# Chapter 13: Vapor cycles¶

## Exa 13.1¶

In [1]:
#A rankine cycle operates with steam conditions 200 psia,750 F and exhaust
#pressure 1 psia. Find the heat supplied, the turbine work, and the pump work
#per pound of steam. Find the cycle efficiency and steam rate?
#initialisation of variables
P= 1 						#psia
P1= 200 					#psia
T= 750 						#F
v3= 0.01614 				#cu ft/lb
h1= 1399.2 					#Bu/lb
h2= 976 					#Btu/lb
h3= 69.7 					#Btu/lb
#CALCULATIONS
dh= v3*(144./778.)*(P1-P)	#Change in enthalpy
h4= h3+dh 					#Enthalpy 4
Q1= h1-h4					#Heat
Wt= h1-h2 					#Work
Wp= h4-h3 					#Work
n= (Wt-Wp)/Q1 				#Efficiency
w= 2545./Wt 				#Steam rate
#RESULTS
print '%s %.3f' %('cycle efficency = ',n)
print '%s %.2f' %(' \n steam rate (lb steam per hphr) = ',w)
raw_input('press enter key to exit')

cycle efficency =  0.318

steam rate (lb steam per hphr) =  6.01
press enter key to exit

Out[1]:
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## Exa 13.2¶

In [ ]:
#A turbine operating under the same steam conditions as given for the cycle
#of example 1 has a measured steam rate 8. Find the engine efficiency of the
#tuebine and the state of the exhaust steam.
#initialisation of variables
wt= 8. 				#lb/hphr
h1= 1399.2 			#Btu/lb
h2s= 976. 			#Btu/lb
h2= 976. 			#Btu/lb
#CACLAULATIONS
Wt= 2545./wt 		#Work per piund
nt= Wt/(h1-h2s) 	#Efficiency
h21= h1-Wt 			#State of echaust steam
#RESULTS
print '%s %.3f' %('Engine efficency = ',nt)
print '%s %.3f' %(' \n state  of the exhaust steam (Btu/lb) = ',h21)
raw_input('press enter key to exit')

Engine efficency =  0.752

state  of the exhaust steam (Btu/lb) =  1081.075


## Exa 13.3¶

In [1]:
#A reheat cycle is to operate with turbines of 85% efficiency, but otherwise
#with idealized processes. the initial pressure is 2000 psia, and exhaust pressure
#is 0.5 psia, reheat=400 psia. Max. temp=1000 F. find efficiency and steam rate
#of this cycle. also of a rankine cycle working between 2000, 1000 and 0.5; also
#of a rankine cycle between 1400,1000,0.5. this being taken as cycle of max.
#permissible pressure without reheat. Use turbines oof 85% efficiecy in the rankine cycles
import math
print '%s' %('All the values have been obtained from steam tables and mollier chart')
#initialisation of variables
h1=1474.5 									#btu/lb
s1=1.5603 									#btu/lb R
h2s=1277.5 									#btu/lb
#Calculations and printfing
h2=h1-0.85*(h1-h2s)
print '%s %.2f' %('h2 (Btu/lb) = ',h2)
h3=1522.4  									#btu/lb
s3=1.7623 									#btu/lb R
h4s=948 #btu/lb
h4=h3- 0.85*(h3-h4s)
print '%s %.2f' %('\n h4 (Btu/lb) = ',h4)
h5=47.6 									#btu/lb
h6=53.5 									#btu/lb
print ('\n For the first rankine cycle')
h7s=840 									#btu/lb
h7=h1-0.85*(h1-h7s)
print '%s %.2f' %('\n h7 (Btu/lb) = ',h7)
print ('\n For the second rankine cycle')
h8=1493.2 									#btu/lb
s8=1.6903 									#btu/lb R
h9s=866 									#btu/lb
h9=h8-0.85*(h8-h9s)
print '%s %.2f' %('\n h9 (Btu/lb) = ',h9)
h11=51.5 									#btu/lb
n1=0.401
n2=0.375
n3=0.366
e1=(n1-n2)/n2 								#Efficiency
print '%s %.2f' %('\n Percentage Efficiency of reheat cycle compared to Rankine cycle for the first case =',e1*100)
e2=(n1-n3)/n3 								#Efficiency
print '%s %.2f' %('\n Percentage Efficiency of reheat cycle compared to Rankine cycle for the second case =',e2*100)
raw_input('press enter key to exit')

All the values have been obtained from steam tables and mollier chart
h2 (Btu/lb) =  1307.05

h4 (Btu/lb) =  1034.16

For the first rankine cycle

h7 (Btu/lb) =  935.18

For the second rankine cycle

h9 (Btu/lb) =  960.08

Percentage Efficiency of reheat cycle compared to Rankine cycle for the first case = 6.93

Percentage Efficiency of reheat cycle compared to Rankine cycle for the second case = 9.56
press enter key to exit

Out[1]:
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## Exa 13.4¶

In [2]:
#A steam plant operates with initial pressure 250 psia and temp 700 F and exhausts
#to a heating system at 25 psia. the condensate from the heating system is
#returned to the boiler plant at 150F, and the heating system utilizes for its
#intended purpose 90% of the energy transferred from the steam it receives
#(a) what fraction of energy supplied to the steam plant serves a useful purpose?
#(b) If two separate steam plants had been setup to produce the same useful energy,
#one to generate power through a cycle working between 250 psia, 700 F and 1 psia,
#what fraction of energy supplied would have served a useful purpose?
#initialisation of variables
h1= 1371 		#Btu/lb
h2s= 1149 		#Btu/lb
h3= 118 		#Btu/lb
Q1= 1253 		#Btu/lb
W= 156. 		#Btu/lb
Qw= 680. 		#Btu/lb
#CALCULATIONS
print '%s' %('All the values have been obtained from steam tables and mollier chart')
Qh= h1-W-h3 	#Heat
y= W+0.9*Qh 	#useful energy
r= y/Q1 		#fraction
x= Qh+Qw 		#total input
z= y/x 			#fraction
#RESULTS
print '%s %.2f' %('Fraction of energy supplied =  ',r)
print '%s %.2f' %(' \n Fraction of energy supplied which appears as useful energy= ',z)
raw_input('press enter key to exit')

All the values have been obtained from steam tables and mollier chart
Fraction of energy supplied =   0.91

Fraction of energy supplied which appears as useful energy=  0.64
press enter key to exit

Out[2]:
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