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diff --git a/Engineering_Thermodynamics/ch13.ipynb b/Engineering_Thermodynamics/ch13.ipynb new file mode 100755 index 00000000..4c7ec6db --- /dev/null +++ b/Engineering_Thermodynamics/ch13.ipynb @@ -0,0 +1,590 @@ +{ + "metadata": { + "name": "", + "signature": "sha256:20c7c69ec3c2fcafe0d93dd099c65cc40aeef92c301c25a624e4ebbb2e24b55e" + }, + "nbformat": 3, + "nbformat_minor": 0, + "worksheets": [ + { + "cells": [ + { + "cell_type": "heading", + "level": 1, + "metadata": {}, + "source": [ + "Chapter 13 : Gas Power Cycles" + ] + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 13.1 Page No : 543" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "\n", + "# Variables\n", + "T1 = 273.+35;\n", + "P1 = 100e03; \t\t\t# in kN/m2\n", + "Q1 = 2100.;\n", + "R = 0.287;\n", + "v1 = 0.884\n", + "v2 = 0.11\n", + "v3 = v2;\n", + "rk = 8.\n", + "g = 1.4; \t\t\t# gamma\n", + "\n", + "# Calculation\n", + "n_cycle = 1-(1./rk**(1.4-1));\n", + "v12 = 8; \t\t\t# v1./v2\n", + "v1 = (R*T1)/P1;\n", + "v2 = v1/8;\n", + "T2 = T1*(v1/v2)**(g-1);\n", + "cv = 0.718;\n", + "T3 = Q1/cv + T2\n", + "P21 = (v1/v2)**g;\n", + "P2 = P21*P1;\n", + "P3 = P2*(T3/T2);\n", + "Wnet = Q1*n_cycle;\n", + "Pm = Wnet/(v1-v2);\n", + "\n", + "# Results\n", + "print \"Maximum pressure is %.2f mPa\"%(P3/1e06)\n", + "print \"Temperature of the cycle is %.2f K\"%T3,\"K\"\n", + "print \"Cycle efficiency is %.2f %%\"%(n_cycle*100)\n", + "print \"Mean effective pressure is %.3f MPa\"%(Pm/1e06)\n" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "Maximum pressure is 9.43 mPa\n", + "Temperature of the cycle is 3632.39 K K\n", + "Cycle efficiency is 56.47 %\n", + "Mean effective pressure is 1.533 MPa\n" + ] + } + ], + "prompt_number": 2 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 13.2 Page No : 544" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "\n", + "# Variables\n", + "rk = 14.;\n", + "k = 0.06\n", + "rc = k*(14-1)+1;\n", + "g = 1.4;\n", + "\n", + "# Calculation\n", + "n_diesel = 1-((1./g))*(1./rk**(g-1))*((rc**(g-1))/(rc-1));\n", + "\n", + "# Results\n", + "print \"Air standard efficiency is %.f %%\"%(n_diesel*100)\n", + "\n", + "# note : rounding off error. please check." + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "Air standard efficiency is 60 %\n" + ] + } + ], + "prompt_number": 2 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 13.3 Page No : 544" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "\n", + "# Variables\n", + "rk = 16.;\n", + "T1 = 273.+15;\n", + "P1 = 100.; \t\t\t# in kN/m2\n", + "T3 = 1480.