In [1]:

```
from __future__ import division
#input data
C1=500#Steam velocity in m/s
U=200#Blade speed in m/s
b2=(90-25)#Exit angle of moving blade measured in axial direction in degree
a1=(90-20)#Nozzle angle in axial direction in degree
m=5#Steam flow rate in kg/s
print 'The scale of the velocity vector diagram is 1:50\n\nThe following values are obtained from the velocity vector diagram'
b1=33#Moving blade inlet angle in degree
a2=56#Direction of steam at the exit in degree
C2=160#Exit velocity of the steam in m/s
Wx1=270#Inlet whirl velocity in m/s
Wx2=285#Exit whirl velocity in m/s
Ca1=175#Inlet axial velocity in m/s
Ca2=135#Exit axial velocity in m/s
#calculations
Wm=U*(Wx1+Wx2)*10**-3#Work done per kg of steam in kW/kg
AT=m*(Ca1-Ca2)#Axial thrust in N
W=m*Wm#Power developed in kW
Ndia=((U*(Wx1+Wx2))/((C1**2)/2))#Diagram or blade efficiency
#output
print '\n\n(a)Moving blade inlet angle is %3i degree\n(b)\n Exit velocity of the steam is %3i m/s\n Direction of steam at the exit is %3i degree\n(c)Work done per kg of steam is %3i kW/kg\n(d)\n Axial thrust is %3i N\n Power developed is %3i kW\n(e)Diagram or blade efficiency is %0.1f %%'%(b1,C2,a2,Wm,AT,W,Ndia*100)
# the answer in the textbook is not correct for axial thrust.
```

In [5]:

```
from math import sin, pi
#input data
U=300#Blade speed in m/s
a=20#Nozzle angle in degree
dhs=473#Isentropic heat drop in kJ/kg
Nn=0.85#Nozzle efficiency
W2W1=0.7#Blade velocity coefficient
nM=0.9#Mechanical efficiency
#initial calculations
dh=Nn*dhs#Useful heat drop converted into kinetic energy in kJ/kg
C1=(2*1000*dh)**(1/2)#Velocity of steam at exit from nozzle in m/s
print 'The scale of the velocity vector diagram is 1:100\n\nThe following values are obtained from the velocity vector diagram'
Ca1=310#Inlet axial velocity in m/s
Ca2=210#Exit axial velocity in m/s
Wx1=550#Inlet whirl velocity in m/s
Wx2=380#Exit whirl velocity in m/s
W1=620#inlet Blade velocity in m/s
#calculations
W2=W2W1*W1#Exit bladde velocity in m/s
AT=Ca1-Ca2#Axial thrust in N/kg
Wm=U*(Wx1+Wx2)*10**-3#Work developed per kg of steam/sec in kW/(kg/s)
P=Wm*nM#Power developed per kg of steam/sec in kW/(kg/s)
m=3600/P#Steam rate per kW.hr in kg
Ndia=((U*(Wx1+Wx2))/((C1**2)/2))#Diagram or blade efficiency
MNdia=(sin((90-a)*pi/180))**(2)#Maximum blade efficiency under optimum conditions
Ns1=Wm/dhs#Stage efficiency
Ns2=Ndia*Nn#Stage efficiency in other method
E=(((W1**2)-(W2**2))/2)*10**-3#Energy loss in blade friction in kJ/kg
#output
print '\n\n(a)Axial thrust is %3i N/kg\n(b)\n Work developed per kg of steam/sec is %3i kW/(kg/s)\n Power developed per kg of steam/sec is %3.1f kW/(kg/s)\n Steam rate per kW.hr is %3.1f kg\n(c)\n Diagram or blade efficiency is %0.1f %%\n Maximum blade efficiency under optimum conditions is %0.1f %%\n Stage efficiency is %0.2f %%\n(d)Energy loss in blade friction is %3.3f kJ/kg'%(AT,Wm,P,m,Ndia*100,MNdia*100,Ns1*100,E)
```

