# CHAPTER 8: INTERNAL COMBUSTION ENGINES: VARIABLE SPECIFIC HEATS¶

## Example 8.1 Page 128¶

In :
#initialisation of variable
from math import pi,sqrt,acos,asin,atan,cos,sin,tan
b=6#in
b1=9.0#in
r1=4.0#ratio
r2=1.0#ratio
p=50#lb/in^2
s=300#r p m
e=30#per cent
v=260#C.H.U
a=1.41
h=0.30#in
g=33000#in
g1=1400#in
A=1-(r2/r1)**0.41#lb/in^2

#CALCULATIONS
I=(p*pi*36/4*9/12*s/2)*1/g#ft^3
X=(I*g)/(g1*v*h)#ft^3
C=X*60/I#ft^3
R=h/A*100#per cent

#RESULTS
print"The fuel consumption in ft^3/h p hr and the efficiency relative to the air standard cycle is",round(R,3),"%"

The fuel consumption in ft^3/h p hr and the efficiency relative to the air standard cycle is 69.195 %


## Example 8.3 Page 129¶

In :
#initialisation of variable
from math import pi,sqrt,acos,asin,atan,cos,sin,tan
h=200.0#r p m
h1=50.0#i h p
P4=33.4#lb/in^2
W=9000.0#ft lb
x=33000.0#ft.lb
p=1728.0#ft/lb

#CALCULATIONS
w=h1*x/100.0#ft lb
T=w/W#ft^3
V =13.0/14.0*T#ft^3
D=((V*p*8)/(3*pi))**(1.0/3.0)#in

#RESULTS
print"The diameter of the cylinder of a single acting and swept volume is",round(D,3),"in"

The diameter of the cylinder of a single acting and swept volume is 13.567 in


## Example 8.6 Page 132¶

In :
#initialisation of variable
from math import pi,sqrt,acos,asin,atan,cos,sin,tan
h=12#in
h1=18#in
v=19000#B.Th.U/lb
T=12600#lb/in^2
m=90#lb/in^2
w=120#gal
t1=140#F
t2=60#F
t3=570#F
Cv=0.24#ft/lb
q=810#ft/lb
n=16.9#lb

#CALCULATIONS
H=(n/t2*v)#B.Th.U
H1=(m*pi*(144/4)*(h1/h)*(T/t2))/(778*2)#B.TH.U/min
H2=1750#B.Th.U
H3=(H1-H2)#B.Th.U
W=(w*10/t2)*(t1-t2)#B,Th.U
G=((q+n)/(t2))*(t3-t2)*Cv#B.TH.U

#RESULTS
print"The heat balance showing heat quantities received and the discharged per min is",round(G,3),"B.TH.u"

The heat balance showing heat quantities received and the discharged per min is 1686.876 B.TH.u


## Example 8.8 Page 133¶

In :
#initialisation of variable
from math import pi,sqrt,acos,asin,atan,cos,sin,tan
v=12.5 #i.p.h
p1=8.25#in
p2=12.0#in
t=110.0#per min
g1=280.0#C.H.U/ft^3
g2=215.0#ft^3
V=25.0#percent
e=0.875#in
T=33000.0#in
v1=0.4170#ft^3

#CALCULATIONS
M=(T*v)/((pi*(p1)**2.0)/(4.0)*(p2/p2)*(t))#lb.in^2
V1=pi*(p1)**2.0/4.0*p2/1728.0*e#ft^3
V2=(pi*(p1)**2.0*p2)/(4.0*4.0*1728.0)#ft^3
G=(g2/60.0*1.0/t)#ft^3
T1=G*g1#C.H.U
T2=(T1/v1)#C.H.U
F=(M/T2)#C.H.U

#RESULTS
print"The value of the Tookey factor for gas engine is",round(F,3),"C.H.U"

The value of the Tookey factor for gas engine is 3.207 C.H.U


## Example 8.10 Page 135¶

In :
#initialisation of variable
from math import pi,sqrt,acos,asin,atan,cos,sin,tan
p1=140#lb/in^2
p2=6.6#lb/in^2
v1=122#r.p.m
v2=1250#b.h.p
t=1425#i.h.p
p3=77.8#lb/in^2
h=0.356#lb
v=10000#C.H.U/lb
h2=2400#lb
q=33000#in
j=1400#in

