Chapter 6 : Heat Engines

Example 6.1 pg : 23

In [2]:
# Variables
m = 1;        #in kg
R = 0.287;    #Universal Gas Consmath.tant
r = 7;        #Compression Ratio
P1 = 1;       #in bar
T1 = 24+273;  #in K
T3 = 2000;    #in K
G = 1.4;      #Gamma

# Calculations and Results
ASE = (1-(1./(r)**(G-1)))*100;
print 'Air standand Efficiency is %3.1f Percent'%(ASE);

P2 = P1*(r)**G;
print 'Pressure at end of Compression is %3.2f Bar'%(P2);

T2 = T1*((r)**(G-1));
print 'Temperature at end of Compression is %3.2f K'%(T2);

Cv = 0.718;
Q = Cv*(T3-T2);
print 'Heat Supplied is %3.2f kJ/kg'%(Q);

W = ASE*Q/100;
V1 = (m*R*T1)/(P1*100);
V2 = V1/r;
V = V1-V2;
Pm = W/V;
print 'Mean Effective Pressure is %3.2f kPa'%(Pm);

Air standand Efficiency is 54.1 Percent
Pressure at end of Compression is 15.25 Bar
Temperature at end of Compression is 646.84 K
Heat Supplied is 971.57 kJ/kg
Mean Effective Pressure is 719.21 kPa

Example 6.2 pg : 24

In [3]:
# Variables
T1 = 323.;         #in K
T2 = 673.;         #in K
G = 1.4;

# Calculations and Results
r_G = T2/T1;
r = (r_G)**(1./(G-1));
print 'Compression Ratio is %2.2f '%(r);


Eff = 100*(1-(1./(r**(G-1))));
print 'Air standand Efficiency is %2.0f Percent '%(Eff);

Compression Ratio is 6.27 
Air standand Efficiency is 52 Percent

Example 6.3 pg : 25

In [4]:
# Variables
P1 = 97.;          #in kPa
T1 = 323.;         #in K
r = 5.;            #Compression Ratio
Q = 930.;          #in kJ/kg
G = 1.4;
Cv = 0.718;

# Calculations and Results
T2 = T1*(r**(G-1));
T3 = (Q/Cv)+T2;
print 'Maximum Temperature Attained is %2.2f K'%(T3);


Eff = 100*(1-(1./(r)**(G-1)));
print 'Thermal Efficiency of cycle is %2.1f Percent'%(Eff);


W = Eff*Q/100;
print 'Work Done is %2.2f kJ/kg'%(W);

Maximum Temperature Attained is 1910.14 K
Thermal Efficiency of cycle is 47.5 Percent
Work Done is 441.47 kJ/kg

Example 6.4 pg : 25

In [5]:
# Variables
T1 = 57.+273;          #in K
T2 = 603.+273;         #in K
T3 = 1950.+273;        #in K
T4 = 870.+273;         #in K
G = 1.4;
P1 = 1.;               #in bar
Cp = 1.005;
Cv = 0.718;

# Calculations and Results
P2 = P1*((T2/T1)**((G)/(G-1)));
print 'Maximum Pressure attained is %2.1f bar'%(P2);


Qs = Cp*(T3-T2);           #Heat Supplied
Qr = Cv*(T4-T1);          #Heat Rejected
Eff = 100*(1-(Qr/Qs));
print 'Efficiency is %2.0f Percent'%(Eff);

Maximum Pressure attained is 30.5 bar
Efficiency is 57 Percent

Example 6.5 pg : 25

In [7]:
# Variables
V2 = 0.2;         #in cm**3
V3 = V2;
Vc = V2;

Vs = 1.2;         #in cm**3
V1 = V2+Vs;
G = 1.4;

# Calculations
r = (V1/V2);
Eff = 100*(1-(1./(r**(G-1))));

# Results
print 'Efficiency of Engine is %2.0f Percent'%(Eff);

Efficiency of Engine is 54 Percent

Example 6.6 pg : 26

In [10]:
# Variables
rc = 14.;          #Adiabatic Compression Ratio
ra = 8.;           #Adiabatic Expansion Ratio
G = 1.4;
Z = rc/ra;        #Cutoff Ratio

