# 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 " 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
Work done in per lb of steam 246500.315
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
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 " 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
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 " 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
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
V1x=Vb
work=1/32.2 *(V1x)*Vb #work done

#results
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