In [6]:

```
#input data
P1=5#Input pressure of steam in bar
P2=3#Exhaust pressure of steam in bar
C0=75#Carry over velocity of steam in m/s
a1=20#Nozzle angle in degree
UC1=0.4#The direction of blade rotation and blade speed ratio
b2=20#Blade exit angle in degree
m=2.5#Steam flow rate in kg/s
W=206#Power Output of the stage in kW
Nn=0.9#Efficiency of the nozzle
print 'Assuming isentropic expansion the enthalpy drop can be found from steam table\n\nThe following values are obtained from steam tables'
h1=2747.5#Enthalpy at initial pressure in kJ/kg
s1=6.819#Entropy at initial pressure in kJ/kg.K
s2=s1#Entropy at final pressure in kJ/kg.K
sfp2=1.647#Entropy of fliud at final pressure in kJ/kg.K
sfgp2=5.367#Entropy of fliud-gas mixture at final pressure in kJ/kg.K
hfg=2170.1#Enthalpy of fliud-gas mixture in kJ/kg
hf=551.5#Enthalpy of fliud in kJ/kg
print '\n\nThe scale of the velocity vector diagram is 1:50\n\nThe following values are obtained from the velocity vector diagram'
W1=280#Relative velocity at inlet in m/s
W2=240#Relative velocity at exit in m/s
#calculations
x2=(s2-sfp2)/sfgp2#The percentage of wet steam
h2s=hf+(x2*hfg)#The isentropic enthalpy at the second stage in kJ/kg
dhs=h1-h2s#Isentropic heat drop in kJ/kg
C1=((2000*Nn*dhs)+(C0**2))**(1/2)#Velocity of steam at exit from nozzle in m/s
U=UC1*C1#Blade speed in m/s
Wx1Wx2=(W*10**3)/(m*U)#The sum of whirl components of velocity in m/s
Ndia=(U*Wx1Wx2)/((C1**2)/2)#Diagram efficiency
RV=W2/W1#Relative velocity ratio
E=dhs+((C0**2)/2000)#Energy supplied per kg in kJ/kg
Ns1=(U*Wx1Wx2)/(E*10**3)#Stage efficiency
Ns2=Ndia*Nn#Stage efficiency in other method
#output
print '\n\n(a)Velocity of steam at exit from nozzle is %3.2f m/s\n(b)Diagram efficiency is %0.2f\n(c)Relative velocity ratio is %3.3f\n(d)\n Stage efficiency in method 1 is %0.2f\n Stage efficiency in method 2 is %0.2f'%(C1,Ndia*100,RV,Ns1*100,Ns2*100)
# the answer in the textbook is not accurate.
```

In [7]:

```
#input data
C1=600#Velocity of steam at exit from nozzle in m/s
U=120#Blade speed in m/s
a1=16#Nozzle angle in degree
b2=18#Discharge angle for first moving ring in degree
a11=21#Discharge angle for the fixed ring in degree
b22=35#Discharge angle for the second moving ring in degree
Wr=0.9#Blade velocity coefficient
m=1#Mass flow rate in kg/s
print '\n\nThe scale of the velocity vector diagram is 1:50\n\nThe following values are obtained from the velocity vector diagram'
W1=485#Relative velocity at inlet for first stage in m/s
W2=Wr*W1#Relative velocity for first stage at exit in m/s
Wx1=460#Inlet whirl velocity for first stage in m/s
Wx2=410#Exit whirl velocity for first stage in m/s
Ca1=170#Inlet axial velocity for first stage in m/s
Ca2=135#Exit axial velocity for first stage in m/s
C2=325#Exit velocity of the steam for first stage in m/s
b1=20#Blade inlet angle for first row of moving blade in degree
C11=Wr*C2#Steam velocity at inlet to second row of moving blades in m/s
W12=190#Relative velocity at inlet for second stage in m/s
W22=Wr*W12#Relative velocity at exit for second stage in m/s
Wx11=155#Inlet whirl velocity for second stage in m/s
Wx22=140#Exit whirl velocity for second stage in m/s
Ca11=110#Inlet axial velocity for second stage in m/s
Ca22=100#Exit axial velocity for second stage in m/s
b11=35#Blade inlet angle for second row of moving blade in degree
dWx1=Wx1+Wx2#Driving force for first stage in m/s
dWx11=Wx11+Wx22#Driving force for second stage in m/s
dW=(dWx1+dWx11)*1#Total driving force for unit mass flow rate in N
AT1=Ca1-Ca2#Axial thrust for first stage in m/s
AT2=Ca11-Ca22#Axial thrust for second stage in m/s
AT=(AT1+AT2)*1#Total axial thrust for unit mass flow rate in N
DP=m*U*(dWx1+dWx11)*10**-3#Diagram power in kW
DE=(U*(dWx1+dWx11))/((C1**2)/2)#Diagram efficiency
MDE=(sin((90-a1)*pi/180))**2#Maximum diagram efficiency
#output
print '\n\n(a)\n Blade inlet angle for first row of moving blade is %3.i degree\n Blade inlet angle for second row of moving blade is %3i degree\n(b)\n Driving force for first stage is %3i m/s\n Driving force for second stage is %3i m/s\n Total driving force for unit mass flow rate is %3i N\nTotal axial thrust for unit mass flow rate is %3i N\n(c)Diagram power is %3.1f kW\n(d)Diagram efficiency is %0.1f\n(e)Maximum diagram efficiency is %0.1f'%(b1,b11,dWx1,dWx11,dW,AT,DP,DE*100,MDE*100)
```