# Calculations
#It is a diesel Cycle
Eff = 100*(1-((1./(rc**(G-1)))*(1./G)*((Z**G)-1)/(Z-1)));

# Results
print 'Efficiency is %2.1f Percent'%(Eff);

Efficiency is 60.6 Percent

Example 6.7 pg : 26

In [11]:
# Variables
Eff = 0.6;        #Efficiency
T2 = 283;         #in K

# Calculations
T1 = T2/(1-Eff);

# Results
print 'Initial Temperature is %2.1f K'%(T1);

Initial Temperature is 707.5 K

Example 6.8 pg : 26

In [13]:
# Variables
D = 10;       #Diameter in cm
L = 15;       #Length in cm
Vs = (22./7)*(1./4)*D*D*L;      #in cm**3
Vc = 250;     #in cm**3
V2 = Vc;
V1 = Vs+Vc;
r = V1/V2;
G = 1.4;

# Calculations
Eff = 100*(1-(1./(r**(G-1))));

# Results
print 'Efficiency is %2.1f Percent'%(Eff);

Efficiency is 50.2 Percent

Example 6.9 pg : 27

In [15]:
import math 

# Variables
T3 = 15+273;      #in K
T4 = T3;
P3 = 1.1;     #in bar
P4 = 4;       #in bar
P1 = 12;      #in bar
N = 150;      #in rpm
G = 1.4;

# Calculations and Results
T1 = T4*((P1/P4)**((G-1)/G));
Eff = 100*(1-(T4/T1));
print 'The Efficiency is %3.2f Percent'%(Eff);

r = P4/P3;
R = 0.287;
m = 1;

W = m*R*(T1-T3)*(math.log(r));
P = W*(N/60);
print 'The Power is %3.1f kW'%(P);

The Efficiency is 26.94 Percent
The Power is 78.7 kW

Example 6.10 pg : 27

In [16]:
# Variables
T3 = 1350+273;        #in K
T1 = 30+273;          #in K
Qs = 750;         #in kJ/kg
Cv = 0.718;
G = 1.4;

# Calculations and Results
#For Process 2-3
T2 = T3-(Qs/Cv);
r = (T2/T1)**(1./(G-1));
print 'The compression Ratio is %3.2f '%(r);


Eff = 100*(1-(1./(r**(G-1))));
print 'The Efficiency is %3.1f Percent'%(Eff);


W = Eff*Qs/100;
print 'The Work Output is %3.0f kJ/kg'%(W);


P21 = (r**G);
P32 = T3/T2;
P31 = P21*P32;
print 'Ratio of maximum to minimum pressure is %3.2f '%(P31);

The compression Ratio is 5.04 
The Efficiency is 47.6 Percent
The Work Output is 357 kJ/kg
Ratio of maximum to minimum pressure is 26.97

Example 6.11 pg : 27

In [17]:
# Variables
Vs = 500;         #in cm**3
Vc = 55;          #in cm**3
T1 = 30+273;      #in K
P1 = 1;           #in bar
T3 = 1450+273;        #in K
G = 1.4;
R = 0.287;
Cv = 0.718;

# Calculations and Results
r = (Vs+Vc)/Vc;
Eff = 100*(1-(1./(r**(G-1))));
print 'The standand air Efficiency is %3.2f Percent'%(Eff);


T2 = T1*(r**(G-1));
Qs = Cv*(T3-T2);
W = Eff*Qs;

V1 = Vc+Vs;
m = (P1*100*V1*(10**-6))/(R*T1);
Pm = (W*m)/(100*(Vs*(10**-6)));
print 'The Mean Effective Pressure is %3.1f kPa'%(Pm);

The standand air Efficiency is 60.19 Percent
The Mean Effective Pressure is 530.6 kPa

Example 6.12 pg : 28

In [18]:
# Variables
r = 6;        #Compression Ratio
T1 = 20+273;  #in K
G = 1.4;
Cv = 0.718;
Qs = 1900;

