{
"metadata": {
"name": ""
},
"nbformat": 3,
"nbformat_minor": 0,
"worksheets": [
{
"cells": [
{
"cell_type": "heading",
"level": 1,
"metadata": {},
"source": [
"Chapter 2 Test"
]
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Example 2.1 Page No: 44"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"#Input data\n",
"d=20.0 #Cylinder bore diameter in cm\n",
"L=25.0 #Stroke length in cm\n",
"Vc=1570.0 #The clearance volume in cm**3\n",
"P1=1.0 #Pressure at the beginning of the compression in bar\n",
"T1=300.0 #Temperature at the beginning of the compression in K\n",
"T3=1673 #The maximum temperature of the cycle in K\n",
"Cv=0.718 #specific heat at constant volume for air in kJ/kgK\n",
"R=0.287 #Real gas constant in kJ/kgK\n",
"g=1.4 #Isentropic index\n",
"c=500.0 #Number of cycles per minute\n",
"\n",
"#Calculations\n",
"import math\n",
"Vs=(math.pi/4.0)*d**2*L\n",
"V1=Vs+Vc\n",
"V2=Vc #cm**3\n",
"r=V1/V2 #Compression ratio\n",
"T2=T1*r**(g-1)\n",
"P2=P1*r**g\n",
"P3=P2*(T3/T2) #In constant volume, process Pressure at point 3 in bar\n",
"T4=T3*(1/r)**(g-1) #In isentropic process, Temperature at point 4 in degree centigrade\n",
"P4=P3*(1/r)**(g) #In isentropic process, Pressure at point 4 in bar\n",
"no=(1-(1/r)**(g-1))*100 #Air standard efficiency of otto cycle\n",
"Q1=Cv*(T3-T2) #Heat supplied in kJ/kg\n",
"Q2=Cv*(T4-T1) #Heat rejected in kJ/kg\n",
"W=Q1-Q2 #Work done per unit mass in kJ/kg\n",
"m=((P1*10**5*V1*10**-6)/(R*T1))/1000.0 #The amount of mass in kg\n",
"W1=W*m #Work done in kJ\n",
"pm=((W1*10**3)/(Vs*10.0**-6))/10.0**5 #Mean effective pressure in N/m**2\n",
"P=W1*(c/60.0) #Power developed in kW\n",
"\n",
"#Output\n",
"print\"Temperature at point 2 = \",round(T2-273.15,1),\"C\"\n",
"print\"Pressure at point 2 =\" ,round(P2,2),\" bar\"\n",
"print\"Pressure at point 3 = \",round(P3,2),\"bar\" \n",
"print\"Temperature at point 4 = \",round(T4-273.15),\" C \\nPressure at point 4 = \",round(P4,3),\"bar\"\n",
"print\"Air standard efficiency of otto cycle = \",round(no,2),\" percent \"\n",
"print\"Work done = \",round(W1,2),\" kJ\"\n",
"print\"Mean effective pressure = \",round(pm,2),\"bar \"\n",
"print\"Power developed = \",round(P,1),\"kW \"\n",
"\n"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"Temperature at point 2 = 341.3 C\n",
"Pressure at point 2 = 12.29 bar\n",
"Pressure at point 3 = 33.47 bar\n",
"Temperature at point 4 = 544.0 C \n",
"Pressure at point 4 = 2.723 bar\n",
"Air standard efficiency of otto cycle = 51.17 percent \n",
"Work done = 4.26 kJ\n",
"Mean effective pressure = 5.42 bar \n",
"Power developed = 35.5 kW \n"
]
}
],
"prompt_number": 13
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Example 2.2 Page No: 46"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"#Input data\n",
"CV=42000.0 #The calorific value of the fuel in kJ/kg\n",
"pa=5.0 #Percentage of compression\n",
