{
"cells": [
{
"cell_type": "markdown",
"metadata": {},
"source": [
"# Chapter 7 - Performance of IC Engines"
]
},
{
"cell_type": "markdown",
"metadata": {
"collapsed": true
},
"source": [
"## Example 1 - pg 7.19"
]
},
{
"cell_type": "code",
"execution_count": 2,
"metadata": {
"collapsed": false
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"(a) Brake torque is (Nm) = 971.2\n",
"(b)Power available at the brakes of the engine is (kW) = 152.48\n",
"The answers given in textbook are wrong. Please verify using a calculator\n"
]
}
],
"source": [
"#pg 7.19\n",
"#calculate the brake torque and Power\n",
"#Input data\n",
"N=1500.;#Engine speed in rpm\n",
"p=110.;#Load on brakes in kg\n",
"L=900.;#Length of brake arm in mm\n",
"g=9.81;#Gravitational force in N/m**2\n",
"pi=3.14;#Mathematical constant\n",
"\n",
"#Calculations\n",
"T=((p*g)*(L/1000.));#Braking torque in Nm\n",
"P=((T/1000)*((2*3.14*N)/60));#Power available at the brakes of the engine in kW\n",
"\n",
"#Output\n",
"print '(a) Brake torque is (Nm) = ',round(T,1)\n",
"print '(b)Power available at the brakes of the engine is (kW) = ',round(P,2)\n",
"print 'The answers given in textbook are wrong. Please verify using a calculator'"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Example 2 - pg 7.19"
]
},
{
"cell_type": "code",
"execution_count": 4,
"metadata": {
"collapsed": false
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"The power available at the brakes is (kW) = 7.125\n"
]
}
],
"source": [
"#pg 7.19\n",
"#calculate the power available\n",
"#Input data\n",
"N=700.;#Engine speed in rpm\n",
"D=0.6;#Diameter of brake drum in m\n",
"d=0.05;#Diameter of rope in m\n",
"W=35.;#Dead load on the brake drum in kg\n",
"S=4.5;#Spring balance reading in kg\n",
"g=9.81;#Gravitational constant in N/m**2\n",
"pi=3.14;#Mathematical constant\n",
"\n",
"#Calculations\n",
"P=(((W-S)*g*pi*(D+d))/1000)*(N/60);#Power in kW\n",
"\n",
"#Output\n",
"print 'The power available at the brakes is (kW) = ',round(P,3)\n"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Example 3 - pg 7.20"
]
},
{
"cell_type": "code",
"execution_count": 5,
"metadata": {
"collapsed": false
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
" Brake thermal efficiency of the engine is (percent) = 34.74\n"
]
}
],
"source": [
"#pg 7.20\n",
"#calculate the brake thermal efficiency\n",
"#Input data\n",
"W=950.;#Load on hydraulic dynamometer in N\n",
"C=7500.;#Dynamometer constant\n",
"f=10.5;#Fuel used per hour in kg\n",
"h=50000.;#Calorific value of fuel in kJ/kg\n",
"N=400.;#Engine speed in rpm\n",
"\n",
"#Calculations\n",
"P=(W*N)/C;#Power available at the brakes in kW\n",
"H=P*60;#Heat equivalent of power at brakes in kJ/min\n",
"Hf=(f*h)/60;#Heat supplied by fuel per minute in kJ/min\n",
"n=(H/Hf)*100;#Brake thermal efficiency in percentage\n",
"\n",
"#Output\n",
"print ' Brake thermal efficiency of the engine is (percent) = ',round(n,2)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Example 4 - pg 7.21"
]
},
{
"cell_type": "code",
"execution_count": 6,
"metadata": {
"collapsed": false
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"(a)Specific fuel consumption is (kg/BHP hr) = 0.238\n",
"(b)Brake mean effective pressure is (kgf/cm^2) = 8.066\n"
]
}
],
"source": [
"#pg 7.21\n",
"#calculate the specific fuel consumption and Brake mean effective pressure\n",
"#Input data\n",
"import math\n",
"n1=50.5;#Air standard efficiency in percentage\n",
"n2=50.;#Brake thermal efficiency in percentage\n",
"N=3000.;#Engine speed in rpm\n",
"H=10500.;#Heating value of fuel in kcal/kg\n",
"T=7.2;#Torque developed in kgf*m\n",
"B=6.3;#Bore diameter in cm\n",
"S=0.09;#stroke in m\n",
"\n",
"#Calculations\n",
"nbt=(n1/100)*(n2/100.);#Brake thermal efficiency in percentage\n",
"B1=(2*(22./7)*N*T)/4500.;#Brake horse power in kW\n",
"B2=B1/4;#Brake horse power per cylinder in kW\n",
"Bsf=(4500*60)/(H*427.*nbt);#Brake specific fuel consumption in kg/BHP hr\n",
"bmep=(B2*4500)/(S*(math.pi*B**2. /4.)*(N/2.));#Brake mean effective pressure in kgf/cm**2\n",
"\n",
"#Output\n",
"print '(a)Specific fuel consumption is (kg/BHP hr) = ',round(Bsf,3)\n",
"print '(b)Brake mean effective pressure is (kgf/cm^2) = ',round(bmep,3)\n"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Example 5 - pg 7.22"
]
},
{
"cell_type": "code",
"execution_count": 8,
"metadata": {
"collapsed": false
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"Mechanical efficiency of the engine is (percent) = 88.54\n"
]
}
],
"source": [
"#pg 7.22\n",
"#calculate the Mechanical efficiency\n",
"#Input data\n",
"W=30.;#The net dynamometer load in kg\n",
"R=0.5;#Radius in m\n",
"N=2400.;#Speed in rpm\n",
"FHP=6.5;#Engine power in hp\n",
"\n",
"#Calculations\n",
"BHP=(2*3.14*R*N*W)/4500;#Brake horse power in kW\n",
"IHP=BHP+FHP;#Indicated horse power in kW\n",
"nm=(BHP/IHP)*100;#Mechanical efficiency in percentage\n",
"\n",
"#Output\n",
"print 'Mechanical efficiency of the engine is (percent) = ',round(nm,2)\n"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Example 6 - pg 7.22"
]
},
{
"cell_type": "code",
"execution_count": 9,
"metadata": {
"collapsed": false