# Calculations and Results
Eff = 100*(1-(1./(r**(G-1))));
print 'The Efficiency is %3.2f Percent'%(Eff);


T2 = T1*(r**(G-1));
print 'The value of T2 is %3.0f K'%(T2);


T3 = (Qs/Cv)+T2;
print 'The value of T3 is %3.0f K'%(T3);


T4 = T3/(r**(G-1));
print 'The value of T4 is %3.0f K'%(T4);


W = Qs*Eff/100;
print 'The Work Output is %3.0f kJ/kg'%(W);

The Efficiency is 51.16 Percent
The value of T2 is 600 K
The value of T3 is 3246 K
The value of T4 is 1585 K
The Work Output is 972 kJ/kg

Example 6.13 pg : 28

In [19]:
# Variables
D = 0.1;      #Diameter
L = 0.12;     #Length
V = (22./7)*(1./4)*D*D*L;
T1 = 19+273;
r = 6.5;      #Compression ratio
P1 = 1;       #in bar
G = 1.4;      #Gamma
Vs = 9.425*(10**-4);

# Calculations and Results
Vc = Vs/(r-1);
V1 = Vc+Vs;
print 'V1 =  %3.5f m**3'%(V1);


V2 = Vc;
V3 = Vc;
P2 = P1*(r**G);
print 'P2 =  %3.1f bar'%(P2);


T2 = T1*(r**(G-1));
print 'T2 =  %3.1f K'%(T2);


#For process 2-3
Qs = 1900;
Cv = 0.718;
T3 = (Qs/Cv)+T2;
print 'T3 =  %3.1f K'%(T3);


P3 = P2*(T3/T2);
print 'P3 =  %3.1f bar'%(P3);


#For process 4-1
V4 = V1;
P4 = P3*((V3/V4)**G);
print 'P4 =  %3.1f bar'%(P4);


T4 = T1*(P4/P1);
print 'T4 =  %3.1f K'%(T4);


Eff = 100*(1-(1./(r**(G-1))));
print 'Efficiency =  %3.1f Percent'%(Eff);


R = 0.287;
m = (P1*100*V1)/(R*T1);
Pm = (Eff*Qs*m)/(10000*Vs);
print 'Mean Effective Pressure =  %3.1f bar'%(Pm);

V1 =  0.00111 m**3
P2 =  13.7 bar
T2 =  617.4 K
T3 =  3263.6 K
P3 =  72.6 bar
P4 =  5.3 bar
T4 =  1543.6 K
Efficiency =  52.7 Percent
Mean Effective Pressure =  14.1 bar

Example 6.14 pg : 29

In [20]:
# Variables
P1 = 1.;       #in bar
T1 = 20.+273;      #in K
P2 = 39.;      #in bar
P3 = P2;
T3 = 1100.+273;        #in K
G = 1.4;

# Calculations
#For reversible Adiabatic Process 1-2
T2 = T1*((P2/P1)**((G-1)/G));
r = (P2/P1)**(1./G);

Z = T3/T2;

Eff = 100*(1-((1./(r**(G-1)))*(1./G)*((Z**G)-1)/(Z-1)));

# Results
print 'Efficiency: %2.2f Percent'%(Eff);

Efficiency: 60.83 Percent

Example 6.15 pg : 30

In [21]:
# Variables
r = 16.;       #Compression Ratio
D = 0.21;     #Diameter
L = 0.3;      #Length
P1 = 1;       #in bar
G = 1.4;
T1 = 17+273;  #in K
Z = (0.1*(r-1)+1)

# Calculations and Results
Vs = (22./7)*(1./4)*D*D*L;
Vc = Vs/15;
V2 = Vc;
print 'Vc =  V2 =  %2.6f m**3'%(Vc);

V1 = Vc+Vs;
print 'V1 =  %2.4f m**3'%(V1);

V3 = (0.1*(Vs))+(V2);
print 'V3 =  %2.4f m**3'%(V3);


