Chapter 3 : Internal Combustion Engines

Example 3.1 Page no : 139

In [1]:
# Variables
d = 200.;			#diameter of cylinder in mm
L = 300.;			#stroke of cylinder in mm
Vc = 1.73;			#Clearance volume in litres
imep = 650.;			#indicated mean effective pressure in kN/(m**2)
g = 6.2;			#gas consumption in (m**3)/h
CV = 38.5;			#Calorific value in MJ/(m**3)
y = 1.4;			#Ratio of specific heats
N = 150.;			#No. of firing cycles per minute

# Calculations
Vs = ((3.1415/4)*(d**2)*L)*(10**-6);			#Stroke volume in litres
Vt = Vs+Vc;			#Total volume in litres
rv = (Vt/Vc);			#Compression ratio
n = (1-(1/rv**(y-1)))*100;			#Air standard efficiency
IP = imep*(Vs*10**-3)*(N/60);			#Indicated power in kW
F = (g*CV*1000)/3600;			#Fuel energy input in kW
nT = (IP/F)*100;			#Indicated thermal efficiency

# Results
# 1st answer is wrong in book
print 'Air Standard Efficiency is %3.1f percent  \
\nIndicated Power is %3.1f kW \
\nIndicated thermal efficiency is %3.0f percent'%(n,IP,nT)
Air Standard Efficiency is 52.5 percent  
Indicated Power is 15.3 kW 
Indicated thermal efficiency is  23 percent

Example 3.2 Page no : 140

In [2]:
# Variables
Vs = 0.0008;			#Swept volume in m**3
Vc = 0.00015;			#Clearance volume in m**3
CV = 38.;			#Calorific value in MJ/(m**3)
v = 0.45;			#volume in m**3
IP = 81.5;			#Indicated power in kW
y = 1.4;			#Ratio of specific heats

# Calculations
rv = (Vs+Vc)/Vc;			#Compression ratio
n = (1-(1/rv**(y-1)));			#Air standard efficiency
Ps = (v*CV*1000.)/60;			#Power supplied in kW
nact = IP/Ps;			#Actual efficiency
nr = (nact/n)*100;			#Relative efficiency


# Results
print 'Relative Efficiency is %3.2f percent'%(nr)

# rounding error in book answer. please check.
Relative Efficiency is 54.77 percent

Example 3.3 Page no : 141

In [2]:
# Variables
n = 6.;			    #No. of cylinders
d = 0.61;			#Diameter in m
L = 1.25;			#Stroke in m
N = 2.;		    	#No.of revolutions per second
m = 340.;			#mass of fuel oil in kg
CV = 44200.;		#Calorific value in kJ/kg
T = 108.;			#Torque in kN-m
imep = 775.;		#Indicated mean efective pressure in kN/(m**2)

# Calculations
IP = (imep*L*3.1415*(d**2)*N)/(8);			#Indicated power in kW
TotalIP = (n*IP);			    #Total indicated power in kW
BP = (2*3.1415*N*T);			#Brake power in kW
PI = (m*CV)/3600.;			    #Power input in kW
nB = (BP/PI)*100.;		    	#Brake thermal efficiency
bmep = (BP*8)/(n*L*3.1415*(d**2)*2);			#Brake mean effective pressure in kN/(m**2)
nM = (BP/TotalIP)*100;			#Mechanical efficiency
bsfc = m/BP;	        		#Brake specific fuel consumption in kg/kWh

# Results
print 'Total Indicated Power is %3.1f kW  \
\nBrake Power is %3.1f kW \
\nBrake thermal efficiency is %3.1f percent  \
\nBrake mean effective pressure is %3.1f kN/m**2 \
\nMechanical efficiency is %3.1f percent  \
\nBrake specific fuel consumption is %3.3f kg/kW.hr'%(TotalIP,BP,nB,bmep,nM,bsfc)
Total Indicated Power is 1698.6 kW  
Brake Power is 1357.1 kW 
Brake thermal efficiency is 32.5 percent  
Brake mean effective pressure is 619.2 kN/m**2 
Mechanical efficiency is 79.9 percent  
Brake specific fuel consumption is 0.251 kg/kW.hr

