# Chapter 19 - Gas Turbines¶

## Example 1 - Pg 398¶

In [1]:
#calculate the compressor work, turbine work and thermal efficiency in all cases
#Initalization of variables
import math
n=1.4
t1=540. #R
tmax=1200. #F
tmax2=1500. #F
pr=5.
cp=0.24
#calculations
t2=t1*math.pow(pr,(n-1)/n)
work=cp*(t2-t1)
t4=(tmax+460) /math.pow(pr,(n-1)/n)
twork=cp*(tmax+460-t4)
net=twork-work
eff=(1- 1/math.pow(pr,(n-1)/n))*100
Qs=cp*(tmax+460-t2)
ett=net/Qs *100
t42=(tmax2+460)/math.pow(pr,(n-1)/n)
twork2=cp*(tmax2+460-t42)
net2=twork2-work
Qs2=cp*(tmax2+460-t2)
eff3=net2/Qs2 *100
#results
print '%s %.1f %s' %("Compressor work =",work,"Btu/lb")
print '%s %.1f %s' %("\n Turbine work =",twork,"Btu/lb")
print '%s %.1f %s' %("\n Net work =",net,"Btu/lb")
print '%s %.1f %s' %("\n Thermal efficiency =",eff,"percent")
print '%s %.1f %s' %("\n In case 2, Thermal efficiency =",ett," percent")
print '%s %.1f %s' %("\n In case 2, Turbine work =",twork2,"Btu/lb")
print '%s %.1f %s' %("\n In case 2, Net work =",net2," Btu/lb")
print '%s %.1f %s' %("\n In case 3, Thermal efficiency =",eff3," percent,")

Compressor work = 75.7 Btu/lb

Turbine work = 146.9 Btu/lb

Net work = 71.2 Btu/lb

Thermal efficiency = 36.9 percent

In case 2, Thermal efficiency = 36.9  percent

In case 2, Turbine work = 173.4 Btu/lb

In case 2, Net work = 97.7  Btu/lb

In case 3, Thermal efficiency = 36.9  percent,


## Example 2 - Pg 400¶

In [2]:
#calculate the indicated compressor work, internal work and thermal efficiency
#Initalization of variables
work=75.9 #Btu/lb
twork=173.5 #Btu/lb
eta=0.8
t2=856 #R
t1=540 #R
t4=1960 #R
cp=0.24
#calculations
cwork=work/eta
internal=twork*eta
net=-cwork+internal
t2d=(t2-t1)/eta + t1
Qs=cp*(t4-t2d)
eff=net/Qs *100
#results
print '%s %.1f %s' %("Indicated compressor work =",cwork," Btu/lb")
print '%s %.1f %s' %("\n Internal work =",internal,"Btu/lb")
print '%s %.1f %s' %("\n Net work =",net," Btu/lb")
print '%s %.2f %s' %("\n Thermal efficiency =",eff,"percent")

Indicated compressor work = 94.9  Btu/lb

Internal work = 138.8 Btu/lb

Net work = 43.9  Btu/lb

Thermal efficiency = 17.86 percent


## Example 3 - Pg 402¶

In [3]:
#calculate the compressor work, turbine work and thermal efficiency
#Initalization of variables
eff=0.97
c1=94.9 #Btu/lb
c2=138.8 #Btu/lb
ntee=246. #Btu/lb
#calculations
cwork=c1/eff
twork=c2*eff
net=twork-cwork
etat=net/ntee *100
#results
print '%s %.1f %s' %("Compressor work =",cwork,"Btu/lb")
print '%s %.1f %s' %("\n Turbine work =",twork," Btu/lb")
print '%s %.1f %s' %("\n Net work =",net," Btu/lb")
print '%s %.1f %s' %("\n Thermal efficiency =",etat,"percent")

Compressor work = 97.8 Btu/lb

Turbine work = 134.6  Btu/lb

Net work = 36.8  Btu/lb

Thermal efficiency = 15.0 percent


## Example 4 - Pg 403¶

In [4]:
#calculate the thermal efficiency
#Initalization of variables
import math
pr=5.
p1=14. #psia
pd=3. #psi
pen=70. #psia
tin=1960.  #R
n=1.4
cp=0.24
Qs=265. #Btu/lb
#calculations
p2=p1*pr
pe=pen-pd
prt=pe/p1
tex=tin/math.pow(prt,(n-1)/n)
twork=cp*(tin-tex)
net=twork-75.9
eff=net/Qs *100.
#results
print '%s %.1f %s' %("Thermal efficiency =",eff,"percent")

