Chapter 7 : Internal combution Engines

Example 7.1 pg : 15

In [1]:
# Variables
Vs = 0.01;      #in m**3
Pm = 600.;     #in kPa
N = 300.;      #in rpm

# Calculations
n = N/2;
IP = (Vs*Pm*n)/60;

# Results
print 'Indicated Power =  %2.0f kW'%(IP);

Indicated Power =  15 kW

Example 7.2 pg : 16

In [8]:
#from sympy import Symbol,solve
#import math
# Variables
n = 6.;        #Number of Cylinders
IP = 90.;      #Indicated Power in kW
Eff = 0.85;       #Mechanical Efficiency
Pmb = 5.;      #in bar
LD = 1.5;
Pm = Pmb/Eff;
N = 800.;
nx = N/2;

# Calculations and Results
#Length = 1.5*D
#D = Symbol("D")
#eq = 588*math.pi/4*D**2*LD*D*nx*n/60 - 90
#ans = solve(eq,D)
#print ans
D = ((IP*60*4)/(Pm*100*(22./7)*LD*nx*n))**(1./3);
print 'D =  %3.4f mm'%(D*100);

L = D*LD;
print 'L =  %3.4f mm'%(L*100);

# It seems book answer wrong. kindly check.

D =  14.8056 mm
L =  22.2084 mm

Example 7.3 pg : 16

In [3]:
# Variables
BP = 22.;      #Brake Power
Eff = 0.85;       #Mechanical Efficiency
IP = BP/Eff;
mf = 6.5;
CV = 30000.;       #Calorific Value

# Calculations and Results
Ebth = BP/((mf/3600)*CV);
print 'Brake Thermal Eff =  %3.1f Percent'%(Ebth*100);


Eith = IP/((mf/3600)*CV);
print 'Indicated Thermal Eff =  %3.1f Percent'%(Eith*100);


BSFC = mf/BP;
print 'BSFC =  %3.1f kg/kWh'%(BSFC);

Brake Thermal Eff =  40.6 Percent
Indicated Thermal Eff =  47.8 Percent
BSFC =  0.3 kg/kWh

Example 7.4 pg : 17

In [9]:
# Variables
BP = 185.;     #Brake Power
Eff = 0.75;
IP = BP/Eff;
LD = 1.5;
N = 35.;
n = N/2;
nx = 4.;
Pm = 830.;     #in kPa
D = ((IP*4)/(Pm*(22./7)*LD*nx*n))**(1./3);
print 'D =  %3.0f mm'%(D*1000);

L = D*LD;
print 'L =  %3.0f mm'%(L*1000);

D =  153 mm
L =  230 mm

Example 7.5 pg : 17

In [10]:
# Variables
Vc = 5*(10**-4);
D = 0.15;
L = 0.2;
Vs = (22./7)*D*D*L*(1./4);
r = (Vc+Vs)/Vc;
G = 1.4;

# Calculations and Results
Ea = (1-(1./(r**(G-1))));
Eith = 0.3;
Erel = Eith/Ea;
print 'Erel =  %3.2f Percent'%(Erel*100);


Pm = 500.;     #in kPa
n = 1000./2;
IP = (Pm*Vs*n)/60;
print 'IP =  %3.2f kW'%(IP);

Erel =  52.98 Percent
IP =  14.73 kW

Example 7.6 pg : 18

In [11]:
# Variables
Pm = 600.;
A = (22./7)*(1./4)*0.11*0.11*0.14;
n = 1000;

# Calculations
IP = (Pm*A*n)/60;
Em = 0.8;
BP = Em*IP;

# Results
print 'BP =  %3.2f kW'%(BP);

BP =  10.65 kW

Example 7.7 pg : 18

In [13]:
# Variables
r = 6.;
G = 1.4;
Ea = 100*(1-(1./(r**(G-1))));

# Calculations
Ebt = Ea/2;
CV = 41500;
BP = 15.;
Mf = BP/(CV*(Ebt/100));

# Results
print 'Mf =  %3.3f kg/hr'%(Mf*3600);

Mf =  5.086 kg/hr

Example 7.8 pg : 18

In [14]:
# Variables
n = 4.;
DL = 1.2;
BP = 32.;
N = 2500.;
Pm = 9.;
Em = 0.86;
Mf = 9.;
CV = 43000.;