+273;\n", + "g = 1.4; \t\t\t# gamma \n", + "R = 0.287;\n", + "T2 = 288*(rk**(g-1));\n", + "\n", + "# Calculation\n", + "rc = T3/T2 ;\n", + "cp = 1.005; cv = 0.718;\n", + "Q1 = cp*(T3-T2);\n", + "T4 = T3*((rc/rk)**(g-1));\n", + "Q2 = cv*(T4-T1);\n", + "n = 1-(Q2/Q1); \t\t\t# cycle efficiency\n", + "n_ = 1-((1./g))*(1./rk**(g-1))*((rc**(g-1))/(rc-1)); \t\t\t# cycle efficiency from another formula\n", + "Wnet = Q1*n;\n", + "v1 = (R*T1)/P1 ;\n", + "v2 = v1/rk;\n", + "Pm = Wnet/(v1-v2);\n", + "\n", + "# Results\n", + "print \"cut-off ratio is %.2f\"%rc\n", + "print \"Heat supplied per kg of air is %.1f kJ/Kg\"%Q1\n", + "print \"Cycle efficiency is %.1f %%\"%(n*100)\n", + "print \"Mean effective pressure is %.2f Kpa\"%Pm\n", + "\n", + "# rounding off error is there." + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "cut-off ratio is 2.01\n", + "Heat supplied per kg of air is 884.3 kJ/Kg\n", + "Cycle efficiency is 61.3 %\n", + "Mean effective pressure is 699.97 Kpa\n" + ] + } + ], + "prompt_number": 3 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 13.4 Page No : 546" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "\n", + "# Variables\n", + "T1 = 273.+50;\n", + "rk = 16.;\n", + "g = 1.4; \t\t\t# gamma\n", + "P3 = 70.; \n", + "cv = 0.718; \n", + "cp = 1.005; \n", + "R = 0.287;\n", + "\n", + "# Calculation\n", + "T2 = T1*((rk**(g-1)));\n", + "P1 = 1; \t\t\t# in bar\n", + "P2 = P1*(rk)**g;\n", + "T3 = T2*(P3/P2);\n", + "Q23 = cv*(T3-T2);\n", + "T4 = (Q23/cp)+T3;\n", + "v43 = T4/T3; \t\t\t# v4/v3\n", + "v54 = rk/v43; \t\t\t# v5/v4 = (v1./v2)*(v3/v4)\n", + "T5 = T4*(1./v54)**(g-1);\n", + "P5 = P1*(T5/T1);\n", + "Q1 = cv*(T3-T2)+cp*(T4-T3);\n", + "Q2 = cv*(T5-T1);\n", + "n_cycle = 1-(Q2/Q1);\n", + "v1 = (R*T1)/P1;\n", + "v12 = (15./16)*v1; \t\t\t# v1-v2\n", + "Wnet = Q1*n_cycle;\n", + "Pm = Wnet/(v12);\n", + "\n", + "# Results\n", + "print \"Efficiency of the cycle is %.2f %%\"%(n_cycle*100)\n", + "print \"Mean effective pressure is %.2f\"%Pm,\"bar\"\n" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "Efficiency of the cycle is 66.31 %\n", + "Mean effective pressure is 4.76 bar\n" + ] + } + ], + "prompt_number": 9 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 13.5 Page No : 547" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "\n", + "# Variables\n", + "P1 = 0.1e06;\n", + "T1 = 303.;\n", + "T3 = 1173.;\n", + "PR = 6.; \t\t\t# Pressure ratio\n", + "rp = 6.; \n", + "nt = 0.8; \n", + "nc = 0.8;\n", + "g = 1.4; \n", + "cv = 0.718; \n", + "cp = 1.005; \n", + "R = 0.287;\n", + "\n", + "# Calculation\n", + "j = (PR)**((g-1)/g);\n", + "T2s = j*T1;\n", + "T4s = T3/j;\n", + "T21 = (T2s-T1)/nc ; \t\t\t# T2-T1\n", + "T34 = nt*(T3-T4s); \t\t\t# T3-T4\n", + "Wt = cp*T34;\n", + "Wc = cp*T21;\n", + "T2 = T21+T1;\n", + "Q1 = cp*(T3-T2);\n", + "n = (Wt-Wc)/Q1;\n", + "T4 = T3-375;\n", + "T6 = 0.75*(T4-T2) + T2 ;\n", + "Q1_ = cp*(T3-T6);\n", + "n_ = (Wt-Wc)/Q1_;\n", + "I = (n_-n)/n ;\n", + "\n", + "# Results\n", + "print \"The percentage efficiency in cycle efficiency due to regeneration is %.f %%\"%(I*100)\n", + "\n", + "# note : rounding off error is there." + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "The percentage efficiency in cycle efficiency due to regeneration is 42 %\n" + ] + } + ], + "prompt_number": 11 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 13.6 Page No : 549" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "import math \n", + "\n", + "# Variables\n", + "cp = 1.005;\n", + "Tmax = 1073.