path: root/Thermodynamics_An_Engineering_Approach/Chapter9.ipynb

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  {
   "cells": [
    {
     "cell_type": "heading",
     "level": 1,
     "metadata": {},
     "source": [
      "Chapter 9: Gas Power Cycles"
     ]
    },
    {
     "cell_type": "heading",
     "level": 2,
     "metadata": {},
     "source": [
      "Example 9-2 ,Page No.498"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "#given data\n",
      "T1=17+273;#temperature of air in K\n",
      "P1=100;#pressure of air in kPa\n",
      "r=8.0;#compression ratio i.e v1/v2\n",
      "qin=800;#heat transfer rate in kJ/kg\n",
      "\n",
      "#constants used\n",
      "R=0.287;#in kPa-m^3/kg-K\n",
      "\n",
      "#from Table A-17\n",
      "#at T1\n",
      "u1=206.91;\n",
      "vr1=676.1;\n",
      "\n",
      "#calculations\n",
      "#Process 1-2\n",
      "vr2=vr1/r;\n",
      "#at this vr2\n",
      "T2=652.4;\n",
      "u2=475.11;\n",
      "P2=P1*(T2/T1)*(r);\n",
      "#Process 2-3\n",
      "u3=qin+u2;\n",
      "#at this u3\n",
      "T3=1575.1;\n",
      "vr3=6.108;\n",
      "P3=P2*(T3/T2)*1;#factor of 1 as v3=v2\n",
      "print'maximum temperature in the cycle %f K'%T3;\n",
      "print'maximum pressure %f MPa'%round((P3/1000),3);#factor of 1000 to convert into MPa\n",
      "#Process 3-4\n",
      "vr4=r*vr3;\n",
      "#at this vr4 \n",
      "T4=795.6;\n",
      "u4=588.74;\n",
      "#Process 4-1\n",
      "qout=u4-u1;\n",
      "Wnet=qin-qout;\n",
      "print'net work output %f kJ/kg'%round(Wnet,2);\n",
      "nth=Wnet/qin;\n",
      "print'thermal efficiency is %f'%round(nth,3);\n",
      "v1=R*T1/P1;\n",
      "MEP=Wnet/(v1*(1-1/r));\n",
      "MEP=round(MEP);\n",
      "print'mean effective pressure %i kPa'%(MEP)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "maximum temperature in the cycle 1575.100000 K\n",
        "maximum pressure 4.345000 MPa\n",
        "net work output 418.170000 kJ/kg\n",
        "thermal efficiency is 0.523000\n",
        "mean effective pressure 574 kPa\n"
       ]
      }
     ],
     "prompt_number": 2
    },
    {
     "cell_type": "heading",
     "level": 2,
     "metadata": {},
     "source": [
      "Example 9-3 ,Page No.501"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "#given data\n",
      "V1=117.0;#intial volumne in in^3\n",
      "T1=80+460.0;#intial temperature in R\n",
      "P1=14.7;#intial pressure in psia\n",
      "r=18.0;#compression ratio\n",
      "rc=2.0;#cut-off ratio\n",
      "\n",
      "#constants used\n",
      "R=0.3704;#in psia ft^3/lbm R\n",
      "cp=0.240;#in Btu/lbm R\n",
      "cv=0.171;#in Btu/lbm R\n",
      "\n",
      "#from Table A-2Ea\n",
      "k=1.4;\n",
      "\n",
      "#calculations\n",
      "V2=V1/r;\n",
      "V3=rc*V2;\n",
      "V4=V1;\n",
      "#Process 1-2\n",
      "T2=T1*(V1/V2)**(k-1);\n",
      "P2=P1*(V1/V2)**k;\n",
      "T2=round(T2);\n",
      "P2=round(P2);\n",
      "print('Process 1-2');\n",
      "print'temperature %i R'%T2;\n",
      "print'pressure %i psia'%P2;\n",
      "#Process 2-3\n",
      "P3=P2;\n",
      "T3=T2*(V3/V2);\n",
      "T3=round(T3);\n",
      "P3=round(P3);\n",
      "print('Process 2-3');\n",
      "print'temperature %i R'%T3;\n",
      "print'pressure %i psia'%P3;\n",
      "#Process 3-4\n",