Thermal efficiency = 35.4 percent


## Example 5 - Pg 403¶

In [5]:
#calculate the thermal efficiency
#Initalization of variables
import math
pr=5.
p1=14. #psia
pd=3. #psi
pen=70. #psia
tin=1960.  #R
n=1.4
cp=0.24
Qs=265.
ef=0.95
#calculations
p2=p1*pr
pe=pen-pd
prt=pe/p1
tex=tin/math.pow(prt,(n-1)/n)
twork=cp*(tin-tex)
net=twork-75.9
Qs2=Qs/ef
eff=net/Qs2 *100.
#results
print '%s %.1f %s' %("Thermal efficiency =",eff,"percent")

Thermal efficiency = 33.6 percent


## Example 6 - Pg 404¶

In [6]:
#calculate the final pressure
#Initalization of variables
pr1=1.0590
pr2=4.396
p1=14. #psia
#calculations
prr=pr2/pr1
p2=p1*prr
#results
print '%s %.1f %s' %("Final pressure =",p2," psia")

Final pressure = 58.1  psia


## Example 7 - Pg 404¶

In [7]:
#calculate the compressor work
#Initalization of variables
t1=540. #R
h1=129.06
pr1=1.386
cr=5.
#calculations
pr2=pr1*cr
print '%s' %("From air tables,")
h2=204.63
cwork=h2-h1
#results
print '%s %.2f %s' %("Compressor work =",cwork,"Btu/lb")

From air tables,
Compressor work = 75.57 Btu/lb


## Example 8 - Pg 405¶

In [8]:
#calculate the turbine work
#Initalization of variables
cr=5.
pr3=176.73 #psia
h3=14580.3 #Btu/mol
M=28.9
#calculations
pr4=pr3/cr
h4=9409.
twork=h3-h4
turb=twork/M
#results
print '%s %.1f %s' %("Turbine work =",turb," Btu/lb")

Turbine work = 178.9  Btu/lb


## Example 9 - Pg 407¶

In [9]:
#calculate the air fuel ratio
#Initalization of variables
chem=19000. #Btu/lb
m1=204.63 #Btu/lb
M=28.9
w=14580.3
#calculations
ma=(chem-w/M)/(w/M -m1)
#results
print '%s %.1f %s' %("Air fuel ratio =",ma,"lb air/lb fuel")

Air fuel ratio = 61.7 lb air/lb fuel


## Example 10 - Pg 409¶

In [10]:
#calculate the thermal efficiency of the unit
#Initalization of variables
cp=0.24
h=138.8
t3=1960. #R
#calculations
t4d=t3-h/cp
Qs=cp*(t3-t4d)
work=43.9 #Btu/lb
etat=work/Qs *100.
#results
print '%s %.1f %s' %("Thermal efficiency of the unit =",etat,"percent")

Thermal efficiency of the unit = 31.6 percent


## Example 11 - Pg 412¶

In [11]:
#calculate the thermal efficiency
#Initalization of variables
import math
n=1.4
t1=540. #R
tmax=1500. #F
pr=5.
cp=0.24
p1=14. #psia
p3=70. #psia
#calculations
pint=p1*math.sqrt(pr)
t2=t1*math.pow(pint/p1,((n-1)/n))
t4=t1*math.pow(p3/pint,((n-1)/n))
w=cp*(t4-t1)
w2=2*w
t6=(tmax+460)/math.pow(p3/pint,((n-1)/n))
t8=(tmax+460)/math.pow(pint/p1,((n-1)/n))
work=cp*(tmax+460-t6)
w22=2*work
net=w22-w2
Qa=cp*(tmax+460-t2)
Qb=cp*(tmax+460-t6)
Qt=Qa+Qb
eta=net/Qt*100.
#results
print '%s %.2f %s' %("Thermal efficiency =",eta,"percent")

Thermal efficiency = 31.25 percent


## Example 12 - Pg 413¶

In [12]:
#calculate the thermal efficiency
#Initalization of variables
import math
n=1.4
t1=540. #R
tmax=1500. #F
pr=5.
cp=0.24
p1=14. #psia
p3=70. #psia
w2=75.9 #Btu/lb
Qa=265 #Btu/lb
#calculations
pint=p1*math.sqrt(pr)
t6=(tmax+460)/math.pow(p3/pint,((n-1)/n))
t8=(tmax+460)/math.pow(pint/p1,((n-1)/n))
work=cp*(tmax+460-t6)
w22=2*work
net=w22-w2
Qb=cp*(tmax+460-t6)
Qt=Qa+Qb
eta=net/Qt*100.
#results
print '%s %.1f %s' %("Thermal efficiency =",eta,"percent")

Thermal efficiency = 32.4 percent


## Example 13 - Pg 413¶

In [13]:
#calculate the thermal efficiency
#Initalization of variables
n=1.4
t1=540. #R
tmax=1500. #F
pr=5.
cp=0.24
t3=1558. #R
net=125.8 #Btu/lb
#calculations
Q=cp*(tmax+460-t3)
Qt=2*Q
eta=net/Qt*100.
#results
print '%s %.1f %s' %("Thermal efficiency =",eta," percent")

Thermal efficiency = 65.2  percent