\n", + "Tmin = 300.;\n", + "\n", + "# Calculation\n", + "Wnet_max = cp*(math.sqrt(Tmax)-math.sqrt(Tmin))**2;\n", + "n_cycle = 1-math.sqrt(Tmin/Tmax);\n", + "n_carnot = 1-(Tmin/Tmax);\n", + "r = n_cycle/n_carnot;\n", + "\n", + "# Results\n", + "print \"Maximum work done per kg of air is %.2f kJ/Kg\"%Wnet_max\n", + "print \"cycle efficiency is %.0f %%\"%(n_cycle*100)\n", + "print \"ratio of brayton and carnot efficiency is %.3f\"%r\n", + "\n", + "# note : rounding off error is there." + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "Maximum work done per kg of air is 239.47 kJ/Kg\n", + "cycle efficiency is 47 %\n", + "ratio of brayton and carnot efficiency is 0.654\n" + ] + } + ], + "prompt_number": 12 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 13.7 Page No : 549" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "\n", + "# Variables\n", + "rp = 6.;\n", + "g = 1.4; \n", + "cv = 0.718; \n", + "cp = 1.005; \n", + "R = 0.287;\n", + "T1 = 300.; \n", + "T3 = 1100.; \n", + "T0 = 300.;\n", + "\n", + "# Calculation\n", + "n_cycle = 1-(1./rp**((g-1)/g));\n", + "j = rp**((g-1)/g);\n", + "T2 = T1*j;\n", + "T4 = T3/j;\n", + "Wc = cp*(T2-T1);\n", + "Wt = cp*(T3-T4);\n", + "WR = (Wt-Wc)/Wt;\n", + "Q1 = 100; \t\t\t# in MW\n", + "PO = n_cycle*Q1;\n", + "m_dot = (Q1*1e06)/(cp*(T3-T2));\n", + "R = m_dot*cp*T0*((T4/T0)-1-math.log(T4/T0));\n", + "\n", + "# Results\n", + "print \"The thermal efficiency of the cycle is %.1f %%\"%(n_cycle*100)\n", + "print \"Work ratio is %.3f\"%WR\n", + "print \"Power output is %.1f MW\"%PO\n", + "print \"Energy flow rate of the exhaust gas stream is %.2f MW\"%(R/1e06)\n", + "\n", + "# rounding error is there." + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "The thermal efficiency of the cycle is 40.1 %\n", + "Work ratio is 0.545\n", + "Power output is 40.1 MW\n", + "Energy flow rate of the exhaust gas stream is 20.53 MW\n" + ] + } + ], + "prompt_number": 13 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 13.8 Page No : 550" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "\n", + "# Variables\n", + "nc = 0.87; \n", + "nt = 0.9; \n", + "T1 = 311.; \n", + "rp = 8.; \t\t\t# P2/P1\n", + "P1 = 1.; \n", + "P2 = 8.; \n", + "P3 = 0.95*P2; \n", + "P4 = 1;\n", + "T3 = 1100.; \n", + "g = 1.4; \n", + "cv = 0.718; \n", + "cp = 1.005; \n", + "R = 0.287;\n", + "\n", + "# Calculation\n", + "# With no cooling\n", + "T2s = T1*((P2/P1)**((g-1)/g));\n", + "T2 = T1 + (T2s-T1)/0.87;\n", + "T4s = T3*(P4/P3)**((g-1)/g);\n", + "n = (((T3-T4s)*nt)-((T2s-T1)/nc))/(T3-T2);\n", + "# With cooling\n", + "n_cycle = n-0.05;\n", + "x = 0.13;\n", + "r = 0.13/1.13;\n", + "\n", + "# Results\n", + "print \"Percentage of air that may be taken from the