      "T4=T3*(V3/V4)**(k-1);\n",
      "P4=P3*(V3/V4)**k;\n",
      "T4=round(T4);\n",
      "print('Process 3-4');\n",
      "print'temperature %i R'%T4;\n",
      "print'pressure %f psia'%round(P4,1);\n",
      "m=P1*V1/(R*T1)/1728;#factor of 1728 to covert to ft^3 from in^3\n",
      "Qin=m*cp*(T3-T2);\n",
      "Qout=m*cv*(T4-T1);\n",
      "Wnet=Qin-Qout ;\n",
      "print'work output %f Btu'%round(Wnet,3);\n",
      "nth=Wnet/Qin;\n",
      "print'thermal efficiency is %f'%round(nth,3);\n",
      "MEP=Wnet/(V1-V2)*778.17*12;#factor of 778.17 and 12 to convert to lbf ft and in from Btu and ft respectively\n",
      "MEP=round(MEP);\n",
      "print'mean effective pressure %i psia'%MEP"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "Process 1-2\n",
        "temperature 1716 R\n",
        "pressure 841 psia\n",
        "Process 2-3\n",
        "temperature 3432 R\n",
        "pressure 841 psia\n",
        "Process 3-4\n",
        "temperature 1425 R\n",
        "pressure 38.800000 psia\n",
        "work output 1.296000 Btu\n",
        "thermal efficiency is 0.633000\n",
        "mean effective pressure 110 psia\n"
       ]
      }
     ],
     "prompt_number": 10
    },
    {
     "cell_type": "heading",
     "level": 2,
     "metadata": {},
     "source": [
      "Example 9-5 ,Page No.511"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "#given data\n",
      "T1=300;#compressor inlet temperature in K\n",
      "r=8;#pressure ratio\n",
      "T3=1300;#turbine inlet temperature in K\n",
      "\n",
      "#calcualtions\n",
      "#Process 1-2\n",
      "#at T1\n",
      "h1=300.19;\n",
      "Pr1=1.386;\n",
      "Pr2=r*Pr1;\n",
      "#at Pr2\n",
      "T2=540;\n",
      "h2=544.35;\n",
      "print'temperature at exit of compressor %i K'%T2;\n",
      "#Process 3-4\n",
      "#at T3\n",
      "h3=1395.17;\n",
      "Pr3=330.9;\n",
      "Pr4=Pr3/r;\n",
      "#at Pr4\n",
      "T4=770;\n",
      "h4=789.37;\n",
      "print'temperature at turbine exit %i K'%T4;\n",
      "Win=h2-h1;\n",
      "Wout=h3-h4;\n",
      "rbw=Win/Wout;\n",
      "print'back work ratio is %f'%round(rbw,3);\n",
      "qin=h3-h2;\n",
      "Wnet=Wout-Win;\n",
      "nth=Wnet/qin;\n",
      "print'thermal efficeincy is %f'%round(nth,3)\n"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "temperature at exit of compressor 540 K\n",
        "temperature at turbine exit 770 K\n",
        "back work ratio is 0.403000\n",
        "thermal efficeincy is 0.425000\n"
       ]
      }
     ],
     "prompt_number": 1
    },
    {
     "cell_type": "heading",
     "level": 2,
     "metadata": {},
     "source": [
      "Example 9-6 ,Page No.513"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "#from 9.5\n",
      "Wsc=244.16;#work input of compressor in kJ/kg\n",
      "Wst=606.60;#work output of turbine in kJ/kg\n",
      "h1=300.19;#process 1-2 data\n",
      "h3=1395.17;#process 3-4 data\n",
      "\n",
      "#given data\n",
      "nC=0.8;#compressor effciency \n",
      "nT=0.85;#turbine efficiency\n",
      "\n",
      "#calculations\n",
      "Win=Wsc/nC;\n",
      "Wout=nT*Wst;\n",
      "rbw=Win/Wout;\n",
      "print'back work ratio is %f'%round(rbw,3);\n",
      "h2a=h1+Win;\n",
      "qin=h3-h2a;\n",
      "Wnet=Wout-Win;\n",
      "nth=Wnet/qin;\n",
      "print'thermal efficeincy is %f'%round(nth,3)\n",
      "h4a=h3-Wout;\n",
      "#from A-17 at h4a\n",
      "T4a=853;\n",
      "print'turbine exit temperature %i K is'%T4a\n"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "back work ratio is 0.592000\n",
        "thermal efficeincy is 0.266000\n",
        "turbine exit temperature 853 K is\n"
       ]
      }
     ],
     "prompt_number": 13
    },
    {
     "cell_type": "heading",
     "level": 2,
     "metadata": {},
     "source": [
      "Example 9-7 ,Page No.516"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "#from 9.6\n",
      "h2a=605.39;#entalpy of air leaving the compressor in kJ/kg\n",
      "h4a=880.36;#entalpy of air leaving the turbinein kJ/kg\n",
      "h3=1395.97;#in kJ/kg\n",
      "Wnet=210.41;#net woek done in kJ/kg\n",
      "\n",
      "#given data\n",
      "n=0.80;#thermal efficiency\n",
      "\n",
      "#calculations\n",
      "# n = (h5 - h2a) / (h4a - h2a)\n",
      "h5=(h4a - h2a)*n+h2a;\n",
      "qin=h3-h5;\n",
      "nth=Wnet/qin;\n",
      "print'thermal efficeincy is %f'%round(nth,3)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "thermal efficeincy is 0.369000\n"
       ]
      }
     ],
     "prompt_number": 14
    },
    {
     "cell_type": "heading",
     "level": 2,
     "metadata": {},
     "source": [
      "Example 9-8 ,Page No.519"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "from math import sqrt\n",
      "\n",
      "#given data\n",
      "T1=300;#inlet temperature of compressor in K\n",
      "T6=1300;#inlet temperature of turbine in K\n",
      "r=8;#overall compression ratio\n",
      "\n",
      "#calculations\n",
      "#as it is case of intercooling\n",
      "ri=sqrt(r);#ri stands for P2/P1 = P4/P3 = P6/P7 = P8/P9\n",
      "#from A-17 at T1\n",
      "h1=300.19;\n",
      "Pr1=1.386;\n",
      "Pr2=ri*Pr1;\n",
      "#from A-17 at Pr2\n",
      "T2=403.3;\n",
      "h2=403.31;\n",
      "#from A-17 at T6\n",
      "h6=1395.97;\n",
      "Pr6=330.9;\n",
      "Pr7=Pr6/ri;\n",
      "#from A-17 at Pr7\n",
      "T7=1006.4;\n",
      "h7=1053.33;\n",
      "#at inlets\n",
      "T3=T1;h3=h1;T8=T6;h8=h6;\n",
      "#et exits\n",
      "T4=T2;h4=h2;T9=T7;h9=h7;h5=h7;\n",
      "Win=2*(h2-h1);\n",
      "Wout=2*(h6-h7);\n",
      "Wnet=Wout-Win;\n",
      "qin=(h6-h4)+(h8-h7);\n",
      "rbw=Win/Wout;\n",
      "print'back work ratio is %f'%round(rbw,3);\n",
      "nth=Wnet/qin;\n",
      "print'thermal efficeincy is %f'%round(nth,3)\n",
      "#part - b\n",
      "print('part - b');\n",
      "qin=(h6-h5)+(h8-h7);\n",
      "nth=Wnet/qin;\n",
      "print'thermal efficeincy is %f'%round(nth,3)\n"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "back work ratio is 0.301000\n",
        "thermal efficeincy is 0.359000\n",
        "part - b\n",
        "thermal efficeincy is 0.699000\n"
       ]
      }
     ],
     "prompt_number": 16
    },
    {
     "cell_type": "heading",
     "level": 2,
     "metadata": {},
     "source": [
      "Example 9-9 ,Page No.523"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "from math import sqrt\n",
      "\n",
      "#given data\n",
      "m=100;\n",
      "P1=5;#air pressue in psia\n",
      "T1=-40+460;#air temperature in R\n",
      "T4=2000+460;#turbine inlet temperature in R\n",
      "V1=850;#aircraft velocity in ft/sec\n",
      "rp=10;#pressure ratio\n",