Example 3.4 Page no : 142

In [2]:
# Variables
Hm = 21.;			#Mean height of indicator diagram in mm
isn = 27.;			#indicator spring number in kN/(m**2)/mm
Vs = 14.;			#Swept volume in litres
N = 6.6;			#Speed of engine in rev/s
Pe = 77.;			#Effective brake load in kg
Re = 0.7;			#Effective vrake radius in m
mf = 0.002;			#fuel consumed in kg/s
CV = 44000.;			#Calorific value of fuel in kJ/kg
mc = 0.15;			#cooling water circulation in kg/s
Ti = 311.;			#cooling water inlet temperature in K
To = 344.;			#cooling water outlet temperature in K
C = 4.18;			#specific heat capacity of water in kJ/kg-K
Ee = 33.6;			#Energy to exhaust gases in kJ/s
g = 9.81;			#Acceleration due to geravity in m/(s**2)

# Calculations
imep = isn*Hm;			#Indicated mean efective pressure in kN/(m**2)
IP = (imep*Vs*N)/(2000);			#Indicated Power in kW
BP = (2*3.1415*N*g*Pe*Re)/1000;			#Brake Power in kW
nM = (BP/IP)*100;			#Mechanical efficiency
Ef = mf*CV;			#Eneergy from fuel in kJ/s
Ec = mc*C*(To-Ti);			#Energy to cooling water in kJ/s
Es = Ef-(BP+Ec+Ee);			#Energy to surroundings in kJ/s
p = (BP*100)/Ef;			#Energy to BP in %
q = (Ec*100)/Ef;			#Energy to coolant in %
r = (Ee*100)/Ef;			#Energy to exhaust in %
w = (Es*100)/Ef;			#Energy to surroundings in %

# Results
print 'Indicated Power is %3.1f kW  \
\nBrake Power is %3.0f kW  \
\nMechanical Efficiency is %3.0f percent  \
\nENERGY BALANCE                     kJ/s     Percentage \
\nEnergy from fuel                  %3.0f        100 \
\nEnergy to BP                      %3.0f        %3.0f \
\nEnergy to coolant                 %3.01f       %3.1f \
\nEnergy to exhaust                 %3.1f        %3.1f \
\nEnergy to surroundings, etc       %3.1f        %3.1f'%(IP,BP,nM,Ef,BP,p,Ec,q,Ee,r,Es,w)
Indicated Power is 26.2 kW  
Brake Power is  22 kW  
Mechanical Efficiency is  84 percent  
ENERGY BALANCE                     kJ/s     Percentage 
Energy from fuel                   88        100 
Energy to BP                       22         25 
Energy to coolant                 20.7       23.5 
Energy to exhaust                 33.6        38.2 
Energy to surroundings, etc       11.8        13.4

Example 3.5 Page no : 143

In [6]:
# Variables
t = 30.;			#duration of trial in minutes
N = 1750.;			#speed in rpm
T = 330.;			#brake torque in Nm
m = 9.35;			#mass of fuel in kg
CV = 42300.;			#Calorific value in kJ/kg
mj = 483.;			#jacket cooling water circulation in kg
Ti = 290.;			#inlet temperature in K
T0 = 350.;			#outlet temperature in K
ma = 182.;			#air consumption in kg
Te = 759.;			#exhaust temperature in K
Ta = 256.;			#atmospheric temperature in K
nM = 0.83;			#Mechanical efficiency
ms = 1.25;			#mean specific heat capacity of exhaust gas in kJ/kg-K
Cw = 4.18;			#specific heat capacity of water in kJ/kg-K

# Calculations
BP = (2*3.1415*T*N)/(60*1000);			#Brake power in kW
sfc = (m*2)/BP;			#specific fuel consumption in kg/kWh
IP = BP/nM;			#Indicated power in kW
nIT = IP/(m*2/3600*CV)*100    			#Indicated thermal efficiency
Ef = (m/t*CV)     			#Eneergy from fuel in kJ/min
EBP = BP*60;			#Energy to BP in kJ/min
Ec = (mj*Cw*(T0-Ti))/t;			#Energy to cooling water in kJ/min
Ee = ((ma+m)*ms*(Te-Ti))/30;			#Energy to exhaust in kJ/min
Es = Ef-(EBP+Ec+Ee);			#Energy to surroundings in kJ/min