"Pa=1.2 #Pressure in the cylinder at 5% compression stroke\n",
"pb=75 #Percentage of compression\n",
"Pb=4.8 #Pressure in the cylinder at 75% compression stroke\n",
"g=1.3 #polytropic index\n",
"g1=1.4 #Isentropic index\n",
"n=0.6 #Air standard efficiency\n",
"\n",
"#Calculations\n",
"V=(Pb/Pa)**(1/1.3)#Ratio of volumes\n",
"r=(V*(pb/100.0)-(pa/100.0))/((1-(pa/100.0))-(V*(1-(pb/100.0)))) #Compression ratio\n",
"n1=((1-(1/r)**(g1-1)))*100 #Relative efficiency\n",
"nthj=n*(n1/100.0) #Indicated thermal efficiency\n",
"x=(1/(CV*nthj))*3600 #Specific fuel consumption in kg/kW.h\n",
"\n",
"#Output\n",
"print\"The compression ratio of the engine is \",round(r,1)\n",
"print\"The specific fuel consumption is \",round(x,3),\"kg/kwh\""
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"The compression ratio of the engine is 9.5\n",
"The specific fuel consumption is 0.241 kg/kwh\n"
]
}
],
"prompt_number": 15
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Example 2.4 Page No: 48"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"#Input data\n",
"d=0.2 #The diameter of the cylinder bore in m\n",
"L=0.3 #The length of the stroke in m\n",
"P1=1 #The pressure at the beginning of the compression in bar\n",
"T1=300.0 #The temperature at the beginning of the compression in K\n",
"r=16.0 #Compression ratio\n",
"V=0.08 #Cutt off takes place at 8& of the stroke\n",
"R=0.287 #Real gas constant in kJ/kgK\n",
"g=1.4 #Isentropic index\n",
"Cp=1.005 #Specific heat at constant prassure in kJ/kgK\n",
"Cv=0.718 #specific heat at constant volume for air in kJ/kgK\n",
"\n",
"#Calculations\n",
"import math\n",
"Vs=(math.pi/4.0)*d**2*L #Swept volume in m**3\n",
"Vc=Vs/(r-1) #Clearance volume in m**3\n",
"V2=Vc #Volume at point 2 in m**3\n",
"V1=Vs+Vc #Volume at point 1 in m**3\n",
"m=(P1*10**5*V1)/(R*T1) #The amount of mass in kg\n",
"P2=P1*(r**g) #Pressure at point 2 in bar\n",
"P3=P2 #Pressure at point 3 in bar\n",
"T2=T1*r**(g-1) #Temperature at point 2 in K\n",
"V3=(V*Vs)+V2 #Volume at point 3 in m**3\n",
"C=V3/V2 #Cut off ratio\n",
"T3=C*T2 #Temperature at point 3 in K\n",
"P4=P3*(C/r)**g #Pressure at the point 4 in bar\n",
"T4=T3*(C/r)**(g-1) #Temperature at point 4 in K\n",
"V4=V1 #Volume at point 4 in m**3\n",
"Q1=(m*Cp*(T3-T2))/1000.0 #Heat supplied in kJ\n",
"Q2=(m*Cv*(T4-T1))/1000.0 #Heat rejected in kJ\n",
"W=(Q1-Q2) #Work done per cycle in kJ\n",
"na=(W/Q1)*100 #Air standard efficiency\n",
"Pm=(W*1000/Vs)/10.0**5 #Mean effective pressure in bar\n",
"\n",
"#Output\n",
"print\"(a) Volume at point 2 = \",round(V2,5),\" m**3 \\nVolume at point 1 = \",round(V1,5),\"m**3 \"\n",
"print\"Pressure at point 2 = \",round(P2,1),\" bar\" \n",
"print\"Temperature at point 2 = \",round(T2,1),\"K\"\n",
"print\"beeta is\",C,\"\\nTemperature at point 3 = \",round(T3,0),\" K \\nPressure at point 4 =\",round(P4,3),\" bar\"\n",
"print\"Temperature at point 4 = \",round(T4,1),\" K \\nVolume at point 4 = \",round(V4,5),\"m**3\" \n",
