Chapter 8: Engine Cycles

Example 8.1, page no. 154

In [17]:
#initialization
ratio = 7.0
Q = 300.0                       #B/lbm
T1 = 60+460.0                   #R
P1 = 14.7                       #lb/in^2
cv = 0.1715                     #B/lvm F
g = 1.4

#calculation
Tratio = (ratio)**(g-1)
T2 = Tratio*T1
T3 = T2+Q/cv
eta = round(1- 1/Tratio,2)
WbyJ = eta*Q
print WbyJ*778
W = 778*WbyJ

#result
print "Final temperature  =  %d R" %T3
print "Thermal efficiency  =  %.3f" %eta
print "Work done  =  %d ft-lb/lbm" %W
#difference in answer due to internal rounding off in Python

126036.0
Final temperature  =  2881 R
Thermal efficiency  =  0.540
Work done  =  126036 ft-lb/lbm

Example 8.2, page no. 157

In [2]:
import math

#initialization
cydia = 3.0                     #in
crdia = 5.0                     #in
ratio = 7.0
rpm = 3000.0                    #rpm
hp = 50.0                       #hp
w = 24.2                        #lbm
Q = 18000.0                     #B/lbm
P1 = 14.7                       #lb/in^2
T1 = 60+460.0                   #R
g = 1.4
cv = 0.1715

#calculation
eta = hp*550*3600/(778*w*Q)
vol = math.pi*(cydia/12)**2 *(crdia/12)*6/4
vdot = vol*rpm/(60*2)
v1 = 53.3*T1/(144*P1)
wdot = vdot/v1
Qdot = w*Q/3600
Qdash = Qdot/wdot
T2 = T1*(ratio)**(g-1)
T3 = T2+Qdash/cv
eta2 = 1- 1/(ratio)**(g-1)
WbyJ = eta2*Qdot
Wdot = WbyJ*778/550.0

#result

print "Part a"
print "Thermal efficiency  =  %.3f " %eta

print "part b"
print "Temperature at the end of compression  =  %d R" %T2
print "Power developed  =  %.1f hp" %Wdot

Part a
Thermal efficiency  =  0.292 
part b
Temperature at the end of compression  =  1132 R
Power developed  =  92.6 hp

Example 8.3, page no. 161

In [20]:
#initialization
Pi = 14.0                       #lb/in^2
T1 = 70+460.0                   #F
ratio = 13.0
T3 = 2500+460.0                 #F
cv = 0.171
cp = 0.23
R = 53.3
g = 1.4

#calculation
T2 = T1*(ratio)**(g-1)
v3ratio = T3/T2
cutoff =  (v3ratio-1)/(ratio-1)
v1ratio = ratio/v3ratio
T4 = T3*(1/v1ratio)**(g-1)
eta = 1.0- cv*(T4-T1)/(T3-T2)/cp
percent = eta*100

#result
print "cut off ratio  =  %.4f" %cutoff
print "T end expansion  =  %d R" %T4
print "Thermal efficiency  =  %.1f" %percent, "%"
#difference in % due to internal rounding off in Python

0.563104145624
cut off ratio  =  0.0835
T end expansion  =  1400 R
Thermal efficiency  =  56.3 %

Example 8.4, page no. 167

In [5]:
#initialization
Pratio = 6.0
P = 14.7                        #lb/in^2
Tt1 = 60+460.0                  #R
Tt3 = 1600+460.0                #R
w = 60.0                        #lb/sec
cp = 0.24                       #B/lbm F
g = 1.4
R = 53.3                        #ft-lb/lbm R

#calculation
Tt2 = Tt1*(Pratio)**((g-1)/g)
Tratio = Tt2/Tt1
Q = cp*(Tt3-Tt2)
eta = 1- 1/Tratio
W = eta*778*Q
Wdot = w*W/550.0

#result
print "Thermal efficiency  =  %.3f" %eta
print "Horsepower output  =  %d hp" %Wdot

Thermal efficiency  =  0.401
Horsepower output  =  9731 hp

Example 8.5, page no. 169

In [11]:
#initialization
P  =  14.7        #lb/in^2
T  =  60+460      #R
e1  =  0.8
P2  =  3          #lb/in^2
T2  =  1600+460   #R
Pt4  =  15.6      #lb/in^2
w  =  60          #lbm/sec
e2  =  0.85

#calculation
# from table 6, initial conditions are
ht1  =  124.3
Prt1  =  1.215
Prt2s  =  6*Prt1
ht2s  =  207.6
ht2 = ht1+(ht2s-ht1)/e1
dht1 = round((ht2s-ht1)/e1, 1)
ht3 = 521.4
Prt3 = 196.2
Pt3 = 6*P-P2
Pratio = Pt3/Pt4
Prt4s = Prt3/Pratio
ht4 = 326.5
dht3 = round(e2*(ht3-ht4), 1)
W = 778*(dht3-dht1)
Q = ht3-ht2
etaf = W/778.0/Q
Wdot = w*W/550.0

#result
print "Thermal efficiency  =  %.3f" %(round(W))
print "Horsepower output  =  %d hp" %Wdot
#difference due to internal rounding off in Python.

Thermal efficiency  =  47925.000
Horsepower output  =  5228 hp

Exmaple 8.6, page no. 172

In [1]:
#initialization
g  =  1.4
Tt4  =  2060                      #R
cp  =  0.24

#calculation
Tt5  =  Tt4/1.67
Tt2  =  868                       #R
Tt3s  =  1234
dTt3  =  (Tt3s-Tt2)/2.0
Tt3  =  Tt2+dTt3
Q  =  cp*(Tt4-Tt3)
eta  =  286*0.401/Q

#result

print "Heat Added is ", round(Q),"B/lbm"
print "eta is ", round(eta, 3)
print "Improvement is around 6.2 percent in overall efficiency"

Heat Added is  242.0 B/lbm
eta is  0.474
Improvement is around 6.2 percent in overall efficiency