# Calculations and Resultse
IP = BP/Em;
D = ((IP*60*4)/(Pm*100*(22./7)*DL*N*n))**(1./3);
print 'D =  %3.0f mm'%(D*1000);


L = DL*D;
print 'L =  %3.0f mm'%(L*1000);


Ebth = BP/(Mf*CV/3600);
print 'Ebth =  %3.2f Percent'%(Ebth*100);


Eith = Ebth/Em;
print 'Eith =  %3.2f Percent'%(Eith*100);

D =   64 mm
L =   77 mm
Ebth =  29.77 Percent
Eith =  34.61 Percent

Example 7.9 pg : 19

In [15]:
# Variables
Eith = 0.29;
Em = 0.77;
BP = 5.5;
SG = 0.87;
CV = 43000;

# Calculations
Ebth = Em*Eith;
Mf = (BP*3600)/(Ebth*CV);
D = SG*1000;
Mff = (Mf*1000)/D

# Results
print 'Mf =  %3.2f litre/hr'%(Mff);

Mf =  2.37 litre/hr

Example 7.10 pg : 20

In [16]:
# Variables
D = 16.;
L = 19.;
Vc = 700.;
Pm = 5.;
N = 1000.;
Eith = 0.32;

# Calculations and Results
Vs = (22./7)*D*D*L*(1./4);
Vc = 700.;
G = 1.4;
r = (Vs+Vc)/Vc;
Ea = (1-(1./(r**(G-1))));
Er = Eith/Ea;
print 'Relative Efficiency =  %3.2f Percent'%(Er*100);


IP = (Pm*100*Vs*(10**-6)*N)/60;
print 'IP =  %3.2f KW'%(IP);

Relative Efficiency =  60.85 Percent
IP =  31.85 KW

Example 7.11 pg : 20

In [17]:
# Variables
T = 50.;
Vst = 870.;
N = 300.;
Pm = 10.;
n = N/2;

# Calculations
BP = (2*(22./7)*N*T)/(60*1000);
IP = (Pm*100*Vst*(10**-6)*N)/(60*2);
Em = BP/IP;

# Results
print 'Mechanical Efficiency =  %3.2f Percent'%(Em*100);

Mechanical Efficiency =  72.25 Percent

Example 7.12 pg: 21

In [18]:
# Variables
Pm = 7.;
A = (22./7)*(1./4)*((0.15/1.25)**2);
n = 900.;
L = 0.15;
N = 2

# Calculations
IP = (Pm*100*A*L*n*N)/(60*2);

# Results
print 'IP =  %3.2f kW'%(IP);

IP =  17.82 kW

Example 7.13 pg : 21

In [19]:
import math 

# Variables
N = 900.;
D = 0.1;
L = 0.14;
Mf = 2.1;
CV = 42000.;
Pm = 7.5;
Vc = 0.15;
G = 1.4;
A = (22./7)*(1./4)*D*D;

# Calculations and Results
IP = (Pm*100*A*L*N*2)/(60*2);
Eith = (IP*3600)/(Mf*CV);
print 'Eith =  %3.1f Percent'%(Eith*100);


r = (1+0.15)/(0.15);
Ea = 1-(1./(r**(G-1)));
Er = Eith/Ea;
print 'Relative Efficiency =  %3.2f Percent'%(Er*100);

Eith =  50.5 Percent
Relative Efficiency =  90.64 Percent

Example 7.14 pg : 22

In [22]:
import math

# Variables
NOC = 6.;
N = 820.;
n = N/2;
IP = 90.;
LD = 1.4;
Pbm = 5;

# Calculations and Results
Em = 0.79;
BP = IP*Em;
D = ((IP*60*2)/(Pbm*100*(math.pi)*(1./4)*LD*N*NOC))**(1./3);
print 'D =  %3.0f mm'%(D*1000);

L = LD*D;
print 'L =  %3.0f mm'%(L*1000);

# rouding off error.

D =  159 mm
L =  222 mm

Example 7.15 pg : 22

In [23]:
import math 

# Variables
NOC = 4;
N = 2500;
n = N/2;
BP = 200;
LD = 1.2;
Pm = 10;
Em = 0.81;
Mf = 65;
CV = 42000;
IP = BP/Em;

# Calculations and Results
D = ((IP*60*2*4)/(Pm*100*(22./7)*(1.2*(N)*NOC)))**(1./3);
print 'D =  %3.0f mm'%(D*1000);


L = LD*D;
print 'L =  %3.0f mm'%(L*1000);