In [10]:

```
from math import cos
#input data
C1=100#Velocity of steam at exit from nozzle in m/s
h=0.04#Mean blade height in m
b2=20#Exit angle of moving blade in degree
CaU=3/4#Ratio of flow velocity and blade speed at mean radius
m=10000/3600#steam flow rate in kg/s
#calculations
a1=b2#Nozzle angle in degree
Ca=C1*cos((90-a1)*pi/180)#Flow velocity in m/s
U=Ca/CaU#Mean blade velocity in m/s
v=0.60553#Specific volume of steam from steam table at 3 bar with dry saturated steam in m**3/kg
A=(m*v)/Ca#Annulus area in m**2
D=A/(3.1415*h)#Mean blade diameter in m
N=(U*60)/(3.14*D)#Rotor speed in rpm
print '\n\nThe scale of the velocity vector diagram is 1:10\n\nThe following values are obtained from the velocity vector diagram'
W1=59#Relative velocity at inlet for first stage in m/s
Wx1Wx2=142#Sum of whirl components of velocity in m/s
DP=m*U*Wx1Wx2*10**-3#Diagram power in kW
Wm=U*(Wx1Wx2)#Work done per kg of steam in kJ/kg
W2=C1#Relative velocity at exit for first stage in m/s
E=((C1**2)/2)+(((W2**2)-(W1**2))/2)#Energy input per kg in kJ/kg when W2=C1
Ndia=Wm/E#Diagram efficiency
RV=(W2-W1)/W1#Percentage increase in relative velocity
dH=((W2**2)-(W1**2))/2*10**-3#Enthalpy drop in the moving blades in kJ/kg
H=2*dH#Total enthalpy drop in two stages in kJ/kg
#output
print '\n\n(a)The rotor speed is %3i rpm\n(b)The diagram power is %3.2f kW\n(c)The diagram efficiency is %0.1f\n(d)Percentage increase in relative velocity is %0.1f\n(e)\n Enthalpy drop in the moving blades is %3.3f kJ/kg\n Total enthalpy drop in two stages is %3.3f kJ/kg'%(N,DP,Ndia*100,RV*100,dH,H)
```

In [11]:

```
#input data
R=0.5#Degree of reaction
P1=14#Initial pressure in bar
T1=588#Initial temperature in K
P2=0.14#Final pressure in bar
Ns=0.75#Stage efficiency
RF=1.04#Reheat factor
N=20#No. of stages
W=11770#Total power output in kW
a1=20#Exit blade angle in degree
hD=1/12#Ratio of blade height to blade mean diameter
#calculations
hs1=3080#Isentropic enthalpy at initial condition from mollier chart in kJ/kg
hs2=2270#Isentropic enthalpy at final condition from mollier chart in kJ/kg
dhs=hs1-hs2#Isentropic enthalpy change in kJ/kg
Nt=Ns*RF#Overall efficiency
dh=Nt*dhs#Actual enthalpy drop in kJ/kg
hs=dh/N#Enthalpy drop per stage in kJ/kg
m=W/dh#Mass flow rate in kg/s
C11=1.43*1#Velocity of steam at exit from nozzle in m/s in terms of U for 0.5 degree of reaction
Wm=1*((2*C11*sin((90-a1)*pi/180))-1)#Work done per mass of steam in terms of U**2 in kJ/kg
U=((hs*10**3)/Wm)**(1/2)#Mean blade velocity in m/s as work done equals enthalpy drop per stage
C1=1.43*U#Velocity of steam at exit from nozzle in m/s
Ca=C1*cos((90-a1)*pi*180)#Flow velocity in m/s
v=1.618#Specific volume of steam from steam table at 1.05 bar with dry saturated steam in m**3/kg
D=((m*v)/(hD*3.14*Ca))**(1/2)#Blade mean diameter in m
N=(U*60)/(3.14*D)#Rotor speed in rpm
#output
print '(a)Mass flow rate of steam is %3.2f kg/s\n(b)Mean blade velocity is %3.1f m/s \n(c)Blade mean diameter is %3.3f m \n(d)Rotor speed is %3i rpm'%(m,U,D,N)
# the answer in the textbook is not correct.
```