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"(a)The indicated horse power is (kW) = 24.35\n",
"(b)The brake horse power is (kW) = 19.48\n",
"(c)Friction horse power is (kW) = 4.87\n"
]
}
],
"source": [
"#pg 7.22\n",
"#calculate the indicated, brake and Friction horse powers\n",
"#Input data\n",
"import math\n",
"d=25.;#Diameter of cylinder in cm\n",
"l=0.4;#Stroke of piston in m\n",
"N=200.;#Speed in rpm\n",
"m=10.;#Misfires per minute\n",
"M=6.2;#Mean effective pressure in kgf/cm**2\n",
"nm=0.8;#Mechanical efficiency in percent\n",
"\n",
"#Calculations\n",
"np=(N/2)-m;#Number of power strokes per minute\n",
"A=(math.pi*d**2)/4;#Area of the cylinder\n",
"I=(M*l*A*np)/4500.;#Indicated horse power in kW\n",
"B=I*nm;#Brake horse power in kW\n",
"F=I-B;#Friction horse power in kW\n",
"\n",
"#Output\n",
"print '(a)The indicated horse power is (kW) = ',round(I,2)\n",
"print '(b)The brake horse power is (kW) = ',round(B,2)\n",
"print '(c)Friction horse power is (kW) = ',round(F,2)\n"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Example 7 - pg 7.23"
]
},
{
"cell_type": "code",
"execution_count": 10,
"metadata": {
"collapsed": false
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"The average piston speed is (m/s) = 117.53\n"
]
}
],
"source": [
"#pg 7.23\n",
"#calculate the average piston speed\n",
"#Input data\n",
"import math\n",
"I=5.;#Indicated power developed by single cylinder of 2 stroke petrol engine\n",
"M=6.5;#Mean effective pressure in bar\n",
"d=0.1;#Diameter of piston in m\n",
"\n",
"#Calculations\n",
"A=(math.pi*d**2)/4;#Area of the cylinder\n",
"LN=(I*1000*60.)/(M*10**5*A);#Product of length of stroke and engine speed\n",
"S=2*LN;#Average piston speed in m/s\n",
"\n",
"#Output\n",
"print 'The average piston speed is (m/s) = ',round(S,2)\n"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Example 8 - pg 7.24"
]
},
{
"cell_type": "code",
"execution_count": 11,
"metadata": {
"collapsed": false
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"(a)Diameter of the bore is (cm) = 35.43\n",
"(b)Stroke length of the piston is (cm) = 61.999\n"
]
}
],
"source": [
"#pg 7.24\n",
"#calculate the diameter and stroke length\n",
"#Input data\n",
"P=60.;#Power developed by oil engine in kW\n",
"M=6.5;#Mean effective pressure in kgf/cm**2\n",
"N=85.;#Number of explosions per minute\n",
"r=1.75;#Ratio of stroke to bore diameter\n",
"nm=0.8;#Mechanical efficiency \n",
"\n",
"#Calculations\n",
"I=P/nm;#Indicated horse power\n",
"d=((I*100*4*4500.)/(M*r*3.14*N))**(1./3);#Bore diameter in cm\n",
"l=r*d;#Stroke length in cm\n",
"\n",
"#Output\n",
"print '(a)Diameter of the bore is (cm) = ',round(d,2)\n",
"print '(b)Stroke length of the piston is (cm) = ',round(l,3)\n"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Example 9 - pg 7.24"
]
},
{
"cell_type": "code",
"execution_count": 13,
"metadata": {
"collapsed": false
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"(a)The bore diameter of the cylinder is (cm) = 11.46\n",
"(b)Stroke length of the piston is (cm) = 14.89\n"
]
}
],
"source": [
"#pg 7.24\n",
"#calculate the bore diameter and stroke length\n",
"#Input data \n",
"I=45.;#Power developed by two cylinder internal combustion engine operating on two stroke principle\n",
"N=1100.;#Speed in rpm\n",
"M=6.;#Mean effective pressure in kgf/cm**2\n",
"r=1.3;#Ratio of stroke to the bore\n",
"nc=2.;#Number of cylinders\n",
"\n",
"#Calculations\n",
"d=((I*4500*4)/(M*(r/100)*3.14*N*nc))**(1./3);#Diameter of the bore in cm\n",
"l=1.3*d;#Stroke length in cm\n",
"\n",
"#Output\n",
"print '(a)The bore diameter of the cylinder is (cm) = ',round(d,2)\n",
"print '(b)Stroke length of the piston is (cm) = ',round(l,2)\n"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Example 10 - pg 7.25"
]
},
{
"cell_type": "code",
"execution_count": 14,
"metadata": {
"collapsed": false
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"The volumetric efficiency is (percent) = 78.5\n"
]
}
],
"source": [
"#pg 7.25\n",
"#calculate the volumetric efficiency\n",
"#Input data\n",
"d=6.;#Diameter of the bore in cm\n",
"l=9.;#Length of the stroke in cm\n",
"m=0.00025;#Mass of charge admitted in each suction stroke\n",
"R=29.27;#Gas constant Kgfm/kg K\n",
"p=1.;#Normal pressure in kgf/cm**2\n",
"T=273.;#Temperature in K\n",
"\n",
"#Calculations\n",
"V=(m*R*T)*10**6/(p*10**4);#Volume of charge admitted in each cycle in m**3\n",
"Vs=(3.14*d**2*l)/4;#Swept volume of the cylinder\n",
"nv=(V/Vs)*100;#Volumetric efficiency in percentage\n",
"\n",
"#Output\n",
"print 'The volumetric efficiency is (percent) = ',round(nv,1)\n"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Example 11 - pg 7.26"
]
},
{
"cell_type": "code",
"execution_count": 16,
"metadata": {
"collapsed": false
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"The volumetric efficiency of the engine is (percent) = 79.21\n"
]
}
],
"source": [
"#pg 7.26\n",
"#calculate the volumetric efficiency of the engine\n",
"#Input data\n",
"import math\n",
"d=0.12;#Diameter of the bore in m\n",
"l=0.13;#Length of stroke in m\n",
"N=2500.;#Speed of the engine in rpm\n",
"d1=0.06;#Diameter of the orifice in m\n",
"Cd=0.70;#Discharge coefficient of orifice\n",