# Results
print 'Break power is %3.1f kW  \
\nSpecific fuel consumption is %3.3f kg/kWh  \
\nIndicated thermal efficiency is %3.1f percent  \
\nEnergy from fuel is %3.0f kJ/min  \
\nEnergy to BP is %3.0f kJ/min  \
\nEnergy to cooling water is %3.0f kJ/min  \
\nEnergy to exhaust is %3.0f kJ/min  \
\nEnergy to surroundings is %d kJ/min'%(BP,sfc,nIT,round(Ef,-2),EBP,Ec,Ee,Es)

# rounding off error
Break power is 60.5 kW  
Specific fuel consumption is 0.309 kg/kWh  
Indicated thermal efficiency is 33.2 percent  
Energy from fuel is 13200 kJ/min  
Energy to BP is 3628 kJ/min  
Energy to cooling water is 4038 kJ/min  
Energy to exhaust is 3739 kJ/min  
Energy to surroundings is 1777 kJ/min

Example 3.6 Page no : 144

In [6]:
# Variables
BP0 = 12.;			#Brake Power output in kW
BP1 = 40.5;			#Brake Power in trial 1 in kW
BP2 = 40.2;			#Brake Power in trial 2 in kW
BP3 = 40.1;			#Brake Power in trial 3 in kW
BP4 = 40.6;			#Brake Power in trial 4 in kW
BP5 = 40.7;			#Brake Power in trial 5 in kW
BP6 = 40.0;			#Brake Power in trial 6 in kW

# Calculations
BPALL = BP0+BP6;			#Total Brake Power in kW
IP1 = BPALL-BP1;			#Indicated Power in trial 1 in kW
IP2 = BPALL-BP2;			#Indicated Power in trial 2 in kW
IP3 = BPALL-BP3;			#Indicated Power in trial 3 in kW
IP4 = BPALL-BP4;			#Indicated Power in trial 4 in kW
IP5 = BPALL-BP5;			#Indicated Power in trial 5 in kW
IP6 = BPALL-BP6;			#Indicated Power in trial 6 in kW
IPALL = IP1+IP2+IP3+IP4+IP5+IP6;			#Total Indicated Power in kW
nM = (BPALL/IPALL)*100;			#Mechanical efficiency

# Results
print 'Indicated Power of the engine is %3.1f kW  \
\nMechanical efficiency of the engine is %3.1f percent'%(IPALL,nM)
Indicated Power of the engine is 69.9 kW  
Mechanical efficiency of the engine is 74.4 percent

Example 3.7 Page no : 145

In [5]:
import math

# Variables
n = 2.;			#No. of cylinders
N = 4000.;			#speed of engine in rpm
nV = 0.77;			#Volumetric efficiency
nM = 0.75;			#Mechanical efficiency
m = 10.;			#fuel consumed in lit/h
g = 0.73;			#spcific gravity of fuel
Raf = 18.;			#air-fuel ratio
Np = 600.;			#piston speed in m/min
imep = 5.;			#Indicated mean efective pressure in bar
R = 281.;			#Universal gas constant in J/kg-K
T = 288.;			#Standard temperature in K
P = 1.013;			#Standard pressure in bar


# Calculations
L = Np/(2*N);			#Piston stroke in m
mf = m*g;			#mass of fuel in kg/h
ma = mf*Raf;			#mass of air required in kg/h
Va = (ma*R*T)/(P*60*(10**5));			#volume of air required in (m**3)/min
D = math.sqrt((2*Va)/(nV*L*N*3.1415));			#Diameter in m
IP = (2*imep*100*L*3.1415*(D**2)*N)/(4.*60);			#Indicated Power in kW
BP = nV*IP;			#Brake Power in kW

# Results
print 'Piston Stroke is %3.3f m  \
\nBore diameter is %3.4f m  \
\nBrake power is %3.1f kW'%(L,D,BP)

# rounding off error
Piston Stroke is 0.075 m  
Bore diameter is 0.0694 m  
Brake power is 14.6 kW