#For Process 1-2
P2 = r**G;
print 'P2 =  %2.1f bar'%(P2);


T2 = T1*(r**(G-1));
print 'T2 =  %2.1f K'%(T2);


T3 = Z*T2;
print 'T3 =  %2.1f K'%(T3);


P3 = P2;
P4 = P3*((V3/V1)**G);
print 'P4 =  %2.1f bar'%(P4);


T4 = T3*((V3/V1)**(G-1));
print 'T4 =  %2.1f K'%(T4);


Cv = 0.718;
Cp = 1.005;

Eff = 100*(1-((Cv*(T4-T1))/(Cp*(T3-T2))));
print 'Efficiency: %2.1f Percent'%(Eff);


R = 0.287;
m = (P1*100*V1)/(R*T1);
Pm = (m*((Cp*(T3-T2))-(Cv*(T4-T1))))/(Vs);
print 'Mean Effective Pressure =  %2.1f kPa'%(Pm);


N = 300;          #Cycles per minute
W = 10.41;
EP = W*(N/60);
print 'Engine Power =  %2.2f kW'%(EP);

Vc =  V2 =  0.000693 m**3
V1 =  0.0111 m**3
V3 =  0.0017 m**3
P2 =  48.5 bar
T2 =  879.1 K
T3 =  2197.8 K
P4 =  3.6 bar
T4 =  1046.0 K
Efficiency: 59.0 Percent
Mean Effective Pressure =  1002.8 kPa
Engine Power =  52.05 kW

Example 6.16 pg : 30

In [23]:
# Variables
r = 19.;       #Compression Ratio
P1 = 1.;       #in bar
T1 = 17.+273;  #in K
Qs = 730.;     #in kJ/cycle
G = 1.4;

# Calculations and Results
#For process 1-2
m = 1;        #in kg
R = 0.287;    #Universal Gas Consmath.tant
V1 = (m*R*T1)/(P1*100);
print 'V1 =  %2.4f m**3/kg'%(V1);


V2 = V1/r;
print 'V2 =  %2.4f m**3/kg'%(V2);


P2 = P1*(r**G);
print 'P2 =  %2.1f bar'%(P2);


T2 = T1*(r**(G-1));
print 'T2 =  %2.1f K'%(T2);


#For Process 2-3
Cv = 0.718;
T3 = (Qs/(Cv*m))+T2;
print 'T3 =  %2.1f K'%(T3);


P3 = P2;
print 'P3 =  %2.1f bar'%(P3);


#As pressure is consmath.tant
V3 = (T3/T2)*V2;
print 'V3 =  %2.4f m**3/kg'%(V3);


#For process 3-4
V4 = V1;
T4 = T3*((V3/V4)**(G-1));
print 'T4 =  %2.1f K'%(T4);


P4 = P3*((V3/V4)**G);
print 'P4 =  %2.2f bar'%(P4);


Cp = 1.005;

W = ((Cp)*(T3-T2))-((Cv*(T4-T1)));
print 'Work Done =  %2.1f kJ/kg'%(W);


Eff = 100*(W/(Cp*(T3-T2)));
print 'Efficiency =  %2.2f Percent'%(Eff);


Pm = W/(V1-V2);
print 'Mean Effective Pressure =  %2.2f kPa'%(Pm);

V1 =  0.8323 m**3/kg
V2 =  0.0438 m**3/kg
P2 =  61.7 bar
T2 =  941.7 K
T3 =  1958.4 K
P3 =  61.7 bar
V3 =  0.0911 m**3/kg
T4 =  808.3 K
P4 =  2.79 bar
Work Done =  649.6 kJ/kg
Efficiency =  63.58 Percent
Mean Effective Pressure =  823.88 kPa

Example 6.17 pg : 31

In [24]:
# Variables
r = 19.;       #Compression Ratio
Re = 9.1;     #Expansion Ratio
Z = r/Re;
G = 1.4;