"print\"(b) cut off ratio = \",round(c,1)\n",
"print\"(c) Work done per cycle = \",round(W,3),\"kJ\" \n",
"print\"(d) air smath.tandard efficiency = \",round(na,1),\" percent\" \n",
"print\"(e)Mean effective pressure = \",round(Pm,2),\" bar \"\n"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"(a) Volume at point 2 = 0.00063 m**3 \n",
"Volume at point 1 = 0.01005 m**3 \n",
"Pressure at point 2 = 48.5 bar\n",
"Temperature at point 2 = 909.4 K\n",
"beeta is 2.2 \n",
"Temperature at point 3 = 2001.0 K \n",
"Pressure at point 4 = 3.016 bar\n",
"Temperature at point 4 = 904.7 K \n",
"Volume at point 4 = 0.01005 m**3\n",
"(b) cut off ratio = 500.0\n",
"(c) Work done per cycle = 7.736 kJ\n",
"(d) air smath.tandard efficiency = 60.4 percent\n",
"(e)Mean effective pressure = 8.21 bar \n"
]
}
],
"prompt_number": 29
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Example 2.5 Page No:50"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"#given\n",
"P1=7\n",
"g=1.4\n",
"r=12\n",
"import numpy as np\n",
"from scipy.optimize import fsolve\n",
"\n",
"def f(b):\n",
" return P1-1/((g-1)*(r-1))*(g*r**g*(b-1)-r*(b**1.4-1))\n",
"b = fsolve(f, 1)\n",
"f(b)\n",
"na=(1-(1/(r**(g-1)))*(((b**g)-1)/(g*(b-1))))*100 #Air standard efficiency\n",
"\n",
"#Output \n",
"print\"The cut off ratio = \",round(b,1),\" \\n The air standard efficiency =\",na,\"percent\"\n",
"#NOTE:In the book Answer is wrong for Air standard efficiency .\n"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"The cut off ratio = 2.2 \n",
" The air standard efficiency = [ 55.47110058] percent\n"
]
}
],
"prompt_number": 22
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Example 2.6 Page no 51"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"#given\n",
"m=30.0 #The air fuel ratio by mass\n",
"T1=300 #The temperature of air at the beginning of the compression in K\n",
"r=16 #The compression ratio\n",
"CV=42000 #The calorific value of the fuel in kJ/kg\n",
"g=1.4 #Isentropic index\n",
"Cp=1.005 #Specific heat at constant prassure in kJ/kgK\n",
"\n",
"#Calculations\n",
"T2=T1*(r**(g-1)) #Temperature at point 2 in K\n",
"T3=((1/m)*(CV/Cp))+T2 #Temperature at point 3 in K\n",
"C=T3/T2 #The cut off ratio\n",
"n=(1-((1/r**(g-1))*(((C**g)-1)/(g*(C-1)))))*100#The ideal efficiency of the engine based on the air standard cycle\n",
"\n",
"#Output\n",
"print\" The ideal efficiency of the engine based on the air standard cycle = \",round(n,1)\n"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
" The ideal efficiency of the engine based on the air standard cycle = 58.9\n"
]
}
],
"prompt_number": 30
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Example 2.7 Page No: 52"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"#given\n",
"p1=1.0 #Inlet pressure in bar\n",
"p2=32.425 #Pressure at the end of isentropic compression in bar\n",