      "\n",
      "#constants used\n",
      "cp=0.240;#in Btu/lbm F\n",
      "k=1.4;\n",
      "\n",
      "#calculations\n",
      "#Process 1-2\n",
      "T2=T1+V1**2/(2*cp)/25037;#factor of 25037 to covert to Btu/lbm\n",
      "P2=P1*(T2/T1)**(k/(k-1));\n",
      "#Process 2-3 \n",
      "P3=rp*P2;\n",
      "P4=P3;\n",
      "T3=T2*(P3/P2)**((k-1)/k);\n",
      "#Win=Wout\n",
      "T5=T4-T3+T2;\n",
      "P5=P4*(T5/T4)**(k/(k-1));\n",
      "T5=round(T5);\n",
      "print'temperature at turbine exit %i R'%T5;\n",
      "print'pressure at turbine exit %f psia'%round(P5,1);\n",
      "#Process 5-6\n",
      "P6=P1;\n",
      "T6=T5*(P6/P5)**((k-1)/k);\n",
      "T6=round(T6);#round off\n",
      "V6=sqrt(2*cp*(T5-T6)*25037);#factor of 25037 to covert to (ft/s)^2\n",
      "print'the velocity of nozzle exit %i ft/s'%(round(V6));\n",
      "Wp=m*(V6-V1)*V1/25037;#factor of 25037 to covert to Btu/lbm\n",
      "Qin=m*cp*(T4-T3);\n",
      "nP=Wp/Qin;\n",
      "print'propulsive efficiency is %f percent'%round(nP*100,1)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "temperature at turbine exit 2013 R\n",
        "pressure at turbine exit 39.600000 psia\n",
        "the velocity of nozzle exit 3285 ft/s\n",
        "propulsive efficiency is 22.500000 percent\n"
       ]
      }
     ],
     "prompt_number": 4
    },
    {
     "cell_type": "heading",
     "level": 2,
     "metadata": {},
     "source": [
      "Example 9-10 ,Page No.529"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "from math import log\n",
      "\n",
      "#from 9.2\n",
      "r=8;#compression ratio i.e v1/v2\n",
      "T0=290.0;#temperature of air in K\n",
      "T1=290.0;#temperature in the begining of the isentropic compression process in K\n",
      "T2=652.4;#temperature in the end of the isentropic compression process in K\n",
      "T3=1575.1;#temperature after process 2-3 in K\n",
      "P2=1.7997;#pressure in the end of the isentropic compression process in MPa\n",
      "P3=4.345;#pressure after process 2-3 in MPa\n",
      "qin=800.0;#heat transfer rate in kJ/kg\n",
      "qout=381.83;#heat rejection in kJ/kg\n",
      "wnet=418.17;#net work in kJ/kg\n",
      "\n",
      "#given data\n",
      "Tsource=1700;#temperature of working fluid at source in K\n",
      "\n",
      "#constants used\n",
      "R=0.287;#in kPa-m^3/kg-K\n",
      "\n",
      "#calculations\n",
      "#s1=s2 ; s3=s4\n",
      "s03=3.5045;\n",
      "s02=2.4975;\n",
      "s32=(s03-s02)-R*log(P3/P2);#s32 stands for s3-s2\n",
      "xdest23=T0*(s32-qin/Tsource);\n",
      "Tsink=T1;\n",
      "xdest41=T0*(-s32+qout/Tsink);\n",
      "xdestcycle=xdest23+xdest41;\n",
      "print'exergy destrustion associated with Otto cycle %f kJ/kg'%round(xdestcycle,1);\n",
      "# X4 = (u4 - u0 )- T0*(s4 - s0) + P0(v4 - v0)\n",
      "# s4 - s0 = s4 - s1 = s32\n",
      "# u4 - u0 = u4 - u1 = qout\n",
      "# v4 - v0 = v4 - v1 = 0\n",
      "#hence x4 is\n",
      "X4=qout-T0*s32;\n",
      "print'exergy destruction of purge stream %f kJ/kg'%round(X4,1)\n"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "exergy destrustion associated with Otto cycle 245.400000 kJ/kg\n",
        "exergy destruction of purge stream 163.200000 kJ/kg\n"
       ]
      }
     ],
     "prompt_number": 5
    }
   ],
   "metadata": {}
  }
 ]
}