"hw=33.;#Heat causing air flow through orifice in cm of water\n",
"p=760.;#Barometric reading in mm of Hg\n",
"T1=298.;#Ambient temperature in degree K\n",
"p1=1.013;#Pressure of air at the end of suction in bar\n",
"T2=22.;#Temperature of air at the end of suction in degree C\n",
"R=0.287;#Universal gas constant\n",
"n=6.;#Number of cylinders in the engine\n",
"n1=1250.;#Number of strokes per minute for a four stroke engine operating at 2500 rpm\n",
"\n",
"#Calculations\n",
"V=(math.pi*d**2*l)/4;#Swept volume of piston in m**3\n",
"Ao=(math.pi*d1**2)/4;#Area of the orifice in m**2\n",
"rho=p1*10**5/((R*T1)*1000);#Density of air at 1.013 bar and 22 degrees C\n",
"Va=840.*Cd*Ao*(hw/rho)**(1./2);#Volume of air passing through the orifice in m**3/min\n",
"V1=8.734/n;#Actual volume of air per cylinder in m**3/min\n",
"As=V1/n1;#Air supplied per cycle per cylinder in m**3\n",
"nv=(As/V)*100;#Volumetric efficiency of the engine in percentage\n",
"\n",
"#Output\n",
"print 'The volumetric efficiency of the engine is (percent) = ',round(nv,2)\n"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Example 12 - pg 7.27"
]
},
{
"cell_type": "code",
"execution_count": 18,
"metadata": {
"collapsed": false
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"(a)The air standard efficiency is (percent) = 46.1\n",
"(b)Indicated power is (kW) = 9.093\n",
"(c)Indicated thermal efficiency is (percent) = 32.5\n"
]
}
],
"source": [
"#pg 7.27\n",
"#calculate the air standard efficiency and Indicated power, thermal efficiency\n",
"#Input data\n",
"import math\n",
"d=0.15;#Diameter of the piston in m\n",
"l=0.19;#Length of the stroke in m\n",
"V=0.00091;#Clearance volume in m**3\n",
"N=250.;#Speed of the engine in rpm\n",
"M=6.5;#Indicated mean effective pressure in bar\n",
"c=6.3;#Gas consumption in m**3/hr\n",
"H=16000.;#Calorific value of the has in kJ/m**3\n",
"r1=1.4;#Polytropic index\n",
"\n",
"#Calculations\n",
"Vs=(math.pi*d**2*l)/4;#Swept volume in m**3\n",
"Vt=Vs+V;#Total cylinder volume in m**3\n",
"r=Vt/V;#Compression ratio\n",
"na=(1-(1/r**(r1-1)))*100;#Air standard efficiency in percent\n",
"A=(math.pi*d**2)/4;#Area of the bore in m\n",
"I=(M*10**5*l*A*N)/(1000*60);#Indicated power in kW\n",
"Hs=(c*H)/(60*60);#Heat supplied per second\n",
"nt=(I/Hs)*100;#Indicated thermal efficiency in percent\n",
"\n",
"#Output\n",
"print '(a)The air standard efficiency is (percent) = ',round(na,1)\n",
"print '(b)Indicated power is (kW) = ',round(I,3)\n",
"print '(c)Indicated thermal efficiency is (percent) = ',round(nt,1)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Example 13 - pg 7.28"
]
},
{
"cell_type": "code",
"execution_count": 19,
"metadata": {
"collapsed": false
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"(a)The diameter of the venturi of the venturi if the air speed is 90 m/s is (cm) = 3.55\n",
"(b)The diameter of the jet if the pressure drop at the jet is 0.8 times the pressure drop at the venturi is (mm) = 2.218\n"
]
}
],
"source": [
"#pg 7.28\n",
"#calculate the diameter in all cases\n",
"#Input data\n",
"import math\n",
"ma=6.;#Air supplied per minute by a single jet carburetor in kg/min\n",
"mf=0.44;#Mass flow rate of petrol in kg/min\n",
"s=0.74;#Specific gravity of petrol in kg/m**3\n",
"p1=1.;#Initial pressure of air in bar\n",
"T1=300.;#Initial temperature of air in K\n",
"Ci=1.35;#Isentropic coefficient of air\n",
"V=90.;#Speed of air in the venturi in m/s\n",
"Vc=0.85;#Velocity coefficient of the venturi in m/s\n",
"Cf=0.66;#Coefficient of discharge for the jet\n",
"Cp=1005.;#Coefficient of pressure in J/kg K\n",
"n=1.35;#Isentropic coefficient of air\n",
"R=0.281;#Real gas constant in Nm/kg K\n",
"rhof=740.;#Density of fuel in mm of Hg\n",
"\n",
"#Calculations\n",
"p2=(1-((V/Vc)**(2)/(2*T1*Cp)))**((n)/(n-1));#Pressure at the venturi in bar\n",
"V1=((R*T1)/(p1*10**5))*1000;#Initial volume in m**3/kg\n",
"V2=V1*((p1/p2)**(0.741));#Final volume in m**3/kg\n",
"A2=((ma*V2)/(V*60.))*10**4;#Throat area of venturi in cm**2\n",
"d=((A2*4.)/math.pi)**(0.5);#Diameter of venturi in cm\n",
"deltaPa=1-p2;#Pressure drop causing air flow in bar\n",
"deltaPf=0.8*deltaPa;#Pressure drop causing fuel flow in bar\n",
"Af=(mf/60.)*(10**4)/((Cf)*(2*rhof*deltaPf*10**5)**(1./2));#Area through which fuel flows in cm**2\n",
"df=((Af*(4/math.pi))**(1./2))*10.;#Diameter of fuel jet in mm\n",
"\n",
"print '(a)The diameter of the venturi of the venturi if the air speed is 90 m/s is (cm) = ',round(d,2)\n",
"print '(b)The diameter of the jet if the pressure drop at the jet is 0.8 times the pressure drop at the venturi is (mm) = ',round(df,3)\n"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Example 14 - pg 7.30"
]
},
{
"cell_type": "code",
"execution_count": 21,
"metadata": {
"collapsed": false
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"The weight of fuel required per 1HP hr is (kg) = 0.1947\n"
]
}
],
"source": [
"#pg 7.30\n",
"#calculate the weight of fuel\n",
"#Input data\n",
"r=14.;#The compression ratio of a diesel engine\n",
"Vc=1.;#Clearance volume in m**3\n",
"c=0.08;#Fuel supply cut off point\n",
"nr=0.55;#Relative efficiency\n",
"H=10000.;#Calorific value of fuel in kcal/kg\n",
