
+ "vratio = (V2/V1)**2.5\n",
+ "\n",
+ "print \"Pressure ratio is \", round(pratio,2)\n",
+ "print \"Volume ratio is \", round(vratio,2)\n",
+ "\n",
+ "#part b\n",
+ "#from table 6\n",
+ "Pr2 = 50.34 #pressure 2\n",
+ "Pr1 = 141.51 #pressure 1\n",
+ "Vr2 = 10.743 #volume 1\n",
+ "Vr1 = 4.974 #volume 2\n",
+ "\n",
+ "pratio = (Pr2/Pr1)\n",
+ "vratio = (Vr2/Vr1)\n",
+ "\n",
+ "print \"Pressure ratio is \", round(pratio,2)\n",
+ "print \"Volume ratio is \", round(vratio,2)"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "Pressure ratio is 0.4\n",
+ "Volume ratio is 1.93\n",
+ "Pressure ratio is 0.36\n",
+ "Volume ratio is 2.16\n"
+ ]
+ }
+ ],
+ "prompt_number": 1
+ }
+ ],
+ "metadata": {}
+ }
+ ]
+} \ No newline at end of file
generated by cgit (git 2.34.1) at 2024-12-20 08:31:22 +0000