# Calculations
Eff = 100*(1-((1./(r**(G-1)))*(1./G)*((Z**G)-1)/(Z-1)));

# Results
print 'Efficiency: %2.2f Percent'%(Eff);

Efficiency: 63.55 Percent

Example 6.18 pg : 31

In [26]:
import math 

# Variables
D = 16.;       #in cm
L = 24.;       #in cm
Vc = 340.;
V2 = Vc;
G = 1.4;

# Calculations
Vs = (22./7)*(1./4)*D*D*L;
V1 = Vs+Vc;
r = V1/V2;

#Cut-off is 6% of the stroke
Co1 = 0.06;

V3 = (Co1*(V1-V2))+V2;
Z = V3/V2;
x = (Z**G)-1;
y = (r**(G-1))*(G)*(Z-1);
Eff1 = 100*(1-((x)/(y)));



#Cut-off is 10% of the stroke
Co2 = 0.10;

V3 = (Co2*(V1-V2))+V2;
Z = V3/V2;
x = (Z**G)-1;
y = (r**(G-1))*(G)*(Z-1);
Eff2 = 100*(1-((x)/(y)));

Loss = ((Eff1-Eff2)*100)/Eff1;

# Results
print 'Loss: %2.2f Percent'%(r);

Loss: 15.20 Percent

Example 6.20 pg : 32

In [28]:
import math 

# Variables
T3 = 1000.+273;        #in K
T1 = 27.+273;          #in K
G = 1.25;

# Calculations and Results
r = (T3/T1)**G;
print 'Compression Ratio: %2.1f '%(r);


T2 = math.sqrt(T1*T3);
T4 = T2;
print 'T2 = T4 =  %2.0f K'%(T2);


Cv = 0.718;
W = Cv*((math.sqrt(T3))-(math.sqrt(T1)))**2;
print 'Maximum Work Done: %2.0f kJ/kg'%(W);

Compression Ratio: 6.1 
T2 = T4 =  618 K
Maximum Work Done: 242 kJ/kg

Example 6.21 pg : 32

In [30]:
# Variables
r = 6;        #Compression Ratio
G = 1.4;

# Calculations and Results
Eff = 100*(1-(1./(r**(G-1))));
print 'Efficiency: %2.2f Percent'%(Eff);


m = 1.;            #in kg
R = 0.287;        #Universal Gas Consmath.tant
T1 = 27.+273;      #in K
P1 = 1.;        #in bar

V1 = (m*R*T1)/(P1*100);
V2 = V1/r;
Vc = V2;
Vs = V1-Vc;

T2 = T1*(r**(G-1));
Cv = 0.718;
Qs = 1046;
T3 = (Qs/Cv)+T2;
T4 = T3/(r**(G-1));
W = Qs-(Cv*(T4-T1));
Pm = W/Vs;
print 'Effective Mean Pressure: %2.2f kPa'%(Pm);

Efficiency: 51.16 Percent
Effective Mean Pressure: 745.89 kPa

Example 6.22 pg : 33

In [31]:
# Variables
T1 = 87.+273;      #in K
r = 14.;       #Compression Ratio
T3 = 1795.+273;        #in K
T4 = 677.+273;     #in K
G = 1.4;

# Calculations and Results
T2 = T1*(r**(G-1));
print 'T2 =  %2.1f K'%(T2);


Cp = 1.005;
Cv = 0.718;
W = (Cp*(T3-T2))-(Cv*(T4-T1))
Qs = Cp*(T3-T2);
Eff = (W*100)/Qs;
print 'Efficiency: %2.1f Percent'%(Eff);

T2 =  1034.6 K
Efficiency: 59.2 Percent

Example 6.23 pg : 33

In [33]:
# Variables
r = 16.;       #Compression Ratio
P1 = 1.;       #in bar
T1 = 20.+273;      #in K
T3 = 1431.+273;        #in K
G = 1.4;
T2 = T1*(r**(G-1))
m = 1;
R = 0.287;
V1 = (m*R*T1)/(P1*100);
V2 = V1/r;