Eith = (IP*3600)/(Mf*CV);
print 'Eith =  %3.2f Percent'%(Eith*100);


Ebth = Eith*Em;
print 'Ebth =  %3.2f Percent'%(Ebth*100);

D =  146 mm
L =  176 mm
Eith =  32.56 Percent
Ebth =  26.37 Percent

Example 7.16 pg : 23

In [25]:
# Variables
IP = 42.;
FP = 7.;
ES = 1800.;

BP = IP-FP;

# Calculations and Results
Em = BP/IP;
print 'Mechanical Efficiency =  %3.0f Percent'%(Em*100);

BSFC = 0.3;
CV = 43000.;

Ebth = 3600/(BSFC*CV);
print 'Brake Thermal Efficiency =  %3.0f Percent'%(Ebth*100);


Eith = Ebth/Em;
print 'Indicated Thermal Efficiency =  %3.2f Percent'%(Eith*100);

Mechanical Efficiency =   83 Percent
Brake Thermal Efficiency =   28 Percent
Indicated Thermal Efficiency =  33.49 Percent

Example 7.17 pg : 25

In [26]:
# Variables
D = 0.3;
L = 0.45;
N = 300.;
Pimep = 6.;
F = 1.5;
Reff = (180+4)/2;

# Calculations and Results
IP = (Pimep*100*L*(22./7)*(1./4)*(D*D)*N)/(2*60);
print 'Indicated Power =  %3.2f kW'%(IP);


BP = (2*(22./7)*N*F*Reff)/6000;
print 'Brake Power =  %3.2f kW'%(BP);


Em = BP/IP;
print 'Mechanical Efficiency =  %3.2f Percent'%(Em*100);

Indicated Power =  47.73 kW
Brake Power =  43.37 kW
Mechanical Efficiency =  90.86 Percent

Example 7.18 pg : 26

In [27]:
# Variables
D = 0.27;
L = 0.38;
Pmep = 6.;
N = 250.;
F = 1000.;
Reff = 0.75;
Mf = 10.;
CV = 44400.;

# Calculations and Results
BP = (2*(22./7)*N*(F*Reff))/60;
print 'Brake Power =  %3.2f kW'%(BP/1000);


A = (22./7)*(1./4)*(D*D);
IP = (Pmep*100*L*A*N)/(2*60);
print 'Indicated Power =  %3.2f kW'%(IP);


Em = BP/(IP*1000);
print 'Mechanical Efficiency =  %3.2f Percent'%(Em*100);


Eith = (IP*3600)/(Mf*CV);
print 'Indicated Thermal Power =  %3.2f Percent'%(Eith*100);

Brake Power =  19.64 kW
Indicated Power =  27.21 kW
Mechanical Efficiency =  72.20 Percent
Indicated Thermal Power =  22.06 Percent

Example 7.19 pg : 27

In [29]:
# Variables
NOC = 6.;
IP = 89.5;
N = 800.;
LD = 1.25;
Em = 0.8;
Pbemp = 5.;
Em = 0.8;
Pimep = Pbemp/0.8;

# Calculations
D3 = (IP*2*60*4)/(Pimep*100*LD*(22./7)*N*NOC);
D = D3**(1./3);
L = LD*D;

# Results
print 'L =  %3.1f mm'%(L*1000);
print 'D =  %3.0f mm'%(D*1000);

L =  192.4 mm
D =  154 mm

Example 7.20 pg: 28

In [30]:
# Variables
D = 0.25;
L = 0.4;
Pm = 6.5;
N = 250;
W = 1080;
Ddrum = 1.5;
Mf = 10;
CV = 44300;

# Calculations and Results
A = (22./7)*(1./4)*D*D;
IP = (Pm*100*A*L*N)/(60*2);
print 'Indicated Power =  %3.2f kW'%(IP);


Reff = Ddrum/2;
W = 1.08;

BP = (2*(22./7)*N*W*Reff)/60;
print 'Brake Power =  %3.2f kW'%(BP);


Em = BP/IP;
Eith = (IP*3600)/(Mf*CV);
print 'Em =  %3.2f Percent'%(Em*100);

print 'Eith =  %3.2f Percent'%(Eith*100);

Indicated Power =  26.60 kW
Brake Power =  21.21 kW
Em =  79.75 Percent
Eith =  21.62 Percent

Example 7.21 pg : 29

In [31]:
# Variables
W = 50;
S = 7;
D = 1.25;
N = 450;
Mf = 4;
CV = 43000;
Em = 0.7;
Reff = 9.81*(D/2);

# Calculations and Results
BP = (2*(22./7)*N*(W-S)*Reff)/(60*1000);
Ebth = (BP*3600)/(Mf*CV);
print 'Ebth =  %3.2f Percent'%(Ebth*100);


Eith = Ebth/Em;
print 'Eith =  %3.2f Percent'%(Eith*100);

Ebth =  26.01 Percent
Eith =  37.16 Percent

Example 7.22 pg : 29

In [32]:
# Variables
T = 640;
D = 0.21;
N = 350;
L = 0.28;
Pm = 5.6;
Mf = 8.16;
CV = 42705;

# Calculations and Results
BP = (2*(22./7)*N*T)/60000;
print 'Brake Power =  %3.2f kW'%(BP/1000);


A = (22./7)*(1./4)*D*D;
IP = (Pm*100*A*L*N)/60;

Em = BP/IP;
print 'Em =  %3.2f Percent'%(Em*100);


Eith = (IP*3600)/(Mf*CV);
print 'Eith =  %3.2f Percent'%(Eith*100);


Ebth = (BP*3600)/(Mf*CV);
print 'Ebth =  %3.2f Percent'%(Ebth*100);


BSFC = Mf/BP;
print 'BSFC =  %3.2f kg/kWh'%(BSFC);

Brake Power =  0.02 kW
Em =  74.04 Percent
Eith =  32.74 Percent
Ebth =  24.24 Percent
BSFC =  0.35 kg/kWh

Example 7.23 pg : 30

In [33]:
# Variables
IP = 37.;
FP = 6.;
BSFC = 0.28;
CV = 44300.;

# Calculations and Results
BP = IP-FP;
Em = (IP-FP)/IP;
print 'Em =  %3.2f Percent'%(Em*100);


Mf = BSFC*BP;
Ebth = (BP*3600)/(Mf*CV);
print 'Ebth =  %3.2f Percent'%(Ebth*100);


Eith = Ebth/Em;
print 'Eith =  %3.2f Percent'%(Eith*100);

Em =  83.78 Percent
Ebth =  29.02 Percent
Eith =  34.64 Percent

Example 7.24 pg : 31

In [34]:
# Variables
D = 0.1;
L = 0.125;
Pm = 2.6;
W = 60;
S = 19;
Reff = 0.4;
r = 6;
Mf = 1;
CV = 42000;
N = 2000;


# Calculations and Results
A = (22./7)*(1./4)*D*D;
IP = (Pm*100*A*L*N)/(60*2);
print 'indicated Power =  %3.2f kW'%(IP);


BP = (2*(22./7)*N*(W-S)*Reff)/60000;
print 'Brake Power =  %3.2f kW'%(BP);


Em = BP/IP;
print 'Em =  %3.2f Percent'%(Em*100);


Ebth = (BP*3600)/(Mf*CV);
print 'Ebth =  %3.2f Percent'%(Ebth*100);


Eith = Ebth/Em;
print 'Eith =  %3.2f Percent'%(Eith*100);


G = 1.4;
Ea = 1-(1./(r**(G-1)));
print 'Ea =  %3.2f Percent'%(Ea*100);


Er = Ebth/Ea;
print 'Er =  %3.2f Percent'%(Er*100);

indicated Power =  4.26 kW
Brake Power =  3.44 kW
Em =  80.74 Percent
Ebth =  29.45 Percent
Eith =  36.48 Percent
Ea =  51.16 Percent
Er =  57.57 Percent

Example 7.25 pg : 32

In [35]:
# Variables
IP = 30.;
N = 2500;
Pm = 800;
Em = 0.8;
LD = 1.5;
Ebth = 0.28;
CV = 44000;

# Calculations and Results
BP = IP*Em;
print 'Brake Power =  %3.2f kW'%(BP);


Mf = (BP/(Ebth*CV));
print 'Mass Flow Rate =  %3.2f kg/hr'%(Mf*3600);

Brake Power =  24.00 kW
Mass Flow Rate =  7.01 kg/hr