Steam Turbines

Example 7.1,Page 390

In [18]:
# Initialization of Variable
from math import pi
from math import atan
from numpy import *
P1=200.0 #psia
T1=500.0 #psia
m=1.0 #lb /s
P4=140.0 #psia
P11=1.0 #psia
x=0.808

#calculations
#"From mollier charts"
h1=1268.9 #Btu/lb
h4=1234.7 #Btu/lb
V4=223.8*sqrt(h1-h4)
v4=3.584 #cu ft/lb
A4=m*v4/V4
h11=907.4 #Btu/lb
V11=223.8*sqrt(h1-h11)
vf=0.01614 #cu ft/lb
vg=333.6 #cu ft/lb
vfg=vg-vf
v11=x*vg
A11=m*v11/V11 #area

#results
print "Area of nozzle in sq ft",round(A4,6)
print " Area of nozzle in sq ft",round(A11,6)

Area of nozzle in sq ft 0.002738
 Area of nozzle in sq ft 0.063347

Example 7.4,Page 410

In [19]:
# Initialization of Variable
from math import pi
from math import atan, cos
from numpy import *
P1=200.0 #psia
T1=500.0 #F
P2=1.0 #psia
alpha=20.0 #degrees
n=3600.0
g=32.2 #ft/s^2

#calculations
#"From mollier charts"
V1=4240.0 #fps
Vb=V1*cos(alpha*pi/180) /2
R=Vb*60/(n*2*pi)
work=1/32.2 *(V1*cos(alpha*pi/180))*Vb
eff=work/(V1**2 /(2*g)) *100 #efficiency

#results
print "Blade velocity in fps",round(Vb,3)
print " Blade radius in ft",round(R,3)
print " Work done in per lb of steam",round(work,3)
print " Blade efficiency in percent",round(eff,3)
print "The answers are a bit different due to rounding off error in textbook"

Blade velocity in fps 1992.148
 Blade radius in ft 5.284
 Work done in per lb of steam 246500.315
 Blade efficiency in percent 88.302
The answers are a bit different due to rounding off error in textbook

Example 7.5,Page 411

In [20]:
# Initialization of Variable
from math import pi
from math import atan
from numpy import *
P1=200.0 #psia
T1=500.0 #F
P2=1.0 #psia
alpha=20.0 #degrees
n=3600.0
g=32.2 #ft/s^2
Vb=1200.0 #fps

#calculations
#"From mollier charts"
V1=4240.0 #fps
V1x=3980.0 #fps
V2x=-1580.0 #fps
work=1/32.2 *(V1x - V2x)*Vb
eff=work/(V1**2 /(2*g)) *100 #efficiency

#results
print " Work done in per lb of steam",round(work,3)
print " Blade efficiency in percent",round(eff,3)
print "The answers are a bit different due to rounding off error in textbook"

 Work done in per lb of steam 207204.969
 Blade efficiency in percent 74.226
The answers are a bit different due to rounding off error in textbook

Example 7.6,Page 413

In [2]:
# Initialization of Variable
from math import pi
from math import atan, cos, tan
from numpy import *
P1=200.0 #psia
T1=500.0 #F
P2=1.0 #psia
alpha=20.0 #degrees
n=3600.0
g=32.2 #ft/s^2

#calculations
#"From mollier charts")
V1=2450 #fps
Vb=V1*cos(alpha*pi/180) /2
R=Vb*60/(n*2*pi)
work=1/32.2 *(V1*cos(alpha*pi/180))*Vb
w3=3*work  #workdone

#results
print "Blade velocity in fps",round(Vb,3)
print "Blade radius in ft",round(R,3)
print " Work done in per lb of steam",round(w3,3)
print "The answers are a bit different due to rounding off error in textbook"

Blade velocity in fps 1151.123
Blade radius in ft 3.053
 Work done in per lb of steam 246910.29
The answers are a bit different due to rounding off error in textbook

Example 7.7, Page 416

In [2]:
# Initialization of Variable
from math import pi
from math import atan
from numpy import *
P1=200.0 #psia
T1=500.0 #F
P2=1.0 #psia
alpha=20.0 #degrees
n=3600.0
g=32.2 #ft/s^2
stage=2.0

#calculations
#"From mollier charts"
V1=4240.0 #fps
Vb=V1*cos(alpha*pi/180) /(2*stage)
R=Vb*60/(n*2*pi)
V1x=3980 #fps
V2x=-1990 #fps
work1=1/g *(V1x-V2x)*Vb #work
work2=1/g *(-V2x)*Vb #work
wt=work1+work2 #work done

#results
print "Blade velocity in fps",round(Vb,3)
print " Blade radius in ft",round(R,3)
print " Work done in per lb of steam",round(wt,3)
print "The answers are a bit different due to rounding off error in textbook"

Blade velocity in fps 996.074
 Blade radius in ft 2.642
 Work done in per lb of steam 246234.486
The answers are a bit different due to rounding off error in textbook

Example 7.8,Page 422

In [3]:
# Initialization of Variable
from math import pi
from math import atan,cos, tan
from numpy import *
alpha=20.0 #degrees
n=3600.0
g=32.2 #ft/s^2
V1=500 #fps

#calculations
Vb=V1*cos(alpha*pi/180) #blade velocity
V1x=Vb
work=1/32.2 *(V1x)*Vb #work done

#results
print "Blade velocity in fps",round(Vb,3)
print " Work done in per lb of steam",round(work,3)
print "The answers are a bit different due to rounding off error in textbook."

Blade velocity in fps 469.846
 Work done in per lb of steam 6855.763
The answers are a bit different due to rounding off error in textbook.

Example 7.9,Page 436

In [5]:
# Initialization of Variable
from math import pi
from math import atan
from numpy import *
power=1000.0 #kw
ms=16000.0 #lb/hr
P=200.0 #psia
T=540 #F

#calculations
#"From mollier charts"
h1=1290.0 #Btu/hr
h2=940.0 #Btu/hr
dh=h1-h2
rate=3413.0/dh
act=ms/power #steam rate

#results
print "Ideal steam rate in per kw hr",round(rate,3)
print " Actual steam rate in per kw hr",round(act,3)

Ideal steam rate in per kw hr 9.751
 Actual steam rate in per kw hr 16.0

Example 7.10,Page 439

In [7]:
# Initialization of Variable
from math import pi
from math import atan
from numpy import *
P=200 #psia
T=540 #F
power=1000 #kw
ms=16000 #lb/hr

#calculations
#"From mollier charts")
h1=1290.0 #Btu/hr
h2=940.0 #Btu/hr
dh=h1-h2
hf2=83.0 #Btu/lb
etat=(h1-h2)/(h1-hf2)
act=power*3413/(ms*(h1-hf2)) #thermal efficiency
etae=act/etat #efficiency of engine

#results
print "Ideal thermal efficiency in percent",round(etat*100,3)
print "Actual thermal efficiency in percent",round(act*100,3)
print " Engine efficiency in percent",round( etae*100,3)

Ideal thermal efficiency in percent 28.998
Actual thermal efficiency in percent 17.673
 Engine efficiency in percent 60.946