# Calculations and Results
#For Constant Pressure Process 2-3
V3 = V2*(T3/T2);
Z = V3/V2;
Eff = 100*(1-((1./(r**(G-1)))*(1./G)*((Z**G)-1)/(Z-1)));
print 'Efficiency is %2.1f Percent'%(Eff);


Cp = 1.005;
Qs = Cp*(T3-T2);
W = Qs*Eff/100;
Vs = V1-V2;
Pm = W/Vs;
print 'Effective Mean Pressure %2.1f kPa'%(Pm);

Efficiency is 61.8 Percent
Effective Mean Pressure 642.5 kPa

Example 6.24 pg : 34

In [35]:
# Variables
r = 8.;
T1 = 310.;     #in K
T3 = 1600.;        #in K
G = 1.4;
Cv = 0.717;

# Calculations and Results
#For process 1-2
T2 = T1*(r**(G-1));

#Now Heat Supplied
Qs = Cv*(T3-T2);
print 'Heat Supplied =  %2.1f kJ/kg'%(Qs);


#Efficiency of Cycle
Eff = 100*(1-(1./(r**(G-1))))
print 'Efficiency is %2.1f Percent'%(Eff);

Heat Supplied =  636.6 kJ/kg
Efficiency is 56.5 Percent

Example 6.25 pg : 34

In [36]:
# Variables
r = 15.;       #Compression Ratio
P1 = 100.;     #in kPa
T1 = 27.+273;
Cp = 1.006;
Cv = 0.717;
G = 1.4;

# Calculations and Results
#Cut off takes place at 12% of Working Stroke
T2 = T1*(r**(G-1));
print 'T2 =  %2.1f K'%(T2);


P2 = P1*(r**G);
print 'P2 =  %2.1f kPa'%(P2);


Z = (0.12*(r-1))+1;
Eff = 100*(1-((1./(r**(G-1)))*(1./G)*((Z**G)-1)/(Z-1)));
print 'Efficiency is %2.1f Percent'%(Eff);

T2 =  886.3 K
P2 =  4431.3 kPa
Efficiency is 57.2 Percent

Example 6.26 pg : 35

In [39]:
# Variables
T1 = 288.;     #in K
T3 = 1673.;        #in K
Qs = 800.;     #in kJ/kg
G = 1.4;
Cv = 0.718;
R = 0.287;
P1 = 1.;

# Calculations and Results
Cp = Cv*G;
T2 = T3-(Qs/Cp);

x = T2/T1;
r = x**(1./(G-1));
print 'Compression Ratio %2.1f '%(r);


Eff = 100*(1-(1./(r**(G-1))))
print 'Efficiency is %2.1f Percent'%(Eff);


P3 = r*T3*P1/T1;
print 'P3 =  %2.1f bar'%(P3);

Compression Ratio 16.2 
Efficiency is 67.2 Percent
P3 =  94.0 bar

Example 6.27 pg : 35

In [40]:
# Variables
T2 = 293;     #in K
Eff = 0.7;

# Calculations
T1 = T2/(1-Eff);

# Results
print 'T1 =  %2.1f K'%(T1);

T1 =  976.7 K

Example 6.28 pg : 36

In [8]:
# Variables
T1 = 330.;     #in K
T2 = 876.;     #in K
T3 = 2223.;        #in K
T4 = 1143.;        #in K
P1 = 1.;       #in bar
G = 1.4;

# Calculations and Results
Cv = 0.718;
Cp = 1.005;
Eff = 100*(1-((Cv*(T4-T1))/(Cp*(T3-T2))));
print 'Efficiency is %2.1f Percent'%(Eff);


#For Process 1-2
P2 = P1*((T2/T1)**(G/(G-1)));
print 'Maximum Pressure %2.2f bar'%(P2);

Efficiency is 56.9 Percent
Maximum Pressure 30.48 bar

Example 6.29 pg : 36

In [2]:
# Variables
T1 = 25.+273;      #in K
T3 = 1500.+273;        #in K
Qa = 900.;     #in kJ/kg
Cv = 0.718;
G = 1.4;