In [12]:

```
from math import tan, pi, degrees, atan
#input data
rh=0.225#Blade roof radius in m
rt=0.375#Blade tip radius in m
b1m=45#Inlet angle of the rotor blade at mid height in degree
a1m=76#Outlet angle of the nozzle blade at mid height in degree
b2m=75#Outlet angle of the rotor blade at mid height in degree
N=6000#Speed of turbine in rpm
#calculations
rm=(rh+rt)/2#Mean radius in m
Um=(2*3.14*rm*N)/60#Mean blade speed at mean radius in m/s
Ca=Um/((tan(a1m*pi/180))-(tan(b1m*pi/180)))#Flow velocity in m/s
Cx1m=Ca*tan(a1m*pi/180)#Velocity of whirl at inlet at mid height in m/s
Cx2m=Ca*tan(b2m*pi/180)-Um#Velocity of whirl at inlet at mid height in m/s
Cx1h=(Cx1m*rm)/rh#Velocity of whirl at inlet at hub height in m/s
a1h=degrees(atan(Cx1h/Ca))#Inlet angle of the nozzle blade at hub height in degree
Uh=(2*3.1415*rh*N)/60#Mean blade speed at hub in m/s
b1h=degrees(atan(tan(a1h*pi/180)-(Uh/Ca)))#Inlet angle of the rotor blade at hub in degree
Cx2h=Cx2m*rm/rh#Velocity of whirl at outlet at hub in m/s
b2h=degrees(atan((Uh+Cx2h)/Ca))#Outlet angle of the rotor blade at hub in degree
Cx1t=Cx1m*rm/rt#Velocity of whirl at inlet at tip in m/s
a1t=degrees(atan(Cx1t/Ca))#Inlet angle of the nozzle blade at tip height in degree
Ut=(2*3.14*rt*N)/60#Mean blade speed at tip in m/s
b1t=degrees(atan(tan(a1t*pi/180)-(Ut/Ca)))#Inlet angle of the rotor blade at tip in degree
Cx2t=Cx2m*rm/rt#Velocity of whirl at outlet at tip in m/s
b2t=degrees(atan((Ut+Cx2t)/Ca))#Outlet angle of the rotor blade at hub in degree
Rh=(Ca/(2*Uh))*(tan(b2h*pi/180)-tan(b1h*pi/180))#Degree of reaction at hub
Rt=(Ca/(2*Ut))*(tan(b2t*pi/180)-tan(b1t*pi/180))#Degree of reaction at tip
#output
print '(a)for hub\n (1)Inlet angle of the nozzle blade at hub height is %3.1f degree\n (2)Inlet angle of the rotor blade at hub is %3i degree\n (3)Outlet angle of the rotor blade at hub is %3.2f degree\n (4)Degree of reaction at hub is %0.2f %%\n(b)for tip\n (1)Inlet angle of the nozzle blade at tip height is %3.2f degree\n (2)Inlet angle of the rotor blade at tip is %3i degree\n (3)Outlet angle of the rotor blade at tip is %3i degree\n (4)Degree of reaction at tip is %0.2f'%(a1h,b1h,b2h,Rh*100,a1t,b1t,b2t,Rt*100)
# Answer for degree of reaction is not correct in the textbook.
```

In [13]:

```
#input data
Ca=180#Air velocity at the exit of nozzle in m/s
a1=(90-27)#Nozzle inclination perpendicular to direction of rotation in degree
R=0.5#Degree of reaction
U=180#Blade speed in m/s
#calculations
Cx1=Ca*tan(a1*pi/180)#Inlet whirl velocity in m/s
b11=degrees(atan((Cx1-U)/Ca))#Inlet angle of the rotor blade at inlet velocity triangle in degree
pi=Ca/U#Ratio of air velocity and blade velocity
b21=degrees(atan((2*R/pi))+tan(b11*pi/180))#Outlet angle of the rotor blade at inlet velocity triangle in degree
C2=Ca#Exit velocity of the steam in m/s
b22=degrees(atan(U/C2))#Outlet angle of the rotor blade at outlet velocity triangle in degree
b12=b11#Inlet angle of the rotor blade at outlet velocity triangle in degree as np change in rotor inlet conditions
R=(pi*(tan(b22*pi/180)-tan(b12*pi/180)))/2#Degree of reaction
#output
print '(a)blade angles\n Inlet angle of the rotor blade at inlet velocity triangle is %3.1f degree\n Outlet angle of the rotor blade at inlet velocity triangle is %3.f degree\n(b)Degree of reaction is %3.4f\n(c)Inlet angle of the rotor blade at outlet velocity triangle is %3.f degree\n(d)Outlet angle of the rotor blade at outlet velocity triangle is %3.1f degree'%(b11,b21,R,b22,b12)
# Answer in the textbook is not correct for some part.
```