#CALCULATIONS
t=(v2*q*60)/(j*h*v2*v)*100#percent
V=(p3*144*v1)/(q*2)#V
V1=(p2*144*v1)/q#V
T=24.16#V
V2=t/T#ft^3
I=V*V2#ft^3
I1=V1*V2#ft^3
H=24904#C/.H.U//mim
T=(I*q*60)/(j*h*v2*v)*100#percent
T1=(I1*q)/(j*H)*100#percent
T2=(h*v2*v)/(60)#C.H.U
H1=(v2*q)/(j)#C.H.U/mim
H2=H-(I1*q*v2)/(j*t)#C.H.U/mim
T3=H1+H2#C.H.U/mim
Tn=T2-T3#C.H.U/mim

#RESULTS
print"the overall thermal effciency is",round(t,3),"%"
print"the cylinder volume is",round(V,3),"ft^3"
print"the thermal efficiency of steam engine is",round(T1,3),"%"
print"total heat in oil.min is",round(Tn,3),"C.H.U/min"

the overall thermal effciency is 39.727 %
the cylinder volume is 20.709 ft^3
the thermal efficiency of steam engine is 0.547 %
total heat in oil.min is 24083.671 C.H.U/min


## Example 8.12 Page 138¶

In :
#initialisation of variable
from math import pi,sqrt,acos,asin,atan,cos,sin,tan
r=14#in
r1=1.8#in
t=30.4#lb
e=0.6#lb
lam=1.4
d=12#in
d1=18#in
v=10000#C.H.U/lb
P=200#r m p

#CALCULATIONS
A=1-(1/(lam*(r)**0.4))*((r1)**lam-1)/(r1-1)#percent
T=e*A#percent
H=t/60*v#C.H.U
H1=H*T#C.H.U
I=(H1*1400)/(33000)#ln/in^2
M=(I*33000)/(2*pi*144/4*d1/12*P/2)#lb/in^2

#RESULTS
print"the indicated hourse-power and the mean effiective pressure of the engine is",round(M,3),"lb/in^2"

the indicated hourse-power and the mean effiective pressure of the engine is 75.666 lb/in^2


## Example 8.19 Page 140¶

In :
#initialisation of variable
from math import pi,sqrt,acos,asin,atan,cos,sin,tan
cv=0.1714#C.H.U
R=100.3#ft.lb
T=500#degree c
J=1400#in
Lam=R/J#C.H.U percent C

#CALCULATIONS
Cp=Lam+cv#C.H.U percent C

#RESULTS
print"The specific heat at constant volume of a gaseous mixture is",round(Cp,3),"C.H.U %"

The specific heat at constant volume of a gaseous mixture is 0.243 C.H.U %


## Example 8.20 Page 141¶

In :
#initialisation of variable
from math import pi,sqrt,acos,asin,atan,cos,sin,tan
a=0.124#in
b=0.000025#in
R=0.0671#heat units

#CALCULATIONS
Cp=(R+a+b)+b#T

#RESULTS
print"the specific heat of a gas at constant volume is",round(Cp,3),"T"

the specific heat of a gas at constant volume is 0.191 T


## Example 8.21 Page 142¶

In :
#initialisation of variable
from math import pi,sqrt,acos,asin,atan,cos,sin,tan
v=18#ft^3
p=14#lb/in^2
p1=150#lb/in^2
Cp=0.242#T
Cv=0.171#T
j=1400#ft
R=j*(Cp-Cv)#ft.lb
p2=144#ft
I1=137500#ft/lb
I2=6.37#ft/lb
v2=3.282#ft^3

#CALCULATIONS
T=(p2*p*v)/R#Degree C
T2=(p2*p1*v2)/(R)#Degree c
W=Cp*(T2-T)+0.00002*((T2)**2-(T)**2)#C.H.U/lb
C=v/v2#ratio

#RESULTS
print"The work done the temperatures at the beginning and end of compression ratio is",round(C,3),"ratio"

The work done the temperatures at the beginning and end of compression ratio is 5.484 ratio


## Example 8.22 Page 144¶

In :
#initialisation of variable
from math import pi,sqrt,acos,asin,atan,cos,sin,tan
r=12.5#rario
p=0.39*10**6#ft.lb
p1=14#lb/in^2
t=373#Degree C
g=18#ft^3
t1=100#Degree C
V=g/r#ft^3
I=0.2*10**6#ft lb/lb
T=0.59*10**6#ft.lb/lb
D=0.221*10**6#ft.lb/lb
A=0.095*10**6#ft.lb/lb
E=0.264*10**6#ft.lb/lb
E1=0.390*10**6#t.lb/lb

#ALCULATIONS
W=(E/E1)*100#ercent
M=(E)/(144*(g-V))#b.in^2

#RSULTS
print"the efficiency of the engine and the m e p on the assumption that the specific heats is",round(M,3),"lb in^2"

the efficiency of the engine and the m e p on the assumption that the specific heats is 110.709 lb in^2