# Calculations and Results
T2 = T3-(Qa/Cv);
r = (T2/T1)**(1./(G-1));
print 'Compression Ratio is %2.1f '%(r);


Eff = 100*(1-(1./(r**(G-1))));
print 'Efficiency is %2.1f Percent'%(Eff);


Px = r**G;     #Max Pressure
Py = T3/T2;       #1./Min Pressure
P = Px*Py;
print 'Pressure Ratio %2.1f '%(P);

Compression Ratio is 4.0 
Efficiency is 42.6 Percent
Pressure Ratio 23.9

Example 6.30 pg : 37

In [7]:
# Variables
P1 = 1.;       #in bar
T1 = 15.+273;      #in K
P2 = 15.;      #in bar
P3 = 40.;      #in bar
G = 1.4;
Cv = 0.718;

# Calculations and Results
r = (P2/P1)**(1./G);
print 'Compression Ratio is %2.1f '%(r);


Eff = 100*(1-(1./r**(G-1)))
print 'Efficiency is %2.1f Percent'%(Eff);

T2 = T1*(r**(G-1));
T3 = T2*(P3/P2);
T4 = T3/(r**(G-1));
W = Cv*(T3-T2+(T1-T4))

R = 0.287;
V1 = (R*T1)/P1;
V2 = V1/r;

Pm = W/(V1-V2);
print 'Mean Effective Pressure %2.4f bar'%(Pm);

Compression Ratio is 6.9 
Efficiency is 53.9 Percent
Mean Effective Pressure 5.6920 bar

Example 6.31 pg : 37

In [6]:
# Variables
P2 = 44.;      #in bar
P3 = P2;
T3 = 1600.+273;        #in K
P1 = 1.;       #in bar
T1 = 27.+273;      #in K
G = 1.4;

# Calculations
T2 = T1*((P2/P1)**((G-1)/G))
R = 0.287;

V1 = (R*T1)/(P1*100);


r = (P2/P1)**(1./G);
Z = T3/T2;
Eff = 100*(1-((1./(r**(G-1)))*(1./G)*((Z**G)-1)/(Z-1)));

# Results
print 'Efficiency is %2.2f Percent'%(Eff);

Efficiency is 59.70 Percent

Example 6.32 pg : 38

In [5]:
# Variables
r = 16.;       #Compression Ratio
P1 = 1.;       #in bar
T1 = 20.+273;
T3 = 1431.+273;        #in K
G = 1.4;

# Calculations and Results
T2 = T1*(r**(G-1));
Z = T3/T2;
T4 = (Z**G)*T1;
Eff = 100*(1-((T4-T1)/(G*(T3-T2))))
print 'Efficiency is %2.1f Percent'%(Eff);


Cp = 1.005;
Qs = Cp*(T3-T2);
W = Eff*(Qs/100);
R = 0.287;
V1 = (R*T1)/(P1*100);
V2 = V1/r;
V = V1-V2;

Pm = W/(V);
print 'Mean Effective Pressure %2.1f kPa'%(Pm);

Efficiency is 61.8 Percent
Mean Effective Pressure 642.5 kPa

Example 6.33 pg : 41

In [46]:
# Variables
P1 = 1.;       #in bar
T1 = 15.+273;      #in K
P2 = 15.;      #in bar
P3 = 40.;      #in bar
G = 1.4;

# Calculations and Results
r = (P2/P1)**(1./G);
Eff = 100*(1-(1./(r**(G-1))))
print 'Efficiency is %2.1f Percent'%(Eff);


T2 = T1*((P2/P1)**((G-1)/G))
T3 = T2*(P3/P2);
Cv = 0.718;

Qs = Cv*(T3-T2);
W = Eff*Qs;
R = 0.287;

V1 = (R*T1)/(P1*100);
V2 = V1/r;

Vs = V1-V2;
Pm = W/(Vs*100);

print 'Mean Effective Pressure is %2.1f kPa'%(Pm);

Efficiency is 53.9 Percent
Mean Effective Pressure is 569.2 kPa
In [ ]: