{ "metadata": { "name": "" }, "nbformat": 3, "nbformat_minor": 0, "worksheets": [ { "cells": [ { "cell_type": "heading", "level": 1, "metadata": {}, "source": [ "Chapter 13 : Gas Power Cycles" ] }, { "cell_type": "heading", "level": 3, "metadata": {}, "source": [ "Example 13.1 Page no : 606" ] }, { "cell_type": "code", "collapsed": false, "input": [ "# Variables\n", "T1 = 671.; \t\t\t#K\n", "T2 = T1;\n", "T3 = 313.; \t\t\t#K\n", "T4 = T3;\n", "W = 130.; \t\t\t#kJ\n", "\n", " \n", " n_th = (T2-T3)/T2;\n", "print (\"(i) Engine thermal efficiency = %.3f\")% (n_th)\n", "\n", "Q = W/n_th;\n", "print (\"(ii) Heat added = %.3f\")% (Q), (\"kJ\")\n", "\n", "\n", "Q_rejected = Q-W;\n", "dS = Q_rejected/T3;\n", "print (\"(iii) The entropy changes during heat rejection process\"),(\" = %.3f\")% (dS), (\"kJ/K\")\n" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "(i) Engine thermal efficiency = 0.534\n", "(ii) Heat added = 243.659 kJ\n", "(iii) The entropy changes during heat rejection process = 0.363 kJ/K\n" ] } ], "prompt_number": 1 }, { "cell_type": "heading", "level": 3, "metadata": {}, "source": [ "Example 13.2 Page no : 607" ] }, { "cell_type": "code", "collapsed": false, "input": [ "import math\n", "\n", "# Variables\n", "cv = 0.721; \t\t\t#kJ/kg K\n", "cp = 1.008; \t\t\t#kJ/kg K\n", "m = 0.5; \t\t\t #kg\n", "n_th = 0.5;\n", "Q_isothermal = 40.; \t#kJ\n", "p1 = 7.*10**5; \t\t\t#Pa\n", "V1 = 0.12; \t\t\t #m**3\n", "R = 287.; \t\t\t #J/kg K\n", "\n", "\n", "# Calculations and Results\n", "print (\"(i) The maximum and minimum temperatures\")\n", "T1 = p1*V1/m/R;\n", "print (\"Maximun temperature = %.3f\")% (T1), (\"K\")\n", "\n", "T2 = (1-n_th)*T1;\n", "print (\"Minimum temperature = %.3f\")% (T2), (\"K\")\n", "\n", "\n", "V2 = V1*math.e**(Q_isothermal*10**3/m/R/T1);\n", "print (\"(ii) The volume at the end of isothermal expansion = %.3f\")% (V2), (\"m**3\")\n", "\n", "print (\"(iii) The heat transfer for each of the four processes\")\n", "\n", "Q1 = Q_isothermal;\n", "print (\"Isothermal expansion %.3f\")% (Q1), (\"kJ\")\n", "\n", "Q2 = 0;\n", "print (\"Adiabatic reversible expansion\"), (Q2)\n", "\n", "Q3 = -Q_isothermal;\n", "print (\"Isothermal compression\"), (Q3)\n", "\n", "Q4 = 0;\n", "print (\"Adiabatic reversible compression\"), (Q4)\n" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "(i) The maximum and minimum temperatures\n", "Maximun temperature = 585.366 K\n", "Minimum temperature = 292.683 K\n", "(ii) The volume at the end of isothermal expansion = 0.193 m**3\n", "(iii) The heat transfer for each of the four processes\n", "Isothermal expansion 40.000 kJ\n", "Adiabatic reversible expansion 0\n", "Isothermal compression -40.0\n", "Adiabatic reversible compression 0\n" ] } ], "prompt_number": 2 }, { "cell_type": "heading", "level": 3, "metadata": {}, "source": [ "Example 13.3 page no : 608" ] }, { "cell_type": "code", "collapsed": false, "input": [ "import math\n", "\n", "# Variables\n", "p1 = 18.*10**5; \t#Pa\n", "T1 = 683.; \t\t\t#K\n", "T2 = T1;\n", "r1 = 6.; \t\t\t#ratio V4/V1; Isentropic compression\n", "r2 = 1.5; \t\t\t#ratio V2/V1; Isothermal expansion\n", "y = 1.4;\n", "V1 = 0.18; \t\t\t#m**3\n", "\n", "# Calculations and Results\n", "print (\"(i) Temperatures and pressures at the main points in the cycle\")\n", "T4 = T1/(r1)**(y-1);\n", "print (\"T4 = %.1f\")% (T4), (\"K\")\n", "\n", "T3 = T4;\n", "print (\"T3 = %.3f\")% (T3), (\"K\")\n", "\n", "p2 = p1/r2;\n", "print (\"p2 = %.3f\")% (p2/10**5), (\"bar\")\n", "\n", "p3 = p2/(r1)**y;\n", "print (\"p3 = %.3f\")% (p3/10**5), (\"bar\")\n", "\n", "p4 = p1/(r1)**y;\n", "print (\"p4 = %.3f\")% (p4/10**5), (\"bar\")\n", "\n", "\n", "dS = p1*V1/T1/10**3*math.log(r2);\n", "print (\"(ii) Change in entropy = %.3f\")% (dS), (\"kJ/K\")\n", "\n", "print (\"(iii) Mean thermal efficiency of the cycle\")\n", "Qs = T1*(dS);\n", "Qr = T4*(dS);\n", "\n", "n = 1-Qr/Qs;\n", "print (\"n = %.3f\")% (n)\n", "\n", "\n", "pm = (Qs-Qr)/8/V1/100; \t\t\t#bar\n", "print (\"(iv) Mean effective pressure of the cycle = %.3f\")% (pm), (\"bar\")\n", "\n", "\n", "n = 210.; \t\t\t#cycles per minute\n", "P = (Qs-Qr)*n/60; \t\t\t#kW\n", "print (\"(v) Power of the engine = %.3f\")% (P), (\"kW\")\n", "\n", "# answers are slightly different because of rounding error." ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "(i) Temperatures and pressures at the main points in the cycle\n", "T4 = 333.5 K\n", "T3 = 333.549 K\n", "p2 = 12.000 bar\n", "p3 = 0.977 bar\n", "p4 = 1.465 bar\n", "(ii) Change in entropy = 0.192 kJ/K\n", "(iii) Mean thermal efficiency of the cycle\n", "n = 0.512\n", "(iv) Mean effective pressure of the cycle = 0.467 bar\n", "(v) Power of the engine = 235.251 kW\n" ] } ], "prompt_number": 5 }, { "cell_type": "heading", "level": 3, "metadata": {}, "source": [ "Example 13.4 page no : 611" ] }, { "cell_type": "code", "collapsed": false, "input": [ "# Calculations\n", "T2 = 1029/0.6;\n", "T1 = 1.2*T2;\n", "\n", "# Results\n", "print (\"Temperature of the source = \"), (T1), (\"K\")\n", "\n", "print (\"Temperature of the math.sink = \"), (T2), (\"K\")\n" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "Temperature of the source = 2058.0 K\n", "Temperature of the math.sink = 1715.0 K\n" ] } ], "prompt_number": 4 }, { "cell_type": "heading", "level": 3, "metadata": {}, "source": [ "Example 13.5 page no : 611" ] }, { "cell_type": "code", "collapsed": false, "input": [ "# Variables\n", "T1 = 1990.; \t\t\t#K\n", "T2 = 850.; \t\t\t#K\n", "Q = 32.5/60; \t\t\t#kJ/s\n", "P = 0.4; \t\t\t#kW\n", "\n", "# Calculations\n", "n_carnot = (T1-T2)/T1;\n", "n_th = P/Q;\n", "\n", "# Results\n", "print (\"most efficient engine is one that works on Carnot cycle %.3f\")% (n_carnot)\n", "\n", "print (\"n_thermal = %.3f\")% (n_th)\n", "\n", "print (\"which is not feasible as no engine can be more efficient than that working on Carnot\")\n", "print (\"Hence claims of the inventor is not true.\")\n" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "most efficient engine is one that works on Carnot cycle 0.573\n", "n_thermal = 0.738\n", "which is not feasible as no engine can be more efficient than that working on Carnot\n", "Hence claims of the inventor is not true.\n" ] } ], "prompt_number": 5 }, { "cell_type": "heading", "level": 3, "metadata": {}, "source": [ "Example 13.7 page no : 615" ] }, { "cell_type": "code", "collapsed": false, "input": [ "# Variables\n", "n = 0.6; \n", "y = 1.5;\n", "\n", "# Calculations\n", "r = (1./(1-n))**(1./(y-1));\n", "\n", "# Results\n", "print (\"Compression ratio = \"), (r)\n" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "Compression ratio = 6.25\n" ] } ], "prompt_number": 6 }, { "cell_type": "heading", "level": 3, "metadata": {}, "source": [ "Example 13.8 page no : 615" ] }, { "cell_type": "code", "collapsed": false, "input": [ "import math\n", "\n", "# Variables\n", "D = 0.25; \t\t\t#m\n", "L = 0.375; \t\t\t#m\n", "Vc = 0.00263; \t\t#m**3\n", "p1 = 1.; \t\t\t#bar\n", "T1 = 323.; \t\t\t#K\n", "p3 = 25.; \t\t\t#bar\n", "\n", "# Calculations and Results\n", "Vs = math.pi/4*D**2*L;\n", "r = (Vs+Vc)/Vc;\n", "y = 1.4;\n", "\n", "n_otto = 1-1/(r**(y-1));\n", "print (\"(i) Air standard efficiency = %.3f\")% (n_otto)\n", "\n", "\n", "\n", "p2 = p1*(r)**(y);\n", "r_p = p3/p2;\n", "\n", "p_m = p1*r*(r**(y-1) - 1)*(r_p - 1)/(y-1)/(r-1);\n", "print (\"(ii)Mean effective pressure = %.3f\")%(p_m), (\"bar\")\n" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "(i) Air standard efficiency = 0.565\n", "(ii)Mean effective pressure = 1.336 bar\n" ] } ], "prompt_number": 6 }, { "cell_type": "heading", "level": 3, "metadata": {}, "source": [ "Example 13.9 page no : 617" ] }, { "cell_type": "code", "collapsed": false, "input": [ "# Variables\n", "cv = 0.72; \t\t\t#kJ/kg K\n", "y = 1.4;\n", "p1 = 1.; \t\t\t#bar\n", "T1 = 300.; \t\t\t#K\n", "Q = 1500.; \t\t\t#kJ/kg\n", "r = 8.;\n", "y = 1.4;\n", "\n", "# Calculations and Results\n", "print (\"(i) Pressures and temperatures at all points\")\n", "T2 = T1*(r)**(y-1);\n", "print (\"T2 = %.3f\")% (T2), (\"K\")\n", "\n", "p2 = p1*(r)**y;\n", "print (\"p2 = %.3f\")%(p2), (\"bar\")\n", "\n", "T3 = Q/cv + T2;\n", "print (\"T3 = %.3f\")% (T3), (\"K\")\n", "\n", "p3 = p2*T3/T2;\n", "print (\"p3 = %.3f\")% (p3), (\"bar\")\n", "\n", "T4 = T3/r**(y-1);\n", "print (\"T4 = %.3f\")% (T4), (\"K\")\n", "\n", "p4 = p3/r**(y);\n", "print (\"p4 = %.3f\")% (p4), (\"bar\")\n", "\n", "\n", "print (\"(ii) Specific work and thermal efficiency\")\n", "SW = cv*((T3-T2) - (T4-T1));\n", "print (\"Specific work = %.3f\")% (SW), (\"kJ/kg\")\n", "\n", "n_th = 1-1./r**(y-1);\n", "print (\"Thermal efficiency = %.3f\")% (n_th)\n" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "(i) Pressures and temperatures at all points\n", "T2 = 689.219 K\n", "p2 = 18.379 bar\n", "T3 = 2772.552 K\n", "p3 = 73.935 bar\n", "T4 = 1206.824 K\n", "p4 = 4.023 bar\n", "(ii) Specific work and thermal efficiency\n", "Specific work = 847.087 kJ/kg\n", "Thermal efficiency = 0.565\n" ] } ], "prompt_number": 8 }, { "cell_type": "heading", "level": 3, "metadata": {}, "source": [ "Example 13.10 page no : 618" ] }, { "cell_type": "code", "collapsed": false, "input": [ "\n", "# Variables\n", "r = 6.; \t\t\t#v1/v2 = v4/v3 = r\n", "p1 = 1.; \t\t\t#bar\n", "T1 = 300.; \t\t\t#K\n", "T3 = 1842.; \t\t#K\n", "y = 1.4;\n", "\n", "# Calculations and Results\n", "print (\"(i) Temperature and pressure after the isentropic expansion\")\n", "p2 = p1*(r)**y;\n", "T2 = T1*r**(y-1);\n", "p3 = p2*(T3/T2);\n", "T4 = T3/r**(y-1);\n", "print (\"T4 = %.3f\")% (T4), (\"K\")\n", "\n", "p4 = p3/(r)**(y);\n", "print (\"p4 = %.3f\")% (p4), (\"bar\")\n", "\n", "print (\"(ii)Process required to complete the cycle is the consmath.tant pressure scavenging. The cycle is called Atkinson cycle\")\n", "print (\"(iii) Percentage improvement/increase in efficiency\")\n", "p5 = 1.; \t\t\t#bar\n", "T5 = T3*(p5/p3)**((y-1)/y);\n", "n_otto = (1-1./r**(y-1))*100;\n", "print (\"n_otto = %.3f\")% (n_otto), (\"%\")\n", "\n", "n_atkinson = (1.-y*(T5-T1)/(T3-T2))*100;\n", "print (\"n_atkinson = %.3f\")% (n_atkinson), (\"%\")\n", "\n", "dn = n_atkinson - n_otto; \t\t\t#Improvement in efficiency\n", "print (\"Improvement in efficiency = %.3f\")% (dn), (\"%\")\n" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "(i) Temperature and pressure after the isentropic expansion\n", "T4 = 899.558 K\n", "p4 = 2.999 bar\n", "(ii)Process required to complete the cycle is the consmath.tant pressure scavenging. The cycle is called Atkinson cycle\n", "(iii) Percentage improvement/increase in efficiency\n", "n_otto = 51.164 %\n", "n_atkinson = 59.254 %\n", "Improvement in efficiency = 8.090 %\n" ] } ], "prompt_number": 7 }, { "cell_type": "heading", "level": 3, "metadata": {}, "source": [ "Example 13.11 page no : 620" ] }, { "cell_type": "code", "collapsed": false, "input": [ "# Variables\n", "p1 = 1.; \t\t\t#bar\n", "T1 = 343.; \t \t\t#K\n", "p2 = 7.; \t\t \t#bar\n", "Qs = 465.; \t\t\t #kJ/kg of air\n", "cp = 1.; \t\t\t #kJ/kg K\n", "cv = 0.706; \t\t\t#kJ/kg K\n", "y = 1.41;\n", "\n", "# Calculations and Results\n", "r = (p2/p1)**(1./y);\n", "print (\"(i) Compression ratio of engine = %.3f\")% (r)\n", "\n", "T2 = T1*(r)**(y-1);\n", "t2 = T2-273;\n", "print (\"(ii) Temperature at the end of compression = %.3f\")% (t2), (\"0C\")\n", "\n", "T3 = Qs/cv+T2;\n", "t3 = T3-273;\n", "print (\"(iii) Temperature at the end of heat addition = %.3f\")% (t3), (\"0C\")\n" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "(i) Compression ratio of engine = 3.975\n", "(ii) Temperature at the end of compression = 330.993 0C\n", "(iii) Temperature at the end of heat addition = 989.633 0C\n" ] } ], "prompt_number": 10 }, { "cell_type": "heading", "level": 3, "metadata": {}, "source": [ "Example 13.12 page no : 621" ] }, { "cell_type": "code", "collapsed": false, "input": [ "\n", "# Variables\n", "y = 1.4;\n", "R = 0.287; \t \t\t#kJ/kg K\n", "T1 = 311.; \t\t\t#K\n", "T3 = 2223.; \t\t\t#K\n", "\n", "#p2/p1 = 15\n", "r = 15**(1/1.4);\n", "print (\"(i) Compression ratio = %.3f\")% (r)\n", "\n", "n_th = 1-1./r**(y-1);\n", "print (\"(ii) Thermal efficiency = %.3f\")% (n_th)\n", "\n", "T2 = T1*(r)**(y-1);\n", "T4 = T3/r**(y-1);\n", "cv = R/(y-1);\n", "\n", "Q_supplied = cv*(T3-T2);\n", "Q_rejected = cv*(T4-T1);\n", "\n", "W = Q_supplied-Q_rejected;\n", "print (\"(iii)Work done = %.3f\")% (W), (\"kJ\")\n" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "(i) Compression ratio = 6.919\n", "(ii) Thermal efficiency = 0.539\n", "(iii)Work done = 598.651 kJ\n" ] } ], "prompt_number": 8 }, { "cell_type": "heading", "level": 3, "metadata": {}, "source": [ "Example 13.13 page no : 623" ] }, { "cell_type": "code", "collapsed": false, "input": [ "# Variables\n", "V1 = 0.45; \t\t\t#m**3\n", "p1 = 1.; \t\t\t#bar\n", "T1 = 303.; \t\t\t#K\n", "p2 = 11.; \t\t\t#bar\n", "Qs = 210.; \t\t\t#kJ\n", "n = 210.; \t\t\t#number of working cycles/min\n", "R = 287.; \t\t\t#J/kg K\n", "cv = 0.71; \t\t\t#kJ/kg K\n", "y = 1.4;\n", "\n", "# Calculations and Results\n", "print (\"(i) Pressures, temperatures and volumes at salient points\")\n", "r = (p2/p1)**(1./y);\n", "\n", "T2 = T1*(r)**(y-1);\n", "print (\"T2 = %.3f\")% (T2), (\"K\")\n", "\n", "V2 = T2/T1*p1/p2*V1;\n", "print (\"V2 = %.3f\")% (V2), (\"m**3\")\n", "\n", "m = p1*10**5*V1/R/T1;\n", "T3 = Qs/m/cv+T2;\n", "print (\"T3 = %.3f\")% (T3), (\"K\")\n", "\n", "p3 = T3/T2*p2;\n", "print (\"p3 = %.3f\")% (p3), (\"bar\")\n", "\n", "V3 = V2;\n", "print (\"V3 = %.3f\")% (V3), (\"m**3\")\n", "\n", "p4 = p3/r**y;\n", "print (\"p4 = %.3f\")%(p4), (\"bar\")\n", "\n", "T4 = T3/r**(y-1);\n", "print (\"T4 = %.3f\")% (T4), (\"K\")\n", "\n", "V4 = V1;\n", "print (\"V4 = %.3f\")%(V4), (\"m**3\")\n", "\n", "Qr = m*cv*(T4-T1);\n", "n_otto = (Qs-Qr)/Qs;\n", "print (\"(iii) Efficiency = %.3f\")% (n_otto)\n", "\n", "\n", "p_m = (Qs-Qr)/(V1-V2)/100; \t\t\t#bar\n", "print (\"(iv) Mean effective pressure = %.3f\")% (p_m), (\"bar\")\n", "\n", "P = (Qs-Qr)*n/60;\n", "print (\"(v) Power developed = %.3f\")% (P), (\"kW\")\n" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "(i) Pressures, temperatures and volumes at salient points\n", "T2 = 601.151 K\n", "V2 = 0.081 m**3\n", "T3 = 1172.725 K\n", "p3 = 21.459 bar\n", "V3 = 0.081 m**3\n", "p4 = 1.951 bar\n", "T4 = 591.093 K\n", "V4 = 0.450 m**3\n", "(iii) Efficiency = 0.496\n", "(iv) Mean effective pressure = 2.824 bar\n", "(v) Power developed = 364.536 kW\n" ] } ], "prompt_number": 9 }, { "cell_type": "heading", "level": 3, "metadata": {}, "source": [ "Example 13.14 page no : 625" ] }, { "cell_type": "code", "collapsed": false, "input": [ "# Variables\n", "print (\"r = (T3/T1)**(1/2/(y-1))\")\n", "print (\"(b)Change in efficiency\")\n", "T3 = 1220.; \t\t\t#K\n", "T1 = 310. \t\t\t#K\n", "\n", "# Calculations and Results\n", "# For air\n", "y = 1.4;\n", "r1 = (T3/T1)**(1./2./(y-1));\n", "n1 = 1-1/r1**(y-1); \t\t\t#air smath.radians(numpy.arcmath.tan(ard Efficiency\n", "print (\"Air standard Efficiency = %.3f\")% (n1)\n", "\n", "#For helium\n", "cp = 5.22; \t\t\t#kJ/kg K\n", "cv = 3.13; \t\t\t#kJ/kg K\n", "y = cp/cv;\n", "r2 = (T3/T1)**(1./2/(y-1));\n", "\n", "n2 = 1-1/r2**(y-1);\n", "print (\"Air standard efficiency for helium = %.3f\")% (n2)\n", "\n", "change = n1-n2;\n", "print (\"Change in efficiency = %.3f\")% (change)\n", "\n", "print (\"Hence change in efficiency is nil\")\n" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "r = (T3/T1)**(1/2/(y-1))\n", "(b)Change in efficiency\n", "Air standard Efficiency = 0.496\n", "Air standard efficiency for helium = 0.496\n", "Change in efficiency = -0.000\n", "Hence change in efficiency is nil\n" ] } ], "prompt_number": 14 }, { "cell_type": "heading", "level": 3, "metadata": {}, "source": [ "Example 13.15 page no : 627" ] }, { "cell_type": "code", "collapsed": false, "input": [ "print (\"(b) Power developed \")\n", "\n", "# Variables\n", "T1 = 310.; \t\t\t#K\n", "T3 = 1450.; \t\t#K\n", "m = 0.38; \t\t\t#kg\n", "cv = 0.71; \t\t\t#kJ/kg K\n", "\n", "# Calculations\n", "T2 = math.sqrt(T1*T3);\n", "T4 = T2;\n", "\n", "W1 = cv*((T3-T2) - (T4-T1)); \t\t\t#Work done\n", "W = m/60*W1; \t\t\t#Work done per second\n", "\n", "# Results\n", "print (\"Power = %.3f\")%(W), (\"kW\")\n" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "(b) Power developed \n", "Power = 1.885 kW\n" ] } ], "prompt_number": 10 }, { "cell_type": "heading", "level": 3, "metadata": {}, "source": [ "Example 13.17 page no : 632" ] }, { "cell_type": "code", "collapsed": false, "input": [ "# Variables\n", "r = 15.;\n", "y = 1.4;\n", "#V3-V2 = 0.06*(V1-V2)\n", "rho = 1.84; \t\t\t#cut off ratio rho = V3/V2\n", "\n", "# Calculations\n", "n_diesel = 1-1/y/r**(y-1)*((rho**y-1)/(rho-1));\n", "\n", "# Results\n", "print (\"efficiency = %.3f\")% (n_diesel)\n" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "efficiency = 0.612\n" ] } ], "prompt_number": 16 }, { "cell_type": "heading", "level": 3, "metadata": {}, "source": [ "Example 13.18 page no : 633" ] }, { "cell_type": "code", "collapsed": false, "input": [ "# Variables\n", "L = 0.25; \t\t\t#m\n", "D = 0.15; \t\t\t#m\n", "V2 = 0.0004; \t\t#m**3\n", "\n", "# Calculations\n", "Vs = math.pi/4*D**2*L;\n", "V_total = Vs+V2;\n", "y = 1.4;\n", "V3 = V2+5./100*Vs;\n", "rho = V3/V2;\n", "r = (Vs+V2)/V2; \t\t\t#V1 = Vs+V2\n", "n_diesel = 1-1/y/r**(y-1)*((rho**y-1)/(rho-1));\n", "\n", "# Results\n", "print (\"efficiency = %.3f\")%(n_diesel)\n" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "efficiency = 0.593\n" ] } ], "prompt_number": 17 }, { "cell_type": "heading", "level": 3, "metadata": {}, "source": [ "Example 13.19 page no : 633" ] }, { "cell_type": "code", "collapsed": false, "input": [ "# Variables\n", "y = 1.4;\n", "r = 14\n", "\n", "# Calculations\n", "#When the fuel is cut-off at 5%\n", "rho1 = 5./100*(r-1)+1;\n", "n_diesel1 = 1-1./y/r**(y-1)*((rho1**y-1)/(rho1-1));\n", "\n", "#When the fuel is cut-off at 8%\n", "rho2 = 8./100*(r-1)+1;\n", "n_diesel2 = 1-1./y/r**(y-1)*((rho2**y-1)/(rho2-1));\n", "loss = (n_diesel1-n_diesel2)*100;\n", "\n", "# Results\n", "print (\"percentage loss in efficiency due to delay in fuel cut off = %.1f\")% (loss), (\"%\")\n" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "percentage loss in efficiency due to delay in fuel cut off = 2.1 %\n" ] } ], "prompt_number": 12 }, { "cell_type": "heading", "level": 3, "metadata": {}, "source": [ "Example 13.20 page no : 634" ] }, { "cell_type": "code", "collapsed": false, "input": [ "# Variables\n", "pm = 7.5; \t\t\t#bar\n", "r = 12.5;\n", "p1 = 1; \t\t\t#bar\n", "y = 1.4;\n", "rho = 2.24;\n", "\n", "# Calculations\n", "cutoff = (rho-1)/(r-1)*100;\n", "\n", "# Results\n", "print (\"cutoff = %.3f\")% (cutoff), (\"%\")\n" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "cutoff = 10.783 %\n" ] } ], "prompt_number": 19 }, { "cell_type": "heading", "level": 3, "metadata": {}, "source": [ "Example 13.21 page no : 634" ] }, { "cell_type": "code", "collapsed": false, "input": [ "\n", "# Variables\n", "D = 0.2; \t\t\t#m\n", "L = 0.3; \t\t\t#m\n", "p1 = 1.; \t\t\t#bar\n", "T1 = 300.; \t\t\t#K\n", "R = 287.;\n", "r = 15.;\n", "y = 1.4;\n", "\n", "# Calculations and Results\n", "print (\"(i) Pressures and temperatures at salient points\")\n", "Vs = math.pi/4*D**2*L;\n", "\n", "V1 = r/(r-1)*Vs;\n", "print (\"V1 = %.3f\")% (V1), (\"m**3\")\n", "\n", "m = p1*10**5*V1/R/T1;\n", "\n", "p2 = p1*r**y;\n", "print (\"p2 = %.3f\")% (p2), (\"bar\")\n", "\n", "T2 = T1*r**(y-1);\n", "print (\"T2 = %.3f\")% (T2), (\"K\")\n", "\n", "V2 = Vs/(r-1);\n", "print (\"V2 = %.5f\")% (V2), (\"m**3\")\n", "\n", "rho = 8./100*(r-1) + 1;\n", "V3 = rho*V2;\n", "print (\"V3 = %.5f\")% (V3), (\"m**3\")\n", "\n", "T3 = T2*V3/V2;\n", "print (\"T3 = %.3f\")% (T3), (\"K\")\n", "\n", "p3 = p2;\n", "print (\"p3 = %.3f\")% (p3), (\"bar\")\n", "\n", "p4 = p3*(rho/r)**y;\n", "print (\"p4 = %.3f\")% (p4), (\"bar\")\n", "\n", "T4 = T3*(rho/r)**(y-1);\n", "print (\"T4 = %.3f\")% (T4), (\"K\")\n", "\n", "V4 = V1;\n", "print (\"V4 = %.3f\")% (V4), (\"m**3\")\n", "\n", "print (\"(ii) Theoretical air standard efficiency = \"),\n", "n_diesel = 1-1/y/r**(y-1)*((rho**y-1)/(rho-1));\n", "print (\"efficiency = %.3f\")% (n_diesel)\n", "\n", "\n", "pm = (p1*r**y*(y*(rho-1) - r**(1-y)*(rho**y-1)))/(y-1)/(r-1);\n", "print (\"(iii) Mean effective pressure = %.3f\")% (pm), (\"bar\")\n", "\n", "n = 380; \t\t\t#number of cycles per min\n", "P = n/60.*pm*Vs*100; \t\t\t#kW\n", "print (\"(iv) Power of the engine = %.3f\")% (P), (\"kW\")\n" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "(i) Pressures and temperatures at salient points\n", "V1 = 0.010 m**3\n", "p2 = 44.313 bar\n", "T2 = 886.253 K\n", "V2 = 0.00067 m**3\n", "V3 = 0.00143 m**3\n", "T3 = 1878.857 K\n", "p3 = 44.313 bar\n", "p4 = 2.863 bar\n", "T4 = 858.997 K\n", "V4 = 0.010 m**3\n", "(ii) Theoretical air standard efficiency = efficiency = 0.598\n", "(iii) Mean effective pressure = 7.417 bar\n", "(iv) Power of the engine = 44.269 kW\n" ] } ], "prompt_number": 12 }, { "cell_type": "heading", "level": 3, "metadata": {}, "source": [ "Example 13.22 page no : 637" ] }, { "cell_type": "code", "collapsed": false, "input": [ "\n", "# Variables\n", "r1 = 15.3; \t\t\t#V1/V2\n", "r2 = 7.5; \t\t\t#V4/V3\n", "p1 = 1.; \t\t\t#bar\n", "T1 = 300.; \t\t\t#K\n", "n_mech = 0.8;\n", "C = 42000.; \t\t#kJ/kg\n", "y = 1.4;\n", "R = 287.;\n", "cp = 1.005;\n", "cv = 0.718;\n", "V2 = 1.; \t\t\t\t\t#Assuming V2 = 1 m**3\n", "\n", "# Calculations\n", "T2 = T1*r1**(y-1);\n", "p2 = p1*r1**y;\n", "T3 = r1/r2*T2;\n", "m = p2*10**5*V2/R/T2;\n", "T4 = T3/r2**(y-1);\n", "\n", "Q_added = m*cp*(T3-T2);\n", "Q_rejected = m*cv*(T4-T1);\n", "W = Q_added-Q_rejected;\n", "\n", "pm = W/(r1-1)/V2/100;\n", "\n", "# Results\n", "print (\"Mean effective pressure = %.3f\")% (pm), (\"bar\")\n", "\n", "ratio = p2/pm;\n", "print (\"Ratio of maximum pressure to mean effective pressure = %.3f\")% (ratio)\n", "\n", "n_cycle = W/Q_added;\n", "print (\"Cycle efficiency = %.3f\")% (n_cycle)\n", "\n", "n_thI = 0.5;\n", "n_cycle1 = n_thI*n_cycle;\n", "\n", "n_thB = n_mech*n_cycle1;\n", "\n", "BP = 1;\n", "mf = BP/C/n_thB*3600;\n", "print (\"Fuel consumption per kWh = %.3f \")% (mf), (\"kg/kWh\")\n" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "Mean effective pressure = 7.017 bar\n", "Ratio of maximum pressure to mean effective pressure = 6.493\n", "Cycle efficiency = 0.605\n", "Fuel consumption per kWh = 0.354 kg/kWh\n" ] } ], "prompt_number": 21 }, { "cell_type": "heading", "level": 3, "metadata": {}, "source": [ "Example 13.23 page no : 642" ] }, { "cell_type": "code", "collapsed": false, "input": [ "# Variables\n", "Vs = 0.0053; \t\t\t#m**3\n", "Vc = 0.00035; \t\t\t#m**3\n", "V3 = Vc;\n", "V2 = V3;\n", "p3 = 65.; \t\t\t#bar\n", "p4 = 65.; \t\t\t#bar\n", "T1 = 353.; \t\t\t#K\n", "p1 = 0.9; \t\t\t#bar\n", "y = 1.4;\n", "\n", "# Calculations\n", "r = (Vs+Vc)/Vc;\n", "rho = (5/100*Vs+V3)/V3;\n", "p2 = p1*(r)**y;\n", "B = p3/p2;\n", "n_dual = 1-1/r**(y-1)*((B*rho**y-1)/((B-1)+B*y*(rho-1)));\n", "\n", "# Results\n", "print (\"Efficiency of the cycle = %.3f\")% (n_dual)\n" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "Efficiency of the cycle = 0.671\n" ] } ], "prompt_number": 22 }, { "cell_type": "heading", "level": 3, "metadata": {}, "source": [ "Example 13.24 page no : 643" ] }, { "cell_type": "code", "collapsed": false, "input": [ "# Variables\n", "r = 14.;\n", "B = 1.4;\n", "rho = 6./100*(r-1) + 1;\n", "y = 1.4;\n", "\n", "# Calculations\n", "n_dual = 1-1./r**(y-1)*((B*rho**y-1)/((B-1)+B*y*(rho-1)))\n", "\n", "# Results\n", "print (\"Efficiency of the cycle = %.3f\")% (n_dual)\n" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "Efficiency of the cycle = 0.614\n" ] } ], "prompt_number": 23 }, { "cell_type": "heading", "level": 3, "metadata": {}, "source": [ "Example 13.25 page no : 643" ] }, { "cell_type": "code", "collapsed": false, "input": [ "\n", "# Variables\n", "D = 0.25; \t\t\t#m\n", "r = 9.; \n", "L = 0.3; \t\t\t#m\n", "cv = 0.71; \t\t\t#kJ/kg K\n", "cp = 1.; \t\t\t#kJ/kg K\n", "p1 = 1.; \t\t\t#bar\n", "T1 = 303.; \t\t\t#K\n", "p3 = 60.; \t\t\t#bar\n", "p4 = p3;\n", "n = 3.; \t\t\t#number of working cycles/ sec\n", "y = 1.4;\n", "R = 287.;\n", "\n", "# Calculations and Results\n", "print (\"(i) Air standard efficiency\")\n", "Vs = math.pi/4*D**2*L;\n", "Vc = Vs/(r-1);\n", "V1 = Vs+Vc;\n", "p2 = p1*(r)**y;\n", "T2 = T1*r**(y-1);\n", "T3 = T2*p3/p2;\n", "rho = 4./100*(r-1)+1;\n", "T4 = T3*rho;\n", "T5 = T4*(rho/r)**(y-1);\n", "p5 = p4*(r/rho)**(y);\n", "Qs = cv*(T3-T2)+cp*(T4-T3)\n", "Qr = cv*(T5-T1);\n", "\n", "n_airsard = (Qs-Qr)/Qs;\n", "print (\"efficiency = %.3f\")% (n_airsard)\n", "\n", "print (\"(ii) Power developed by the engine\")\n", "m = p1*10**5*V1/R/T1;\n", "\n", "W = m*(Qs-Qr);\n", "\n", "P = W*n;\n", "print (\"P = %.3f\")% (P), (\"kW\")\n" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "(i) Air standard efficiency\n", "efficiency = 0.575\n", "(ii) Power developed by the engine\n", "P = 51.392 kW\n" ] } ], "prompt_number": 24 }, { "cell_type": "heading", "level": 3, "metadata": {}, "source": [ "Example 13.26 page no : 646" ] }, { "cell_type": "code", "collapsed": false, "input": [ "\n", "# Variables\n", "p1 = 1.; \t\t\t#bar\n", "T1 = 363.; \t\t\t#K\n", "r = 9.; \n", "p3 = 68.; \t\t\t#bar\n", "p4 = 68.; \t\t\t#bar\n", "Q = 1750.; \t\t\t#kJ/kg\n", "y = 1.4;\n", "cv = 0.71;\n", "cp = 1.0;\n", "\n", "# Calculations and Results\n", "print (\"(i) Pressures and temperatures at salient points\")\n", "p2 = p1*(r)**y;\n", "print (\"p2 = %.3f\")% (p2), (\"bar\")\n", "\n", "T2 = T1*r**(y-1);\n", "print (\"T2 = %.3f\")% (T2), (\"K\")\n", "\n", "print (\"p3 = %.3f\")% (p3), (\"bar\")\n", "\n", "print (\"p4 = %.3f\")% (p4), (\"bar\")\n", "\n", "T3 = T2*(p3/p2);\n", "print (\"T3 = %.3f\")% (T3), (\"K\")\n", "\n", "Q1 = cv*(T3-T2); \t\t\t#heat added at consmath.tant volume\n", "Q2 = Q-Q1; \t \t\t#heat added at consmath.tant pressure\n", "\n", "T4 = Q2/cp+T3;\n", "print (\"T4 = %.3f\")% (T4), (\"K\")\n", "\n", "rho = T4/T3; \t\t\t#V4/V3 = T4/T3\n", "\n", "p5 = p4*(rho/r)**y;\n", "print (\"p5 = %.3f\")% (p5), (\"bar\")\n", "\n", "T5 = T4*(rho/r)**(y-1);\n", "print (\"T5 = %.3f\")% (T5), (\"K\")\n", "\n", "\n", "Qr = cv*(T5-T1);\n", "n_airard = (Q-Qr)/Q;\n", "print (\"(ii) Air standard efficiency = %.3f\")% (n_airard)\n", "\n", "\n", "pm = 1./(r-1)*(p3*(rho-1) + (p4*rho-p5*r)/(y-1) - (p2-p1*r)/(y-1));\n", "print (\"(iii) Mean effective pressure = %.3f\")% (pm), (\"bar\")\n" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "(i) Pressures and temperatures at salient points\n", "p2 = 21.674 bar\n", "T2 = 874.186 K\n", "p3 = 68.000 bar\n", "p4 = 68.000 bar\n", "T3 = 2742.667 K\n", "T4 = 3166.045 K\n", "p5 = 3.836 bar\n", "T5 = 1392.380 K\n", "(ii) Air standard efficiency = 0.582\n", "(iii) Mean effective pressure = 11.094 bar\n" ] } ], "prompt_number": 25 }, { "cell_type": "heading", "level": 3, "metadata": {}, "source": [ "Example 13.27 page no : 648" ] }, { "cell_type": "code", "collapsed": false, "input": [ "# Variables\n", "T1 = 300.; \t\t\t#K\n", "r = 15.;\n", "y = 1.4;\n", "\n", "# Calculations\n", "#p3/p1 = 70\n", "T2 = T1*(r)**(y-1);\n", "#p2/p1 = r**y\n", "#p2 = 44.3*p1\n", "T3 = 1400.; \t\t\t#K; T3 = T2*p3/p2\n", "T4 = T3 + (T3-T2)/y;\n", "T5 = 656.9; \t\t\t#K\n", "n_airard = 1-(T5-T1)/((T3-T2) + y*(T4-T3));\n", "\n", "# Results\n", "print (\"Efficiency = %.3f\")% (n_airard)\n" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "Efficiency = 0.653\n" ] } ], "prompt_number": 13 }, { "cell_type": "heading", "level": 3, "metadata": {}, "source": [ "Example 13.28 page no : 650" ] }, { "cell_type": "code", "collapsed": false, "input": [ "# Variables\n", "T1 = 373.; \t\t\t#K\n", "p1 = 1.; \t\t\t#bar\n", "p3 = 65.; \t\t\t#bar\n", "p4 = p3;\n", "Vs = 0.0085; \t\t\t#m**3\n", "ratio = 21.; \t\t\t#Air fuel ratio\n", "r = 15.;\n", "C = 43890.; \t\t\t#kJ/kg\n", "cp = 1.;\n", "cv = 0.71;\n", "V2 = 0.0006; \t\t\t#m**3\n", "V1 = 0.009; \t\t\t#m**3\n", "y = 1.41;\n", "V5 = V1;\n", "V3 = V2;\n", "R = 287.;\n", "\n", "# Calculations\n", "p2 = p1*(r)**y;\n", "T2 = T1*r**(y-1);\n", "T3 = T2*p3/p2;\n", "m = p1*10**5*V1/R/T1;\n", "Q1 = m*cv*(T3-T2); \t\t\t#Heat added during consmath.tant volume process 2-3\n", "amt = Q1/C; \t\t\t #Amount of fuel added during the consmath.tant volume process 2-3\n", "total = m/ratio; \t\t\t#Total amount of fuel added\n", "quantity = total-amt; \t\t#Quantity of fuel added during the process 3-4\n", "Q2 = quantity*C; \t\t\t#Heat added during consmath.tant pressure process\n", "T4 = Q2/(m+total)/cp+T3;\n", "V4 = V3*T4/T3;\n", "T5 = T4*(V4/V5)**(y-1);\n", "Q3 = (m+total)*cv*(T5-T1); \t#Heat rejected during consmath.tant volume process 5-1\n", "W = (Q1+Q2) - Q3;\n", "n_th = W/(Q1+Q2);\n", "\n", "# Results\n", "print (\"Thermal efficiency = %.3f\")% (n_th)\n" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "Thermal efficiency = 0.618\n" ] } ], "prompt_number": 27 }, { "cell_type": "heading", "level": 3, "metadata": {}, "source": [ "Example 13.29 page no : 652" ] }, { "cell_type": "code", "collapsed": false, "input": [ "# Variables\n", "T1 = 303.; \t\t\t#K\n", "p1 = 1.; \t\t\t#bar\n", "rc = 9.;\n", "re = 5.;\n", "n = 1.25;\n", "D = 0.25; \t\t\t#m\n", "L = 0.4; \t\t\t#m\n", "R = 287.;\n", "cv = 0.71;\n", "cp = 1.;\n", "num = 8.; \t\t\t#no. 0f cycles/sec\n", "\n", "# Calculations and Results\n", "print (\"(i) Pressure and temperatures at all salient points = \"),\n", "p2 = p1*(rc)**n;\n", "print (\"p2 = %.3f\")% (p2), (\"bar\")\n", "\n", "T2 = T1*(rc)**(n-1);\n", "print (\"T2 = \"), (T2), (\"K\")\n", "\n", "rho = rc/re;\n", "T3 = 1201.9; \t\t\t#K\n", "print (\"T3 = \"), (T3), (\"K\")\n", "\n", "p3 = p2*T3/T2;\n", "print (\"p3 = \"), (p3), (\"bar\")\n", "\n", "p4 = p3;\n", "print (\"p4 = \"),(p4), (\"bar\")\n", "\n", "T4 = 1.8*T3;\n", "print (\"T4 = \"), (T4), (\"K\")\n", "\n", "p5 = p4*(1./re)**(n);\n", "print (\"p5 = %.3f\")%(p5), (\"bar\")\n", "\n", "T5 = T4*(1./re)**(n-1)\n", "print (\"T5 = %.3f\")%(T5),(\"K\")\n", "\n", "\n", "pm = 1./(rc-1)*(p3*(rho-1)+(p4*rho-p5*rc)/(n-1)-(p2-p1*rc)/(n-1));\n", "print (\"(ii) Mean effective pressure = %.3f\")% (pm), (\"bar\")\n", "\n", "print (\"(iii) Efficiency of the cycle\")\n", "Vs = math.pi/4*D**2*L;\n", "W = pm*10**5*Vs/1000;\n", "\n", "V1 = rc/(rc-1)*Vs\n", "m = p1*10**5*V1/R/T1;\n", "Q = m*(cv*(T3-T2) + cp*(T4-T3));\n", "\n", "Efficiency = W/Q;\n", "print (\"Efficiency = %.3f\")% (Efficiency)\n", "\n", "P = W*num;\n", "print (\"(iv) Power of the engine = %.3f\")% (P), (\"kW\")\n" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "(i) Pressure and temperatures at all salient points = p2 = 15.588 bar\n", "T2 = 524.811394693 K\n", "T3 = 1201.9 K\n", "p3 = 35.7 bar\n", "p4 = 35.7 bar\n", "T4 = 2163.42 K\n", "p5 = 4.775 bar\n", "T5 = 1446.766 K\n", "(ii) Mean effective pressure = 10.919 bar\n", "(iii) Efficiency of the cycle\n", "Efficiency = 0.585\n", "(iv) Power of the engine = 171.518 kW\n" ] } ], "prompt_number": 15 }, { "cell_type": "heading", "level": 3, "metadata": {}, "source": [ "Example 13.30 page no : 657" ] }, { "cell_type": "code", "collapsed": false, "input": [ "%pylab inline\n", "\n", "from numpy import *\n", "from matplotlib.pyplot import *\n", "\n", "v = linspace(10,100,90)\n", "def f(v):\n", " return 1./v**1.4;\n", "\n", "f1 = f(v)\n", "plot(v,f1)\n", "v = [10, 20]\n", "p = [f(10), f(10)]\n", "plot(v,p,'r')\n", "\n", "v = linspace(20,100,80)\n", "def fa(v):\n", " return 2.6515/v**1.4;\n", "f1 = fa(v)\n", "plot(v,f1,'g')\n", "\n", "v = [100, 100]\n", "p = [f(100), fa(100)]\n", "plot(v,p,'--p')\n", "\n", "v = [15, 15]\n", "p = [f(15), 0.040]\n", "plot(v,p,'--')\n", "\n", "v = [20 ,20]\n", "p = [f(20), 0.040]\n", "plot(v,p,'--r')\n", "\n", "s = linspace(10,50,40);\n", "\n", "def fb(s):\n", " return s**2\n", "f1 = fb(s)\n", "plot(s,f1)\n", "\n", "s = linspace(10,50,40)\n", "\n", "def fc(s):\n", " return (s+30)**2\n", "f1 = fc(s)\n", "plot(s,f1,'r')\n", "\n", "s = [12, 12];\n", "T = [fb(12), fc(12)];\n", "plot(s,T,'--p')\n", "\n", "s = [45, 45];\n", "T = [fb(45) ,fc(45)]\n", "plot(s,T,'m')\n", "\n", "s = linspace(10,27,17);\n", "T = 5*(s)**2;\n", "plot(s,T,'g')\n", "\n", "s = linspace(10,20,10);\n", "T = 7*s**2;\n", "plot(s,T,'--r')\n", "\n", "\n", "print (\"Thus, \u03b7diesel > \u03b7dual > \u03b7otto\")\n" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "Populating the interactive namespace from numpy and matplotlib\n", "Thus, \u03b7diesel > \u03b7dual > \u03b7otto" ] }, { "output_type": "stream", "stream": "stdout", "text": [ "\n" ] }, { "metadata": {}, "output_type": "display_data", "png": 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1Vm5u2VLriEII4RAaTCHY99M+5jOfjj91pFfvXpetL62sJPXsWYyF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\ngg==\n", "text": [ "" ] } ], "prompt_number": 1 }, { "cell_type": "heading", "level": 3, "metadata": {}, "source": [ "Example 13.31 page no : 659" ] }, { "cell_type": "code", "collapsed": false, "input": [ "# Variables\n", "cp = 0.92;\n", "cv = 0.75;\n", "y = 1.22; \t\t\t#y = cp/cv\n", "p1 = 1.; \t\t\t#bar\n", "p2 = p1;\n", "p3 = 4.; \t\t\t#bar\n", "p4 = 16.; \t\t\t#bar\n", "T2 = 300.; \t\t\t#K\n", "\n", "# Calculations and Results\n", "T3 = T2*(p3/p2)**((y-1)/y);\n", "T4 = p4/p3*T3;\n", "T1 = T4/(p4/p1)**((y-1)/y);\n", "\n", "print (\"(i) Work done per kg of gas \")\n", "Q_supplied = cv*(T4-T3);\n", "Q_rejected = cp*(T1-T2);\n", "\n", "W = Q_supplied-Q_rejected;\n", "print (\"W = %.3f\")% (W), (\"kJ/kg\")\n", "\n", "n = W/Q_supplied;\n", "print (\"(ii) Efficiency of the cycle = %.3f\")%(n)\n" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "(i) Work done per kg of gas \n", "W = 282.900 kJ/kg\n", "(ii) Efficiency of the cycle = 0.326\n" ] } ], "prompt_number": 32 }, { "cell_type": "heading", "level": 3, "metadata": {}, "source": [ "Example 13.32 page no : 680" ] }, { "cell_type": "code", "collapsed": false, "input": [ "# Variables\n", "p1 = 101.325; \t\t#kPa\n", "T1 = 300.; \t\t\t#K\n", "rp = 6.;\n", "y = 1.4;\n", "\n", "# Calculations\n", "T2 = T1*rp**((y-1)/y);\n", "T3 = 2.5*(T2-T1)/(1-1/1.668);\n", "\n", "# Results\n", "print (\"(i) Maximum temperature in the cycle = %.3f\")% (T3), (\"K\")\n", "\n", "\n", "T4 = T3/1.668;\n", "\n", "n_cycle = ((T3-T4) - (T2-T1))/(T3-T2);\n", "print (\"(ii)Cycle efficiency = %.3f\")% (n_cycle)\n" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "(i) Maximum temperature in the cycle = 1251.956 K\n", "(ii)Cycle efficiency = 0.400\n" ] } ], "prompt_number": 16 }, { "cell_type": "heading", "level": 3, "metadata": {}, "source": [ "Example 13.33 page no : 681" ] }, { "cell_type": "code", "collapsed": false, "input": [ "%pylab inline\n", "from numpy import *\n", "from matplotlib.pyplot import *\n", "\n", "# Variables\n", "p1 = 1.; \t\t\t#bar\n", "p2 = 5.; \t\t\t#bar\n", "T3 = 1000.; \t\t\t#K\n", "cp = 1.0425; \t\t\t#kJ/kg K\n", "cv = 0.7662; \t\t\t#kJ/kg K\n", "y = cp/cv;\n", "\n", "print (\"(i)Temperature entropy diagram\")\n", "\n", "# Calculations\n", "s = linspace(10,50,40);\n", "def fb(s):\n", " return s**2\n", "\n", "plot(s,fb(s),'--')\n", "\n", "s = linspace(10,50,40);\n", "\n", "def fc(s):\n", " return (s+30)**2\n", "\n", "plot(s,fc(s),'r')\n", "\n", "s = [12, 12];\n", "T = [fb(12), fc(12)];\n", "plot(s,T,'m')\n", "\n", "s = [45 ,45];\n", "T = [fb(45), fc(45)]\n", "plot(s,T,'g')\n", "\n", "\n", "# Results\n", "print (\"(ii) Power required = \")\n", "T4 = T3*(p1/p2)**((y-1)/y);\n", "P = cp*(T3-T4);\n", "print (\"P = %.3f\")% (P), (\"kW\")\n", "show()" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "Populating the interactive namespace from numpy and matplotlib\n", "(i)Temperature entropy diagram\n", "(ii) Power required = \n", "P = 362.007 kW\n" ] }, { "output_type": "stream", "stream": "stderr", "text": [ "WARNING: pylab import has clobbered these variables: ['draw_if_interactive', 'new_figure_manager']\n", "`%pylab --no-import-all` prevents importing * from pylab and numpy\n" ] }, { "metadata": {}, "output_type": "display_data", "png": 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rTSv/hRdg9GgT+A89dPLrp4pI0Dh0yEy7WbECnnsOfvQjMz4jVBzdKF6wYEG3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\nTkSuQmCC\n", "text": [ "" ] } ], "prompt_number": 36 }, { "cell_type": "heading", "level": 3, "metadata": {}, "source": [ "Example 13.34 page no : 682" ] }, { "cell_type": "code", "collapsed": false, "input": [ "# Variables\n", "m = 0.1; \t\t\t#kg/s\n", "p1 = 1.; \t\t\t#bar\n", "T4 = 285.; \t\t\t#K\n", "p2 = 4.; \t\t\t#bar\n", "cp = 1.; \t\t\t#kJ/kg K\n", "y = 1.4;\n", "\n", "# Calculations and Results\n", "T3 = T4*(p2/p1)**((y-1)/y);\n", "print (\"Temperature at turbine inlet = %.3f\")% (T3), (\"K\")\n", "\n", "P = m*cp*(T3-T4);\n", "print (\"Power developed = %.3f\")% (P), (\"kW\")\n" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "Temperature at turbine inlet = 423.508 K\n", "Power developed = 13.851 kW\n" ] } ], "prompt_number": 37 }, { "cell_type": "heading", "level": 3, "metadata": {}, "source": [ "Example 13.35 page no : 682" ] }, { "cell_type": "code", "collapsed": false, "input": [ "\n", "\n", "# Variables\n", "y = 1.4;\n", "cp = 1.005; \t\t\t#kJ/kg K\n", "p1 = 1.; \t\t\t#bar\n", "T1 = 293.; \t \t\t#K\n", "p2 = 3.5; \t\t \t#bar\n", "T3 = 873.; \t\t\t #K\n", "rp = p2/p1;\n", "\n", "# Calculations and Results\n", "n_cycle = 1-1/rp**((y-1)/y);\n", "print (\"(i) Efficiency of the cycle = %.3f\")% (n_cycle)\n", "\n", "T2 = T1*(p2/p1)**((y-1)/y);\n", "Q1 = cp*(T3-T2);\n", "print (\"(ii) Heat supplied to air = %.3f\")%(Q1),(\"kJ/kg\")\n", "\n", "W = n_cycle*Q1;\n", "print (\"(iii) Work available at the shaft = %.3f\")%(W),(\"kJ/kg\")\n", "\n", "Q2 = Q1-W;\n", "print (\"(iv) Heat rejected in the cooler = %.3f\")%(Q2),(\"kJ/kg\")\n", "\n", "T4 = T3/rp**((y-1)/y);\n", "print (\"(v) Temperature of air leaving the turbine = %.3f\")%(T4), (\"K\")\n" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "(i) Efficiency of the cycle = 0.301\n", "(ii) Heat supplied to air = 456.171 kJ/kg\n", "(iii) Work available at the shaft = 137.253 kJ/kg\n", "(iv) Heat rejected in the cooler = 318.919 kJ/kg\n", "(v) Temperature of air leaving the turbine = 610.332 K\n" ] } ], "prompt_number": 38 }, { "cell_type": "heading", "level": 3, "metadata": {}, "source": [ "Example 13.36 page no : 683" ] }, { "cell_type": "code", "collapsed": false, "input": [ "import math\n", "\n", "# Variables\n", "T1 = 303.; \t\t\t#K\n", "T3 = 1073.; \t\t\t#K\n", "C = 45000.; \t\t\t#kJ/kg\n", "cp = 1.; \t\t\t#kJ/kg K\n", "y = 1.4;\n", "\n", "# Calculations\n", "T2 = math.sqrt(T1*T3);\n", "T4 = T2;\n", "\n", "#W_turbine-W_compressor = m_f*C*n = 100;\n", "\n", "m_f = 100./C/(1-(T4-T1)/(T3-T2));\n", "\n", "# Results\n", "print (\"m_f = %.6f\")%(m_f), (\"kg/s\")\n", "\n", "m_a = (100-m_f*(T3-T4))/(T3-T4-T2+T1);\n", "print (\"m_a = %.3f\")% (m_a), (\"kg/s\")\n" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "m_f = 0.004742 kg/s\n", "m_a = 0.414 kg/s\n" ] } ], "prompt_number": 17 }, { "cell_type": "heading", "level": 3, "metadata": {}, "source": [ "Example 13.37 page no : 684" ] }, { "cell_type": "code", "collapsed": false, "input": [ "\n", "import math \n", "\n", "# Variables\n", "T1 = 300.; \t\t\t#K\n", "p1 = 1.; \t\t\t#bar\n", "rp = 6.25;\n", "T3 = 1073.; \t\t#K\n", "n_comp = 0.8;\n", "n_turbine = 0.8;\n", "cp = 1.005; \t\t#kJ/kg K\n", "y = 1.4;\n", "\n", "# Calculations and Results\n", "T2 = T1*(rp)**((y-1)/y);\n", "\n", "#Let T2' = T2a\n", "T2a = (T2-T1)/n_comp + T1;\n", "\n", "W_comp = cp*(T2a-T1);\n", "print (\"Compressor work = %.3f\")% (W_comp), (\"kJ/kg\")\n", "\n", "T4 = T3/rp**((y-1)/y);\n", "T4a = T3-n_turbine*(T3-T4);\n", "\n", "W_turbine = cp*(T3-T4a);\n", "print (\"Turbine work = %.3f\")% (W_turbine), (\"kJ/kg\")\n", "\n", "Q_s = cp*(T3-T2a);\n", "print (\"Heat supplied = %.3f\")% (Q_s), (\"kJ/kg\")\n", "\n", "W_net = W_turbine - W_comp;\n", "\n", "n_cycle = W_net/Q_s*100;\n", "print (\"n_cycle %.3f\")% (n_cycle), (\"%\")\n", "\n", "t4a = T4a-273;\n", "print (\"Turbine exhaust temperature = %.3f\")% (t4a), (\"0C\")\n" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "Compressor work = 259.322 kJ/kg\n", "Turbine work = 351.644 kJ/kg\n", "Heat supplied = 517.543 kJ/kg\n", "n_cycle 17.839 %\n", "Turbine exhaust temperature = 450.105 0C\n" ] } ], "prompt_number": 40 }, { "cell_type": "heading", "level": 3, "metadata": {}, "source": [ "Example 13.38 page no : 685" ] }, { "cell_type": "code", "collapsed": false, "input": [ "\n", "# Variables\n", "n_turbine = 0.85;\n", "n_compressor = 0.80;\n", "T3 = 1148.; \t\t#K\n", "T1 = 300.; \t\t\t#K\n", "cp = 1.; \t\t\t#kJ/kg K\n", "y = 1.4;\n", "p1 = 1.; \t\t\t#bar\n", "p2 = 4.; \t\t\t#bar\n", "C = 42000.; \t\t#kJ/kg K\n", "n_cc = 0.90;\n", "\n", "# Calculations\n", "T2 = T1*(p2/p1)**((y-1)/y);\n", "T2a = (T2-T1)/n_compressor + T1;\n", "ratio = 0.9*C/cp/(T3-T2a) - 1; \t\t\t#ratio = ma/mf\n", "\n", "# Results\n", "print (\"A/F ratio = %.3f\")% (ratio)\n" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "A/F ratio = 55.778\n" ] } ], "prompt_number": 41 }, { "cell_type": "heading", "level": 3, "metadata": {}, "source": [ "Example 13.39 page no : 686" ] }, { "cell_type": "code", "collapsed": false, "input": [ "# Variables\n", "cp = 1.005; \t\t#kJ/kg K\n", "y1 = 1.4;\n", "y2 = 1.333;\n", "p1 = 1.; \t\t\t#bar\n", "p4 = p1;\n", "T1 = 300.; \t\t\t#K\n", "p2 = 6.2; \t\t\t#bar\n", "p3 = p2;\n", "n_compressor = 0.88;\n", "C = 44186.; \t\t\t#kJ/kg\n", "ratio = 0.017; \t\t\t#Fuel-air ratio; kJ/kg of air\n", "n_turbine = 0.9; \t\t\n", "cpg = 1.147;\n", "\n", "# Calculations\n", "T2 = T1*(p2/p1)**((y1-1)/y1);\n", "T2a = (T2-T1)/n_compressor + T1; \t\t#T2'\n", "T3 = ratio*C/(1+ratio)/cp + T2a;\n", "T4 = T3*(p4/p3)**((y2-1)/y2);\n", "T4a = T3-n_turbine*(T3-T4);\n", "W_compressor = cp*(T2a-T1);\n", "W_turbine = cpg*(T3-T4a);\n", "W_net = W_turbine-W_compressor;\n", "Qs = ratio*C;\n", "n_th = W_net/Qs*100;\n", "\n", "# Results\n", "print (\"Thermal efficiency = %.3f\")% (n_th), (\"%\")\n" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "Thermal efficiency = 32.590 %\n" ] } ], "prompt_number": 42 }, { "cell_type": "heading", "level": 3, "metadata": {}, "source": [ "Example 13.40 page no : 688" ] }, { "cell_type": "code", "collapsed": false, "input": [ "# Variables\n", "cp = 1.; \t\t\t#kJ/kg K\n", "y = 1.4;\n", "C = 41800.; \t\t#kJ/kg\n", "p1 = 1.; \t\t\t#bar\n", "T1 = 293.; \t\t\t#K\n", "p2 = 4.; \t\t\t#bar\n", "p4 = p1;\n", "p3 = p2;\n", "n_compressor = 0.80;\n", "n_turbine = 0.85; \n", "ratio = 90.; \t\t\t#Air-Fuel ratio\n", "m_a = 3.; \t\t\t#kg/s\n", "\n", "# Calculations and Results\n", "print (\"(i)Power developed \")\n", "T2 = T1*(p2/p1)**((y-1)/y);\n", "T2a = (T2-T1)/n_compressor + T1;\n", "T3 = C/(1+ratio)/cp + T2a;\n", "T4 = T3*(p4/p3)**((y-1)/y);\n", "T4a = T3-n_turbine*(T3-T4);\n", "\n", "W_turbine = (ratio+1)/ratio*cp*(T3-T4a);\n", "W_compressor = cp*(T2a-T1);\n", "W_net = W_turbine-W_compressor;\n", "Qs = 1/ratio*C;\n", "\n", "P = m_a*W_net;\n", "print (\"Power = %.3f\")% (P), (\"kW/kg of air\")\n", "\n", "n_thermal = W_net/Qs;\n", "print (\"(ii) Thermal efficiency of cycle = %.3f\")%(n_thermal), (\"%\")\n" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "(i)Power developed \n", "Power = 250.514 kW/kg of air\n", "(ii) Thermal efficiency of cycle = 0.180 %\n" ] } ], "prompt_number": 43 }, { "cell_type": "heading", "level": 3, "metadata": {}, "source": [ "Example 13.41 page no : 689" ] }, { "cell_type": "code", "collapsed": false, "input": [ "# Variables\n", "T1 = 288.; \t\t\t#K\n", "T3 = 883.; \t\t\t#K\n", "rp = 6.; \t\t\t#rp = p2/p1\n", "n_compressor = 0.80;\n", "n_turbine = 0.82;\n", "m_a = 16.; \t\t\t#kg/s\n", "cp1 = 1.005; \t\t#kJ/kg K, For compression process\n", "y1 = 1.4; \t\t\t# For compression process\n", "cp2 = 1.11; \t\t#kJ/kg K\n", "y2 = 1.333;\n", "\n", "# Calculations\n", "T2 = T1*(rp)**((y1-1)/y1);\n", "T2a = (T2-T1)/n_compressor + T1;\n", "T4 = T3/rp**((y2-1)/y2);\n", "T4a = T3-n_turbine*(T3-T4);\n", "\n", "W_compressor = cp1*(T2a-T1);\n", "W_turbine = cp2*(T3-T4a);\n", "W_net = W_turbine-W_compressor;\n", "Power = m_a*W_net;\n", "\n", "# Results\n", "print (\"Power = %.3f\")%(Power), (\"kW\")\n" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "Power = 770.306 kW\n" ] } ], "prompt_number": 44 }, { "cell_type": "heading", "level": 3, "metadata": {}, "source": [ "Example 13.42 page no : 691" ] }, { "cell_type": "code", "collapsed": false, "input": [ "# Variables\n", "cp = 1.11;\n", "T3 = 883.; \t\t\t#K\n", "T2a = 529.; \t\t#K\n", "W_turbine = 290.4; \t#kJ/kg\n", "W_net = 48.2; \t\t#kJ/kg\n", "\n", "# Calculations\n", "Qs = cp*(T3-T2a);\n", "n_thermal = W_net/Qs*100;\n", "W_ratio = W_net/W_turbine; \t\t\t#Work ratio = net work output/Gross work output\n", "\n", "# Results\n", "print (\"Thermal efficiency = %.3f\")%(n_thermal),(\"%\")\n", "\n", "print (\"Work ratio = %.3f\")% (W_ratio)\n" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "Thermal efficiency = 12.267 %\n", "Work ratio = 0.166\n" ] } ], "prompt_number": 45 }, { "cell_type": "heading", "level": 3, "metadata": {}, "source": [ "Example 13.43 page no : 691" ] }, { "cell_type": "code", "collapsed": false, "input": [ "# Variables\n", "p1 = 1.; \t\t\t#bar\n", "p2 = 5.; \t\t\t#bar\n", "p3 = 4.9; \t\t\t#bar\n", "p4 = 1.; \t\t\t#bar\n", "T1 = 293.; \t\t\t#K\n", "T3 = 953.; \t\t\t#K\n", "n_compressor = 0.85;\n", "n_turbine = 0.80;\n", "n_combustion = 0.85;\n", "y = 1.4;\n", "cp = 1.024; \t\t\t#kJ/kg K\n", "P = 1065.; \t\t\t#kW\n", "\n", "# Calculations and Results\n", "print (\"(i) The quantity of air circulation\")\n", "T2 = T1*(p2/p1)**((y-1)/y);\n", "T2a = (T2-T1)/n_compressor + T1;\n", "T4 = T3*(p4/p3)**((y-1)/y);\n", "T4a = T3-n_turbine*(T3-T4);\n", "\n", "W_compressor = cp*(T2a-T1);\n", "W_turbine = cp*(T3-T4a);\n", "W_net = W_turbine-W_compressor;\n", "\n", "m_a = P/W_net;\n", "print (\"m_a = %.3f\")% (m_a), (\"kg\")\n", "\n", "\n", "Qs = cp*(T3-T2a)/n_combustion;\n", "print (\"(ii) Heat supplied per kg of air circulation = %.3f\")%(Qs), (\"kJ/kg\")\n", "\n", "n_thermal = W_net/Qs*100;\n", "print (\"(iii) Thermal efficiency of the cycle = %.3f\")% (n_thermal), (\"%\")\n" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "(i) The quantity of air circulation\n", "m_a = 13.507 kg\n", "(ii) Heat supplied per kg of air circulation = 552.664 kJ/kg\n", "(iii) Thermal efficiency of the cycle = 14.267 %\n" ] } ], "prompt_number": 46 }, { "cell_type": "heading", "level": 3, "metadata": {}, "source": [ "Example 13.44 page no : 693" ] }, { "cell_type": "code", "collapsed": false, "input": [ "# Variables\n", "m_a = 20.; \t\t\t#kg/s\n", "T1 = 300.; \t\t\t#K\n", "T3 = 1000.; \t\t#K\n", "rp = 4.; \t\t\t#rp = p2/p1\n", "cp = 1.; \t\t\t#kJ/kg K\n", "y = 1.4;\n", "\n", "# Calculations\n", "T2 = T1*(rp)**((y-1)/y);\n", "T4 = T3-T2+T1;\n", "r1 = (T3/T4)**(y/(y-1));\n", "\n", "r2 = 1./4*r1;\n", "P_ratio = 1./r2; \t\t\t#Pressure ratio of low pressure turbine\n", "\n", "# Results\n", "print (\"Pressure ratio of low pressure turbine = %.3f\")% (P_ratio)\n", "\n", "T5 = T4/(P_ratio)**((y-1)/y);\n", "print (\"Temperature of the exhaust from the unit = %.3f\")%(T5), (\"K\")\n" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "Pressure ratio of low pressure turbine = 2.304\n", "Temperature of the exhaust from the unit = 672.950 K\n" ] } ], "prompt_number": 47 }, { "cell_type": "heading", "level": 3, "metadata": {}, "source": [ "Example 13.45 page no : 694" ] }, { "cell_type": "code", "collapsed": false, "input": [ "# Variables\n", "T1 = 288.; \t\t\t#K\n", "p1 = 1.01; \t\t\t#bar\n", "rp = 7.;\n", "p2 = rp*p1;\n", "p3 = p2;\n", "p5 = p1;\n", "n_compressor = 0.82;\n", "n_turbine = 0.85;\n", "n_turbine = 0.85;\n", "T3 = 883.; \t\t\t#K\n", "cpa = 1.005;\n", "cpg = 1.15;\n", "y1 = 1.4;\n", "y2 = 1.33;\n", "\n", "# Calculations and Results\n", "print (\"(i) Pressure and temperature of the gases entering the power turbine \")\n", "T2 = T1*rp**((y1-1)/y1);\n", "T2a = (T2-T1)/n_compressor + T1;\n", "W_compressor = cpa*(T2a-T1);\n", "\n", "T4a = (cpg*T3-W_compressor)/cpg;\n", "print (\"Temperature of gases entering the power turbine = %.3f\")% (T4a), (\"K\")\n", "\n", "T4 = T3-(T3-T4a)/n_turbine;\n", "\n", "p4 = p3/(T3/T4)**(y2/(y2-1));\n", "print (\"Pressure of gases entering the power turbine = %.3f\")%(p4),(\"bar\")\n", "\n", "print (\"(ii) Net power developed per kg/s mass flow\")\n", "T5 = T4a/(p4/p5)**((y2-1)/y2);\n", "T5a = T4a-n_turbine*(T4a-T5);\n", "\n", "W_turbine = cpg*(T4a-T5a);\n", "print (\" Net power developed per kg/s mass flow = %.3f\")%(W_turbine), (\"kW\")\n", "\n", "\n", "W_ratio = W_turbine/(W_turbine+W_compressor);\n", "print (\"(iii) Work ratio = %.3f\")% (W_ratio)\n", "\n", "\n", "print (\"(iv) Thermal efficiency of the unit\")\n", "Qs = cpg*(T3-T2a);\n", "n_thermal = W_turbine/Qs*100;\n", "print (\"n_thermal = %.3f\")% (n_thermal), (\"%\")\n" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "(i) Pressure and temperature of the gases entering the power turbine \n", "Temperature of gases entering the power turbine = 654.751 K\n", "Pressure of gases entering the power turbine = 1.640 bar\n", "(ii) Net power developed per kg/s mass flow\n", " Net power developed per kg/s mass flow = 72.519 kW\n", "(iii) Work ratio = 0.216\n", "(iv) Thermal efficiency of the unit\n", "n_thermal = 18.890 %\n" ] } ], "prompt_number": 18 }, { "cell_type": "heading", "level": 3, "metadata": {}, "source": [ "Example 13.46 page no : 696" ] }, { "cell_type": "code", "collapsed": false, "input": [ "# Variables\n", "T1 = 288.; \t\t\t#K\n", "rp = 4.; \t\t\t#rp = p2/p1 = p3/p4\n", "n_compressor = 0.82;\n", "e = 0.78; \t\t\t#Effectiveness of the heat exchanger\n", "n_turbine = 0.70;\n", "T3 = 873.; \t\t\t#K\n", "y = 1.4;\n", "R = 0.287;\n", "\n", "# Calculations\n", "T2 = T1*(rp)**((y-1)/y);\n", "T2a = (T2-T1)/n_compressor + T1;\n", "T4 = T3/rp**((y-1)/y);\n", "T4a = T3-n_turbine*(T3-T4);\n", "\n", "cp = R*y/(y-1);\n", "W_compressor = cp*(T2a-T1);\n", "W_turbine = cp*(T3-T4a);\n", "W_net = W_turbine-W_compressor;\n", "\n", "T5 = e*(T4a-T2a) + T2a;\n", "Qs = cp*(T3-T5);\n", "\n", "n_cycle = W_net/Qs*100;\n", "\n", "# Results\n", "print (\"Efficiency = %.3f\")% (n_cycle), (\"%\")\n" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "Efficiency = 11.808 %\n" ] } ], "prompt_number": 50 }, { "cell_type": "heading", "level": 3, "metadata": {}, "source": [ "Example 13.47 page no : 698" ] }, { "cell_type": "code", "collapsed": false, "input": [ "# Variables\n", "p2 = 4.; \t\t\t#bar\n", "p1 = 1.; \t\t\t#bar\n", "T1 = 293.;\n", "n_compressor = 0.8;\n", "n_turbine = 0.85;\n", "ratio = 90.; \t\t\t#Air Fuel ratio\n", "C = 41800.; \t\t\t#kJ/kg\n", "cp = 1.024;\n", "p4 = 1.01; \t\t\t#bar\n", "p3 = 3.9; \t\t\t#bar\n", "y = 1.4;\n", "e = 0.72; \t\t\t#thermal ratio\n", "\n", "# Calculations and Results\n", "T2 = T1*(p2/p1)**((y-1)/y);\n", "T2a = (T2-T1)/n_compressor + T1;\n", "T3 = C/cp/(ratio+1)+471;\n", "T4 = T3*(p4/p3)**((y-1)/y);\n", "T4a = T3-n_turbine*(T3-T4);\n", "n_thermal1 = ((T3-T4a)-(T2a-T1))/(T3-T2a)*100;\n", "\n", "print (\"Thermal efficiency of simple cycle = %.3f\")% (n_thermal1), (\"%\")\n", "\n", "\n", "T2a = 471.; \t\t\t# K (as for simple cycle)\n", "T3 = 919.5; \t\t\t# K (as for simple cycle)\n", "p3 = 4.04-0.14-0.05; \t\t\t#bar\n", "p4 = 1.01+0.05; \t\t\t#bar\n", "\n", "T4 = T3*(p4/p3)**((y-1)/y);\n", "T4a = T3-n_turbine*(T3-T4);\n", "T5 = e*(T4a-T2a) + T2a;\n", "n_thermal2 = ((T3-T4a) - (T2a-T1))/(T3-T5)*100;\n", "\n", "print (\"Thermal efficiency of heat exchanger cycle = %.3f\")%(n_thermal2), (\"%\")\n", "\n", "dn = n_thermal2-n_thermal1;\n", "print (\"Increase in thermal efficiency = %.3f\")% (dn), (\"%\")\n" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "Thermal efficiency of simple cycle = 16.120 %\n", "Thermal efficiency of heat exchanger cycle = 21.038 %\n", "Increase in thermal efficiency = 4.918 %\n" ] } ], "prompt_number": 51 }, { "cell_type": "heading", "level": 3, "metadata": {}, "source": [ "Example 13.48 page no : 700" ] }, { "cell_type": "code", "collapsed": false, "input": [ "# Variables\n", "T1 = 293.; \t\t\t#K\n", "T6 = 898.; \t\t\t#K\n", "T8 = T6;\n", "n_c = 0.8; \t\t\t#Efficiency of each compressor stage\n", "n_t = 0.85; \t\t\t#Efficiency of each turbine stage\n", "n_mech = 0.95;\n", "e = 0.8;\n", "cpa = 1.005; \t\t\t#kJ/kg K\n", "cpg = 1.15; \t\t\t#kJ/kg K\n", "y1 = 1.4;\n", "y2 = 1.333;\n", "\n", "# Calculations and Results\n", "print (\"(i) Thermal efficiency\")\n", "T3 = T1;\n", "\n", "# p2/p1 = math.sqrt(9) = 3\n", "T2 = T1*(3)**((y1-1)/y1);\n", "T2a = (T2-T1)/n_c + T1;\n", "T4a = T2a;\n", "W_c = cpa*(T2a-T1); \t\t\t#Work input per compressor stage\n", "W_t = 2*W_c/n_mech; \t\t\t#Work output of H.P. turbine\n", "T7a = T6-W_t/cpg;\n", "T7 = T6-(T6-T7a)/n_t;\n", "\n", "T9 = T8/(1.86)**((y2-1)/y2);\n", "T9a = T8-n_t*(T8-T9);\n", "\n", "W = cpg*(T8-T9a)*n_mech; \t\t\t#Net work output\n", "T5 = e*(T9a-T4a)+T4a;\n", "\n", "Q = cpg*(T6-T5)+cpg*(T8-T7a); \t\t\t#Heat supplied\n", "n_thermal = W/Q*100;\n", "\n", "print (\"n_thermal = %.3f\")% (n_thermal), (\"%\")\n", "\n", "print (\"(ii) Work ratio\")\n", "Gross_work = W_t+W/n_mech;\n", "W_ratio = W/Gross_work;\n", "print (\"Work ratio = %.3f\")% (W_ratio)\n", "\n", "m = 4500./W;\n", "print (\"(iii) Mass flow rate = %.3f\")%(m), (\"kg/s\")\n", "\n", "# Note : answers are different because of rounding error.\n" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "(i) Thermal efficiency\n", "n_thermal = 24.209 %\n", "(ii) Work ratio\n", "Work ratio = 0.291\n", "(iii) Mass flow rate = 37.576 kg/s\n" ] } ], "prompt_number": 14 }, { "cell_type": "heading", "level": 3, "metadata": {}, "source": [ "Example 13.49 page no : 704" ] }, { "cell_type": "code", "collapsed": false, "input": [ "import math \n", "\n", "# Variables\n", "T1 = 293.; \t\t\t#K\n", "T5 = 1023.; \t\t#K\n", "T7 = T5;\n", "p1 = 1.5; \t\t\t#bar\n", "p2 = 6.; \t\t\t#bar\n", "n_c = 0.82;\n", "n_t = 0.82;\n", "e = 0.70;\n", "P = 350.; \t\t\t#kW\n", "cp = 1.005; \t\t#kJ/kg K\n", "y = 1.4;\n", "\n", "# Calculations\n", "T3 = T1;\n", "px = math.sqrt(p1*p2);\n", "T2 = T1*(px/p1)**((y-1)/y);\n", "T2a = T1+(T2-T1)/n_c;\n", "T4a = T2a;\n", "p5 = p2;\n", "T6 = T5/(p5/px)**((y-1)/y);\n", "T6a = T5-n_t*(T5-T6);\n", "T8a = T6a;\n", "Ta = T4a+e*(T8a-T4a);\n", "W_net = 2*cp*((T5-T6a)-(T2a-T1));\n", "Q1 = cp*(T5-T4a)+cp*(T7-T6a); \t\t\t#Without regenerator\n", "Q2 = cp*(T5-Ta)+cp*(T7-T6a);\n", "\n", "# Results\n", "n1 = W_net/Q1*100;\n", "print (\"n_thermal without regenerator = %.3f\")%(n1), (\"%\")\n", "\n", "n2 = W_net/Q2*100;\n", "print (\"n_thermal woth regenerator = %.3f\")% (n2), (\"%\")\n", "\n", "m = P/W_net;\n", "print (\"(iii) Mass of fluid circulated = %.3f\")% (m), (\"kg/s\")\n" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "n_thermal without regenerator = 18.059 %\n", "n_thermal woth regenerator = 32.079 %\n", "(iii) Mass of fluid circulated = 2.403 kg/s\n" ] } ], "prompt_number": 53 } ], "metadata": {} } ] }