"r=6.0 #Ratio of expansion\n",
"r1=1.4 #Isentropic index\n",
"\n",
"#Calculations\n",
"rc=(p2/p1)**(1/r1) #Compression ratio\n",
"b=(rc/r) #cut-off ratio\n",
"n=(1-((b**r1-1)/(rc**(r1-1)*r1*(b-1))))*100 \n",
"pm=((p1*rc**r1*n/100.0*r1*(b-1))/((r1-1)*(rc-1))) \n",
"\n",
"#Output\n",
"print\"Air-smath efficiency is \",round(n,3),\"percent\"\n",
"print\"Mean effective pressure is \",round(pm,3),\"bar\""
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"Air-smath efficiency is 56.671 percent\n",
"Mean effective pressure is 5.847 bar\n"
]
}
],
"prompt_number": 31
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Example 2.8 Page No: 52"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"#Input data\n",
"rc=15.0 #Compression ratio\n",
"p1=1 #Pressure at which compression begins in bar\n",
"T1=27.0+273.0 #Temperature in K\n",
"pm=60 #Maximum pressure in bar\n",
"h=2 #Heat transfered to air at constant volume is twice that at consmath.tant pressure\n",
"g=1.4 #Isentropic index\n",
"Cv=0.718 #specific heat at constant volume for air in kJ/kgK\n",
"Cp=1.005 #specific heat at constant pressure for air in kJ/kgK\n",
"R=0.287 #Real gas constant in kJ/kgK\n",
"\n",
"#Calculations\n",
"T2=(T1*rc**(g-1)) #Temperature in K\n",
"p2=(p1*rc**g) #Pressure in bar\n",
"T3=(T2*(pm/p2)) #Temperature in K\n",
"T4=(Cv*(T3-T2))/(2*Cp)+T3 #Temperature in K\n",
"b=(T4/T3) #Cut-off ratio\n",
"T5=(T4*(b/rc)**(g-1)) #Temperature in K\n",
"p5=(p1*(T5/T1)) #Pressure in bar\n",
"Q1=(Cv*(T3-T2))+(Cp*(T4-T3))#Heat supplied per unit mass in kJ/kg\n",
"Q2=Cv*(T5-T1) #Heat rejected per unit mass in kJ/kg\n",
"W=(Q1-Q2) #Workdone in kJ/kg\n",
"n=(W/Q1)*100 #Air standard efficiency\n",
"Vs=((1*R*1000*T1)/(p1*10**5))*(1-1/rc) #Swept volume in m**3/kg\n",
"pmean=((W*1000)/Vs)/10.0**5 #Mean-effective pressure in bar\n",
"\n",
"#Output\n",
"print\"(a) The pressures and temperatures at the cardinal points of the cycle are \"\n",
"print\"T2 =\",round(T2,1),\" K \\np2 =\", round(p2,1),\" bar \\nT3 = \",round(T3,1), \"K \\np3 =\",round(p3,1),\"bar\"\n",
"print\"T4 =\",round(T4,1),\"K \\nT5 = \",round(T5,1), \"K \\np5 = \",round(p5,1),\"bar\"\n",
"print\"(b) The cycle efficiency is\",round(n,0),\"percent\" \n",
"print\"(c) The mean effective pressure of the cycle is \",round(pmean,1),\"bar\"\n"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"(a) The pressures and temperatures at the cardinal points of the cycle are \n",
"T2 = 886.3 K \n",
"p2 = 44.3 bar \n",
"T3 = 1200.0 K \n",
"p3 = 52.2 bar\n",
"T4 = 1312.1 K \n",
"T5 = 460.3 K \n",
"p5 = 1.5 bar\n",
"(b) The cycle efficiency is 66.0 percent\n",
"(c) The mean effective pressure of the cycle is 2.8 bar\n"
]
}
],
"prompt_number": 29
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Example 2.9 Page No: 55"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"#Input data\n",
"r=12.0 #Compression ratio\n",
"B=1.615 #Cut off ratio\n",