"r1=1.4;#Ratio of specific heat of air\n",
"Vs=13.;#Stroke volume in m**3\n",
"\n",
"#Calculations\n",
"rho=Vc+(c*Vs);#Cut off ratio\n",
"na=1-(1*(rho**r1-1)/((r**(r1-1)*r1)*(rho-1)));#Air standard efficiency of diesel cycle in percent\n",
"In=(na*nr);#Indicated thermal efficiency in percent\n",
"H1=(4500*60)/(In*427.);#Heat in fuel supplied/1HP hr\n",
"W=H1/10**4;#Weight of fuel required/1HP hr\n",
"\n",
"#Output\n",
"print 'The weight of fuel required per 1HP hr is (kg) = ',round(W,4)\n"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Example 15 - pg 7.31"
]
},
{
"cell_type": "code",
"execution_count": 24,
"metadata": {
"collapsed": false
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"The quantity of fuel to be injected per cycle per cylinder is (cc) = 0.0654\n"
]
}
],
"source": [
"#pg 7.31\n",
"#calculate the quantity of fuel\n",
"#Input data\n",
"P=120;#Power developed by a six cykinder four stroke diesel engine\n",
"N=2400;#Speed in rpm\n",
"f=0.2;#Brake specific fuel consumption in kg/kWh\n",
"s=0.85;#Specific gravity of fuel\n",
"\n",
"#Calculations\n",
"F=f*P;#Fuel consumed per hour in kg\n",
"F1=F/6;#Fuel consumed per cylinder in kg/h\n",
"n=(N*60.)/2;#Number of cycles per hour\n",
"F2=(F1/n)*10**3;#Fuel consumption per cycle in gm\n",
"V=F2/s;#Volume of fuel to be injected per cycle in cc\n",
"\n",
"#Output\n",
"print 'The quantity of fuel to be injected per cycle per cylinder is (cc) = ',round(V,4)\n"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Example 16 - pg 7.32"
]
},
{
"cell_type": "code",
"execution_count": 25,
"metadata": {
"collapsed": false
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"The diameter of the orifice is (mm) = 0.6165\n"
]
}
],
"source": [
"#pg 7.32\n",
"#calculate the diameter of the orifice\n",
"#Input data\n",
"P=20.;#Power developed by a four stroke diesel engine per cylinder in kW\n",
"N=2000.;#Operating speed of the diesel engine in rpm\n",
"s=0.25;#Specific fuel consumption in kh/kW\n",
"p1=180.;#Pressure of fuel injected in bar\n",
"d=25.;#Distance travelled by crank in degrees\n",
"p2=38.;#Pressure in the combustion chamber in bar\n",
"Cd=0.85;#Coefficient of velocity\n",
"A=30.;#API in degrees\n",
"\n",
"#Calculations\n",
"T=d/(360.*(N/60));#Duration of fuel injection in s\n",
"SG=(141.5/(131.5+A))*10**3;#Specific gravity of fuel\n",
"V=Cd*(2*(p1-p2)*10**5/SG)**(1./2);#Velocity of fuel injection in m/s\n",
"Vf=(s/60.)*P/((N/2)*SG);#Volume of fuel injected per cycle in m**3/cycle\n",
"Na=Vf/(V*T);#Nozzle orifice area in m**2\n",
"d=(((4*Na)/3.14)**(1./2))*10**3;#Diameter of the orifice of the fuel injector in mm\n",
"\n",
"#Output\n",
"print 'The diameter of the orifice is (mm) = ',round(d,4)\n"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Example 17 - pg 7.33"
]
},
{
"cell_type": "code",
"execution_count": 26,
"metadata": {
"collapsed": false
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"The total orifice area required per injector if the injection takes place over 16 degree crank angle is (m^2) = 4.8796e-07\n"
]
}
],
"source": [
"#pg 7.33\n",
"#calculate the total orifice area\n",
"#Input data\n",
"P=200.;#Power developed by a six cylinder diesel engine in kW\n",
"N=2000.;#Operating speed of the engine in rpm\n",
"bs=0.2;#The brake specific fuel consumption in kg/kWh\n",
"p1=35.;#The pressure of air in the cylinder at the beginning of injection in bar\n",
"p2=55.;#Maximum cylinder pressure in bar\n",
"p3=180.;#Initial injection pressure in bar\n",
"p4=520.;#Maximum pressure at the injector in bar\n",
"Cd=0.75;#Coefficient of discharge\n",
"S=850.;#Specific gravity of fuel\n",
"p5=1.;#Atmospheric pressure in bar\n",
"a=16.;#The crank angle over which injection takes place in degrees\n",
"\n",
"#Calculations\n",
"Po=P/6.;#Power output per cylinder in kW\n",
"F=(Po*bs)/60.;#Fuel consumed per cylinder in kg/min\n",
"Fi=F/(N/2.);#Fuel injected per cycle in kg\n",
"T=a/(360.*(N/60));#Duration of injection in s\n",
"deltaP1=p3-p1;#Pressure difference at the beginning of injection in bar\n",
"deltaP2=p4-p2;#Pressure difference at the end of injection in bar\n",
"avP=(deltaP1+deltaP2)/2;#Average pressure difference in bar\n",
"V=Cd*(2.*(avP*10**5)/S)**(1./2);#Velocity of injection of fuel jet in m/s\n",
"Vo=Fi/S;#Volume of fuel injected per cycle in m**3/cycle\n",
"A=(Vo/(V*T));#Area of fuel orifices in m**2\n",
"\n",
"#Output\n",
"print 'The total orifice area required per injector if the injection takes place over 16 degree crank angle is (m^2) = ',round(A,11)\n"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Example 18 - pg 7.34"
]
},
{
"cell_type": "code",
"execution_count": 27,
"metadata": {
"collapsed": false
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"(a)The indicated mean effective pressure is (bar) = 8.25\n",
"(b)Indicated power is (kW) = 2.81\n"
]
}
],
"source": [
"#pg 7.34\n",
"#calculate the indicated mean effective pressure and indicated power\n",
"#Input data\n",
"A=450.;#Area of indicator diagram in mm^2\n",
"l=60.;#Length of indicator diagram in mm\n",
"s=1.1;#Spring number in bar/mm\n",
"d=0.1;#Diameter of piston in m\n",
"L=0.13;#Length of stroke in m\n",
"N=400.;#Operating speed of the engine in rpm\n",
"\n",
"#Calculations\n",
"Av=A/l;#Average height of indicator diagram in mm\n",
"pm=Av*s;#Mean effective pressure in bar\n",
"np=N/2.;#Number of power strokes per minute for a four stroke diesel engine\n",
"Ar=(3.14*d**2)/4;#Area of the piston in m^2\n",
"I=(pm*10**5*L*Ar*np)/(1000*60);#Indicated power in kW\n",
"\n",
"#Output\n",
"print '(a)The indicated mean effective pressure is (bar) = ',pm\n",
"print '(b)Indicated power is (kW) = ',round(I,2)\n"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Example 19 - pg 7.35"
]
},
{
"cell_type": "code",
"execution_count": 28,
"metadata": {
"collapsed": false
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"(a)The brake horse power is (kW) = 28.26\n",
"(b)Indicated horse power is (kW) = 35.063\n",
"(c)Thermal efficiency on IHP basis is (percent) = 37.33\n",
"(d)Thermal efficiency on BHP basis is (percent) = 30.08\n"
]
}
],
"source": [
"#pg 7.35\n",
"#calculate the brake, Indicated horse power and Thermal efficiency\n",
"#Input data\n",
"d=25.;#Diameter of the bore in cm\n",
"l=0.4;#Stroke length in m\n",
"N=300.;#Operating speed of the engine in rpm\n",
"n=120.;#Number of explosions per minute\n",
"pm=6.7;#Mean effective pressure in kgf/cm**2\n",
"Tnet=90.;#Net brake load in kg\n",
"R=0.75;#Radius of brake drum in m\n",
"f=0.22;#Fuel supplied per minute in m**3\n",
"C=4500.;#Calorific value of fuel in kcal/m**3\n",
"\n",
"#Calculations\n",
"BHP=(2*3.14*R*N*Tnet)/4500;#Brake horse power in kW\n",
"A=(3.14*d**2)/4;#Area of the cylinder in cm**2\n",
"IHP=(pm*l*A*n)/4500;#Indicated horse power in kW\n",
"H=f*C;#Heat supplied by fuel per minute in kcal\n",
"nt1=((IHP*C)/(990*427))*100;#Thermal efficiency on IHP basis in percent\n",
"nt2=((BHP*C)/(990*427))*100;#Thermal efficiency on BHP basis in percent\n",
"\n",
"#Output\n",
"print '(a)The brake horse power is (kW) = ',round(BHP,2)\n",
"print '(b)Indicated horse power is (kW) = ',round(IHP,3)\n",
"print '(c)Thermal efficiency on IHP basis is (percent) = ',round(nt1,2)\n",
"print '(d)Thermal efficiency on BHP basis is (percent) = ',round(nt2,2)\n"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Example 20 - pg 7.36"
]
},
{
"cell_type": "code",
"execution_count": 29,
"metadata": {
"collapsed": false
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"(a)The brake horse power is (kW) = 3.62\n",
"(b)Indicated horse power is (kW) = 4.341\n",
"(c)Mechanical efficiency is (percent) = 83.4\n",
"(d)Indicated thermal efficiency is (percent) = 33.0\n",
"(e)Brake thermal efficiency is (percent) = 27.5\n"
]
}
],
"source": [
"#pg 7.36\n",
"#calculate the brake, Indicated horse power and Thermal efficiency\n",
"#Input data\n",
"D=0.6;#Brake wheel diameter of a constant speed compression ignition engine operating on four stroke cycle in m\n",
"t=0.01;#Thickness of brake band in m\n",
"N=500.;#Operating speed of the engine in rpm\n",
"W=20.;#Load on brake band in kgf\n",
"S=3.;#Spring balance reading in kgf\n",
"l=6.25;#Length of indicator diagram in cm\n",
"A=4.35;#Area of indicator diagram in cm**2\n",
"Sn=11.;#Spring number in kgf/cm**2/cm\n",
"d=10.;#Diameter of the bore in cm\n",
"L=0.13;#Length of the stroke in m\n",
"F=0.23;#Specific fuel consumption in kg/BHP hr\n",
"CV=10000.;#Heating value of fuel in kcal/kg\n",
"\n",
"#Calculations\n",
"BHP=(3.14*(D+t)*N*(W-S))/4500;#Brake horse power in kW\n",
"MEP=(A*Sn)/l;#Mean effective pressure in kgf/cm**2\n",
"Ar=(3.14*d**2)/4;#Area of the cylinder in cm**2\n",
"np=N/2;#Number of explosions per minute\n",
"IHP=(MEP*L*Ar*np)/4500;#Indicated horse power in kW\n",
"nm=(BHP/IHP)*100;#Mechanical efficiency in percentage\n",
"Wf=F*BHP;#Fuel consumption per hr in kg/hr\n",
"nt=((IHP*4500*60)/(Wf*CV*427))*100;#Indicated thermal efficiency in percentage\n",
"nb=((BHP*4500*60)/(Wf*CV*427))*100;#Brake thermal efficiency in kW\n",
"\n",
"#Output\n",
"print '(a)The brake horse power is (kW) = ',round(BHP,2)\n",
"print '(b)Indicated horse power is (kW) = ',round(IHP,3)\n",
"print '(c)Mechanical efficiency is (percent) = ',round(nm,1)\n",
"print '(d)Indicated thermal efficiency is (percent) = ',round(nt,0)\n",
"print '(e)Brake thermal efficiency is (percent) = ',round(nb,1)\n"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Example 21 - pg 7.38"
]
},
{
"cell_type": "code",
"execution_count": 31,
"metadata": {
"collapsed": false
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"The indicated thermal efficiency is (percent) = 30.9\n",
"Mechanical efficiency is (percent) = 82.0\n",
"Brake thermal efficiency is (percent) = 25.3\n"
]
}
],
"source": [
"#pg 7.38\n",
"#calculate the indicated thermal efficiency\n",
"#Input data\n",
"N=1200.;#Operating speed of a four cylinder engine in rpm\n",
"BHP=25.3;#The brake horse power when all 4 cylinders are operating in kW\n",
"T=10.5;#The average torque when one cylinder was cut out in mkgf\n",
"CV=10000.;#Calorific value of the fuel used in kcal/kg\n",
"f=0.25;#The amount of petrol used in engine per BHP hour\n",
"J=427.;#\n",
"\n",
"#Calculations\n",
"BHP1=(2*3.14*N*T)/4500.;#BHP for 3 cylinders when 1 cylinder is cut out in kW\n",
"IHP=BHP-BHP1;#IHP of one cylinder in kW\n",
"IHPt=IHP*4.;#Total IHP of the engine with 4 cylinders\n",
"Wf=(f*BHP)/60.;#Fuel used per minute in kg\n",
"ni=((IHPt*4500.)/(Wf*CV*J))*100;#Indicated thermal efficiency in percent\n",
"nm=(BHP/IHPt)*100;#Mechanical efficiency in percent\n",
"nb=(IHPt*nm)/100;#Brake thermal efficiency in percent\n",
"\n",
"#Output\n",
"print 'The indicated thermal efficiency is (percent) = ',round(ni,1)\n",
"print 'Mechanical efficiency is (percent) = ',round(nm,1)\n",
"print 'Brake thermal efficiency is (percent) = ',round(nb,1)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Example 22 - pg 7.39"
]
},
{
"cell_type": "code",
"execution_count": 32,
"metadata": {
"collapsed": false
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"(a)The IHP of the engine is (kW) = 38.6\n",
"(b)Mechanical efficiency is (percent) = 82.9\n"
]
}
],
"source": [
"#pg 7.39\n",
"#calculate the IHP of the engine and Mechanical efficiency\n",
"#Input data\n",
"B=32.;#Brake horse power in kW with all cylinders working\n",
"B1=21.6;#BHP with number 1 cylinder cut out in kW\n",
"B2=22.3;#BHP with number 2 cylinder cut out in kW\n",
"B3=22.5;#BHP with number 3 cylinder cut out in kW\n",
"B4=23.;#BHP with number 4 cylinder cut out in kW\n",
"\n",
"#Calculations\n",
"I1=B-B1;#Indicated horse power of number 1 cylinder in kW\n",
"I2=B-B2;#IHP of number 2 cylinder in kW\n",
"I3=B-B3;#IHP of number 3 cylinder in kW\n",
"I4=B-B4;#IHP of number 4 cylinder in kW\n",
"I=I1+I2+I3+I4;#Total IHP of the engine in kW\n",
"nm=(B/I)*100;#Mechanical efficiency in percent\n",
"\n",
"#Output\n",
"print '(a)The IHP of the engine is (kW) = ',I\n",
"print '(b)Mechanical efficiency is (percent) = ',round(nm,1)\n"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Example 23 - pg 7.40"
]
},
{
"cell_type": "code",
"execution_count": 33,
"metadata": {
"collapsed": false
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"(a)Compression ratio = 6.6\n",
"(b)Indicated thermal efficiency is (percent) = 34.45\n",
"(c)Brake specific fuel consumption is (kg/kW sec) = 7.59e-05\n",
"(d)Bore diameter of the engine is (mm) = 98.99\n",
"(e)Stroke length of the engine is (mm) = 128.7\n"
]
}
],
"source": [
"#pg 7.40\n",
"#calculate the Compression ratio, indicated thermal efficiency, brake specific fuel consumption and bore diameter\n",
"#Input data\n",
"r=15.;#The air fuel ratio by weight\n",
"CV=45000.;#Calorific value of fuel in kJ/kg\n",
"nm=85.;#Mechanical efficiency of 4 stroke 4 cylinder engine in percent\n",
"na=53.;#Air standard efficiency of the engine in percent\n",
"nr=65.;#Relative efficiency of the engine in percent\n",
"nv=80.;#Volumetric efficiency of the engine in percent\n",
"r1=1.3;#Stroke to bore ratio\n",
"p1=1.;#Suction pressure in bar\n",
"T=303.;#Suction temperature in K\n",
"S=3000.;#The operating speed of the engine in rpm\n",
"P=75.;#Power at brakes in kW\n",
"r2=1.4;#Ratio of specific heats for air\n",
"R1=0.287;#Characteristic gas constant for air fuel mixture in kJ/kg K\n",
"\n",
"#Calculations\n",
"R=(1/(1-(na/100)))**(1/(r2-1));#Compression ratio of the engine\n",
"nti=((na/100)*(nr/100))*100;#The indicated thermal efficiency in percent\n",
"Pi=P/(nm/100);#Indicated power in kW\n",
"F=Pi/((nti*CV)/100);#Fuel per second injected in kg/sec\n",
"B=F/P;#Brake specific fuel consumption in kg/kWsec\n",
"A=1+r;#Mass of fuel mixture entering the engine foe every one kg of fuel in kg\n",
"m=A*F;#Mass of air fuel mixture per second in kg\n",
"V=(m*R1*T)/(p1*10**5/1000);#Volume of air fuel mixture supplied to the engine per sec\n",
"Vs=V/(nv/100);#Swept volume per second in m**3/sec\n",
"d=((Vs*2*60*4)/(S*3.14*r1*4))**(1./3)*1000;#Diameter of the bore in mm\n",
"L=r1*d;#Stroke length in mm\n",
"\n",
"#Output\n",
"print '(a)Compression ratio = ',round(R,1)\n",
"print '(b)Indicated thermal efficiency is (percent) = ',nti\n",
"print '(c)Brake specific fuel consumption is (kg/kW sec) = ',round(B,7)\n",
"print '(d)Bore diameter of the engine is (mm) = ',round(d,2)\n",
"print '(e)Stroke length of the engine is (mm) = ',round(L,1)\n"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Example 24 - pg 7.42"
]
},
{
"cell_type": "code",
"execution_count": 34,
"metadata": {
"collapsed": false
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"(a)Power available at brakes is (kW) = 24.23\n",
"(b)Indicated power developed is (kW) = 34.19\n",
"(c)Mechanical efficiency is (percent) = 70.85\n",
"(d)Brake Thermal efficiency is (percent) = 27.69\n",
"(e)Indicated thermal efficiency is (percent) = 39.08\n",
"Heat balance :\n",
"Heat supplied by fuel (kJ/hr) = 315000.0\n",
"Heat equivalent of power of brakes (percent) = 26.9\n",
"Heat equivalent of loss in friction (percent) = 11.4\n",
"Heat equivalent of removed through jacket (percent) = 26.6\n",
"Heat equivalent of carried away by gases (percent) = 26.91\n",
"Heat equivalent of unaccounted (percent) = 7.4\n"
]
}
],
"source": [
"#pg 7.42\n",
"#calculate the power and efficiency in all cases\n",
"#Input data\n",
"d=0.3;#Diameter of the bore in m\n",
"L=0.45;#Stroke length in m\n",
"N=220.;#Operating speed of the engine in rpm\n",
"T=3600.;#Duration of trial in sec\n",
"F=7.;#Fuel consumption in kg per minute\n",
"CV=45000.;#Calorific value of fuel in kJ/kg\n",
"A=320.;#Area of indicator diagram in mm**2\n",
"l=60.;#Length of indicator diagram in mm\n",
"S=1.1;#Spring index in bar/mm\n",
"W=130.;#Net load on brakes in kg\n",
"D=1.65;#Diameter of brake drum in m\n",
"W1=500.;#Total weight of jacket cooling water in kg\n",
"t=40.;#Temperature rise of jacket cooling water in degrees celsius\n",
"t1=300.;#Temperature of exhaust gases in degrees celsius\n",
"ma=300.;#Air consumption in kg\n",
"sg=1.004;#Specific heat of exhaust gas in kJ/kgK\n",
"sw=4.185;#Specific heat of water in kJ/kgK\n",
"t2=25.;#Room temperature in degrees celsius\n",
"g=9.81;#gravity\n",
"\n",
"#Calculations\n",
"P=(W*g*3.14*D*N)/(1000*60);#Power available at brakes in kW\n",
"pm=(A*S)/l;#Mean effective pressure in bar\n",
"I=(pm*10**5*L*((3.14*d**2)/4)*N)/(1000.*2*60);#Indicated power developed in kW\n",
"nm=(P/I)*100;#Mechanical efficiency in percent\n",
"nt=(P/((F/T)*CV))*100;#Brake thermal efficiency in percent\n",
"ni=(I/((F/T)*CV))*100;#Indicated thermal efficiency in percent\n",
"Hs=F*CV;#Heat supplied on one hour basis\n",
"Hp=P*T;#Heat equivalent of brake power in kJ\n",
"Hf=(I-P)*3600;#Heat lost in friction in kJ\n",
"Hc=W1*t*sw;#Heat carried away by cooling water in kJ\n",
"He=(ma+F)*(t1-t2)*sg;#Heat carried away by exhaust gas in kJ\n",
"Hu=Hs-(Hp+Hf+Hc+He);#Heat unaccounted in kJ\n",
"nb=(He/Hs)*100;#Heat equivalent of power at brakes in percent\n",
"nf=(Hf/Hs)*100;#Heat lost in friction in percent\n",
"nw=(Hc/Hs)*100;#Heat removed by jacket water in percent\n",
"ne=(He/Hs)*100;#Heat carried away by exhaust gases in percent\n",
"nu=(Hu/Hs)*100;#Heat unaccounted in percent\n",
"\n",
"#Output\n",
"print '(a)Power available at brakes is (kW) = ',round(P,2)\n",
"print '(b)Indicated power developed is (kW) = ',round(I,2)\n",
"print '(c)Mechanical efficiency is (percent) = ',nm\n",
"print '(d)Brake Thermal efficiency is (percent) = ',round(nt,2)\n",
"print '(e)Indicated thermal efficiency is (percent) = ',round(ni,2)\n",
"print 'Heat balance :'\n",
"print 'Heat supplied by fuel (kJ/hr) = ',Hs\n",
"print 'Heat equivalent of power of brakes (percent) = ',round(nb,1)\n",
"print 'Heat equivalent of loss in friction (percent) = ',round(nf,1)\n",
"print 'Heat equivalent of removed through jacket (percent) = ',round(nw,1)\n",
"print 'Heat equivalent of carried away by gases (percent) = ',round(ne,2)\n",
"print 'Heat equivalent of unaccounted (percent) = ',round(nu,1)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Example 25 - pg 7.46"
]
},
{
"cell_type": "code",
"execution_count": 35,
"metadata": {
"collapsed": false
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"(a)Indicated horse power is (kcal) = 42.62\n",
"(b)Brake horse power developed is (kcal) = 34.93\n",
"(c)Heat equivalent of friction is (kcal) = 81.0\n"
]
}
],
"source": [
"#pg 7.46\n",
"#calculate the Indicated, brake horse power\n",
"#Input data\n",
"d=25.;#The bore diameter of a single cylinder 4 stroke engine in cm\n",
"l=0.38;#Stroke length in m\n",
"t=3600.;#Duration of test in sec\n",
"r=19710.;#Total number of revolutions\n",
"F=6.25;#Fuel oil used in kg\n",
"A=5.7;#Area of indicator diagram in cm**2\n",
"L=7.6;#Length of indicator diagram in cm\n",
"S=8.35;#Spring number in kgf/cm**3\n",
"P=63.5;#Net load on brake drum in kg\n",
"R=1.2;#Radius of brake drum in m\n",
"Ww=5.7;#Rate of coolant flow in kg/min\n",
"deltaT=44.;#Temperature rise of coolant in degrees celsius\n",
"T1=15.5;#Atmospheric temperature in degrees celsius\n",
"As=30.;#Air supplied per kg of fuel\n",
"CV=10600.;#Calorific value of fuel in kcal/kg\n",
"Te=390.;#Exhaust gas temperature in degrees celsius\n",
"sm=0.25;#Mean specific heat of exhaust gas\n",
"\n",
"#Calculations\n",
"Hs=(F*CV)/60.;#Heat supplied by fuel per minute in kcal\n",
"pm=(A*S)/L;#Mean effective pressure in kgf/cm**2\n",
"I=(pm*l*(3.14*d**2)*r)/(4*60.*2*4500);#Indicated horse power in kW\n",
"B=(P*R*2*3.14*r)/(4500*60);#Brake horse power in kW\n",
"Hei=(I*4500)/427.;#Heat equivalent of IHP/min in kcal\n",
"Heb=(B*4500)/427.;#Heat equivalent of BHP/min in kcal\n",
"Hf=Hei-Heb;#Heat in friction per minute in kcal\n",
"Hc=Ww*deltaT;#Heat carried away by coolant in kcal\n",
"We=(F+(As*F))/60.;#Weight of exhaust gases per minute\n",
"He=We*(Te-T1)*sm;#Heat carried away by exhaust gases in kcal\n",
"\n",
"#Output\n",
"print '(a)Indicated horse power is (kcal) = ',round(I,2)\n",
"print '(b)Brake horse power developed is (kcal) = ',round(B,2)\n",
"print '(c)Heat equivalent of friction is (kcal) = ',round(Hf,1)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Example 26 - pg 7.48"
]
},
{
"cell_type": "code",
"execution_count": 36,
"metadata": {
"collapsed": false
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"Percentage of heat carried away by exhaust gas is (percent) = 24.06\n"
]
}
],
"source": [
"#pg 7.48\n",
"#calculate the percentage of heat carried away\n",
"#Input\n",
"F=10.;#Quantity of fuel supplied during the trial of a diesel engine in kg/hr\n",
"CV=42500.;#Calorific value of fuel in kJ/kg\n",
"r=20.;#Air fuel ratio\n",
"T=20.;#Ambient temperature in degrees celsius\n",
"mw=585.;#Water circulated through the gas calorimeter in litres/hr\n",
"T1=35.;#Temperature rise of water through the calorimeter in degrees celsius\n",
"T2=95.;#Temperature of gases at exit from the calorimeter in degrees celsius\n",
"se=1.05;#Specific heat of exhaust gases in kJ/kgK\n",
"sw=4.186;#Specific heat of water in kJ/kgK\n",
"\n",
"#Calculations\n",
"M=(F/60.)*(r+1);#Mass of exhaust gases formed per minute\n",
"H=((mw/60.)*sw*T1)+(M*se*(T2-T));#Heat carried away by the exhaust gases per minute in kJ/min\n",
"Hs=(F/60.)*CV;#Heat supplied by fuel per minute in kJ/min\n",
"nh=(H/Hs)*100;#Percentage of heat carried away by the exhaust gas\n",
"\n",
"#Output\n",
"print 'Percentage of heat carried away by exhaust gas is (percent) = ',round(nh,2)\n"
]
},
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"cell_type": "markdown",
"metadata": {},
"source": [
"## Example 27 - pg 7.49"
]
},
{
"cell_type": "code",
"execution_count": 37,
"metadata": {
"collapsed": false
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"Percentage of heat carried away by exhaust gases is (percent) = 27.9\n"
]
}
],
"source": [
"#pg 7.49\n",
"#calculate the Percentage of heat carried away\n",
"#Input data\n",
"F=11.;#Fuel used per hour observed during the trial of a single cylinder four stroke diesel engine in kg\n",
"mc=85.;#Carbon present in the fuel in percent\n",
"mh=14.;#Hydrogen present in the fuel in percent\n",
"mn=1.;#Non combustibles present in the fuel in percent\n",
"CV=50000.;#Calorific value of fuel in kJ/kg\n",
"Vc=8.5;#Percentage of carbon dioxide present in exhaust gas by Volumetric analysis\n",
"Vo=10.;#Oxygen present in exhaust gases in percent\n",
"Vn=81.5;#Nitrogen present in exhaust gases in percent\n",
"Te=400.;#Temperature of exhaust gases in degrees celsius\n",
"se=1.05;#Specific heat of exhaust gas in kJ/kg\n",
"Pp=0.030;#Partial pressure of steam in the exhaust in bar\n",
"Ta=20.;#Ambient temperature in degrees celsius\n",
"hs=2545.6;#Enthalpy of saturated steam in kJ/kg\n",
"Tsa=24.1;#Saturation temperature from graph in degrees celcius\n",
"Cp=2.1;#Specific heat in kJ/kg K\n",
"hst=3335.;#Enthalpy of super heated steam in kJ/kg\n",
"F1=9.\n",
"#Calculations\n",
"Ma=(Vn*mc)/(33.*Vc);#Mass of air supplied per kg of fuel in kg\n",
"Me=Ma+1;#Mass of exhaust gases formed per kg of fuel in kg\n",
"me=(Me*F)/60.;#Mass of exhaust gases formed per minute in kg\n",
"ms=F1*(mh/100.);#Mass of steam formed per kg of fuel in kg\n",
"ms1=(ms*F)/60.;#Mass of steam formed per minute in kg\n",
"mde=me-ms1;#Mass of dry exhaust gases formed per minute in kg\n",
"H=mde*se*(Te-Ta);#Heat carried away by the dry exhaust gases per minute in kJ/min\n",
"Es=hs+(Cp*(Te-Tsa));#Enthalpy of superheated steam in kJ/kg\n",
"He=ms1*hst;#Heat carried away by steam in the exhaust gases in kJ/min\n",
"Hl=H+He;#Total heat lost through dry exhaust gases and steam in kJ/min\n",
"Hf=(F/60.)*CV;#Heat supplied by fuel per minute in kJ/min\n",
"nh=(Hl/Hf)*100.;#Percentage of heat carried away by exhaust gases\n",
"\n",
"#Output\n",
"print 'Percentage of heat carried away by exhaust gases is (percent) = ',round(nh,1)\n"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Example 28 - pg 7.51"
]
},
{
"cell_type": "code",
"execution_count": 38,
"metadata": {
"collapsed": false
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"The net increase in brake power is (kW) = 29.15\n"
]
}
],
"source": [
"#pg 7.51\n",
"#calculate the net increase in brake power\n",
"#Input data\n",
"C=0.0033;#The capacity of a four stroke engine of compression ignition type\n",
"I=13.;#Average indicated power developed in kW/m**3\n",
"N=3500.;#Operating speed of the engine\n",
"nv=80.;#Volumetric efficiency in percentage\n",
"p1=1.013;#Initial pressure in bar\n",
"T1=298.;#Initial temperature in K\n",
"r=1.75;#Pressure ratio of the engine\n",
"ni=75.;#The isentropic efficiency in percentage\n",
"nm=80.;#mechanical efficiency in percentage\n",
"r1=1.4;#Polytropic index\n",
"\n",
"#Calculations\n",
"Vs=(N/2.)*C;#Swept volume in m**3/min\n",
"Vi=Vs*(nv/100);#Unsupercharged engine inducted volume in m**3/min\n",
"Pb=p1*r;#Blower delivery pressure in bar\n",
"T2s=((r)**((r1-1)/r1))*T1;#Final temperature in K\n",
"T2=((T2s-T1)/(ni/100.))+T1;#Blower delivery temperature in K\n",
"Ve=((Pb*Vs)*T1)/(T2*p1);#Equivalent volume at 1.013 bar and 298K in m**3/min\n",
"Vin=Ve-Vi;#Increase in inducted volume of air in m**3/min\n",
"Pin=Vin*I;#Increase in indicated power due to extra air inducted in kW\n",
"Pinp=((Pb-p1)*Vs*100.)/60.;#Increase in indicated power due to increase in induction pressure in kW\n",
"Pt=Pin+Pinp;#Total increase in indicated power in kW\n",
"nb=Pt*(nm/100.);#Total increase in brake power efficiency in kW\n",
"ma=(Pb*Vs*100.)/(60*0.287*T2);#Mass of air delivered by the blower in kg/s\n",
"Wb=ma*1.005*(T2-T1);#Work input to air by blower in kW\n",
"Pb1=Wb/(nv/100.);#Power required to drive the blower in kW\n",
"Pb2=nb-Pb1;#Net increase in brake power in kW\n",
"\n",
"#Output\n",
"print 'The net increase in brake power is (kW) = ',round(Pb2,2)\n"
]
}
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