compressor is %.1f%%\"%(r*100)\n", + "\n" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "Percentage of air that may be taken from the compressor is 11.5%\n" + ] + } + ], + "prompt_number": 1 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 13.10 Page No : 555" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "\n", + "# Variables\n", + "T1 = 233.; \n", + "V1 = 300.; \n", + "cp = 1.005; \n", + "g = 1.4;\n", + "\n", + "# Calculation and Results\n", + "T2 = T1+((V1**2)/(2*cp))*1e-03 ;\n", + "P1 = 35;\n", + "P2 = P1*(T2/T1)**(g/(g-1));\n", + "rp = 10; \t\t\t# Pressure ratio\n", + "P3 = rp*P2;\n", + "T3 = T2*(P3/P2)**((g-1)/g);\n", + "T4 = 1373;\n", + "T5 = T4-T3+T2;\n", + "P4 = P3;\n", + "P5 = P4*(T5/T4)**(g/(g-1));\n", + "print \"Temperature at the turbine exit is %.2f K\"%T5\n", + "print \"Pressure at the turbine exit is %.2f kPa\"%P5\n", + "P6 = P1;\n", + "T6 = T5*(P6/P5)**((g-1)/g);\n", + "V6 = (2*cp*1000*(T5-T6))**0.5 ;\n", + "\n", + "print \"Velocity of the gas at the nozzle exit is %.1f m/s\"%V6\n", + "w = 50.;\n", + "Ve = V6; Vi = 300.;\n", + "Wp_dot = w*Vi*(Ve-Vi);\n", + "h4 = 1373.; \n", + "h3 = 536.66;\n", + "Q1 = w*cp*(h4-h3); \t\t\t# in kJ/kg\n", + "np = Wp_dot/(Q1*1000);\n", + "print \"The propulsive efficiency of the cycle is %.1f %%\"%(np*100)\n" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "Temperature at the turbine exit is 1114.47 K\n", + "Pressure at the turbine exit is 312.00 kPa\n", + "Velocity of the gas at the nozzle exit is 1020.3 m/s\n", + "The propulsive efficiency of the cycle is 25.7 %\n" + ] + } + ], + "prompt_number": 17 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 13.11 Page No : 556" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "\n", + "# Variables\n", + "Ta = 288.;\n", + "rp = 8.; \t\t\t# Pb/Pa\n", + "g = 1.33; \n", + "g1 = 1.44; \n", + "cv = 0.718; \n", + "cpa = 1.005; \n", + "cpg = 1.11; \n", + "R = 0.287;\n", + "\n", + "# Calculation\n", + "Tb = Ta*(rp)**((g1-1)/g1);\n", + "Tc = 1073.; \n", + "Tm = 800.+273; \n", + "Tmin = 100.+273;\n", + "Td = Tc/(rp**((g-1)/g));\n", + "Wgt = cpg*(Tc-Td)-cpa*(Tb-Ta);\n", + "Q1 = cpg*(Tc-Tb);\n", + "Q1_ = cpg*(Tc-Td);\n", + "h1 = 3775.; h2 = 2183.; h3 = 138.; h4 = h3;\n", + "Q1_st = h1-h3; \t\t\t# Q1'\n", + "Q_fe = cpg*(Tm-Tmin);\n", + "was = Q1_st/Q_fe; \t\t\t# wa/ws\n", + "Wst = h1-h2;\n", + "PO = 190e03; \t\t\t# in kW\n", + "ws = PO/(was*Wgt+Wst);\n", + "wa = 322.5;\n", + "CV = 43300.; \t\t\t# in kJ/kg\n", + "waf = round(CV/(1095.),1)\n", + "FEI = (wa/waf)*CV;\n", + "noA = PO/FEI;\n", + "\n", + "# Results\n", + "print \"Air fuel ratio is %.2f\"%waf\n", + "print \"Overall efficiency of combined plant is %.1f %%\"%(noA*100)\n" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "Air fuel ratio is 39.50\n", + "Overall efficiency of combined plant is 53.7 %\n" + ] + } + ], + "prompt_number": 10 + } + ], + "metadata": {} + } + ] +}
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