"p3=52.17 #Maximum pressure in bar\n",
"p4=p3 #Maximum pressure in bar\n",
"p1=1 #Initial pressure in bar\n",
"T1=(62+273) #Initial temperature in K\n",
"n=1.35 #Indices of compression and expansion\n",
"g=1.4 #Adiabatic exponent\n",
"mR=0.287 #Real gas constant in kJ/kgK\n",
"Cv=0.718 #specific heat at constant volume for air in kJ/kgK\n",
"Cp=1.005 #specific heat at constant pressure for air in kJ/kgK\n",
"\n",
"#Calculations\n",
"T2=T1*r**(n-1) #The temperature at point 2 in K\n",
"p2=p1*(r)**n #The pressure at point 2 in bar\n",
"T3=T2*(p3/p2) #The temperature at point 3 in K\n",
"T4=T3*B #The temperature at point 4 in K\n",
"T5=T4*(B/r)**(n-1) #The temperature at point 5 in K\n",
"Q12=((g-n)/(g-1))*mR*((T1-T2)/(n-1)) # kJ/kg\n",
"Q23=Cv*(T3-T2) \n",
"Q34=Cp*(T4-T3) \n",
"Q45=((g-n)/(g-1))*mR*((T4-T5)/(n-1)) \n",
"Q51=Cv*(T1-T5) \n",
"Q1=Q23+Q34+Q45 \n",
"Q2=-Q12+(-Q51) \n",
"W=Q1-Q2 \n",
"E=(W/Q1)*100 \n",
"Vs=((mR*T1)/p1)*(r-1)/r # m**3/kg\n",
"pm=(W*1000/Vs)/10.0**3 #Mean effective pressure in bar\n",
"\n",
"#Output\n",
"print\"(a)The temperature at cardinal points \\nT2 =\",round(T2,0),\" K\\nT3 = \",round(T3,0),\"K \\nT4 = \",round(T4,0),\"K \\nT5 = \",round(T5,0),\"K \" \n",
"print\"(b) The cycle efficiency = \",round(E,1),\" percent\"\n",
"print\"(c) The mean effective pressure of the cycle = \",round(pm,3),\"bar\"\n"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"(a)The temperature at cardinal points \n",
"T2 = 799.0 K\n",
"T3 = 1456.0 K \n",
"T4 = 2352.0 K \n",
"T5 = 1166.0 K \n",
"(b) The cycle efficiency = 56.9 percent\n",
"(c) The mean effective pressure of the cycle = 9.638 bar\n"
]
}
],
"prompt_number": 12
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Example 2.10 Page No: 57"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"#Input data\n",
"p1=1.0 #Inlet pressure in bar\n",
"T1=27.0+273.0 #Temperature in K\n",
"p2=4.0 #pressure at point 2 in bar\n",
"p3=16.0 #Maximum pressure in bar\n",
"Cv=0.573 #specific heat at constant volume for gas in kJ/kgK\n",
"Cp=0.761 #specific heat at constant pressure for gas in kJ/kgK\n",
"\n",
"#Calculations\n",
"g=(Cp/Cv) \n",
"T2=(T1*(p2/p1)**((g-1)/g)) # K\n",
"T3=(p3/p2)*T2 \n",
"T4=T3*(p1/p3)**((g-1)/g) \n",
"Q1=Cv*(T3-T2) #kJ/kg\n",
"Q2=Cp*(T4-T1) \n",
"W=Q1-Q2 \n",
"n=(W/Q1)*100 \n",
"r=(p2/p1)**(1/g)\n",
"R=(Cp-Cv) #kJ/kg.K\n",
"Vs=(R*1000*T1*(r-1))/(p1*10.0**5*r) #m**3/kg\n",
"pm=(W/(Vs*100.0)) \n",
"\n",
"#Output\n",
"print\"(a) The work done per kg of gas is \",round(W,1),\"kJ/kg\"\n",
"print\"(b) The efficiency of the cycle is \",round(n,1),\"percent \"\n",
"print\"(c) Mean effective pressure is \",round(pm,1),\"bar\""
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"(a) The work done per kg of gas is 306.2 kJ/kg\n",
"(b) The efficiency of the cycle is 42.2 percent \n",
"(c) Mean effective pressure is 8.4 bar\n"
]
}
],
"prompt_number": 5
}
],
"metadata": {}
}
]
}