In [14]:

```
from math import cos
#input data
U=300#Blade speed of turbine in m/s
m=2.5#Mass flow rate in kg/s
T0=773#Gas temperature at turbine inlet in K
T2=573#Gaas temperature at turbine outlet in K
a1=70#Fixed blade outlet angle in degree
Ca=200#Axial velocity in m/s
Cp=1.005#Specific heat of gas at constant pressure in kJ/kg.K
#calculations
W=m*Cp*(T0-T2)#Power developed by turbine in kW
Wm=Cp*(T0-T2)#Stage work done per unit mass flow rate in kJ/kg
Wx1Wx2=Wm*10**3/U#Sum of whirl components of velocity at inlet and outlet in m/s
Wx1=(Ca*tan(a1*pi/180))-U#Inlet whirl velocity in m/s
Wx2=Wx1Wx2-Wx1#Outlet whirl velocity in m/s
R=(Wx2-Wx1)/(2*U)#Degree of reaction
Wx2Wx1=Wm*10**3*R#Energy input due to whirl component velocity in (m/s)**2
C1=Ca/cos(a1*pi/180)#Velocity of steam at exit from nozzle in m/s
nb=(Wm*10**3)/(((C1**2)/2)+Wx2Wx1)#Blade efficiency
#output
print '(a)Power developed by turbine is %3.1f kW\n(b)Degree of reaction is %0.2f %%\n(c)Blade efficiency is %0.2f %%\n'%(W,R*100,nb*100)
```

In [15]:

```
from __future__ import division
#input data
R=0.5#Degree of reaction
P0=2.2#Inlet pressure in bar
T0=443#Inlet temperature in K
N=2400#Rotor running speed in rpm
Dm=0.5#Rotor mean diameter in m
a1=36#Rotor inlet angle in degree
a2=19#Stator exit angle in degree
ns=0.88#Stage efficiency
m=1#Mass flow rate of steam in kg/s
#calculations
b2=a1#Outlet angle of the rotor blade in degree
b1=a2#Inlet angle of the rotor blade in degree
U=(3.1415*Dm*N)/60#Mean blade speed in m/s
Ca=(2*U*R)/(tan(b2*pi/180)-tan(b1*pi/180))#Axial velocity in m/s
W=m*U*Ca*(tan(a1*pi/180)+tan(a2*pi/180))*10**-3#Power output in kW
dh=W/ns#Stage enthalpy drop in kJ/kg
#output
print '(a)Power output is %3.2f kW\n(b)Stage enthalpy drop is %3.2f kJ/kg'%(W,dh)
# Answer in the textbook is not correct.
```

In [16]:

```
from __future__ import division
#input data
P0=800#Inlet pressure of hot gas in kPa
T1=973#Inlet temperature of hot gas in K
P2=100#Final pressure of hot gas in kPa
a1=73#Nozzle angle in degree
m=35#Mass flow rate in kg/s
ns=0.9#Nozzle efficiency
Cp=1.005#Specific heat of gas at constant pressure in kJ/kg.K
r=1.4#Ratio of specific heats of air
#calculations
b1=degrees(atan(tan(a1*pi/180)/2))#Inlet angle of the rotor blade in degree
b2=b1#Outlet angle of the rotor blade in degree
pi=2/tan(a1*pi/180)#Flow coefficient
psil=pi*(tan(b1*pi/180)+tan(b2*pi/180))#Blade loading coefficient
dh=ns*Cp*T1*(1-(P2/P0)**((r-1)/r))#Change in enthalpy in kJ/kg
W=m*dh*10**-3#Power developed in MW
#output
print '(a)Rotor blade angles\n Inlet angle of the rotor blade is %3.2f degree\n Outlet angle of the rotor blade is %3.2f degree\n(b)Flow coefficient is %3.3f\n(c)Blade loading coefficient is %3.f\n(d)Power developed is %3.1f MW'%(b1,b2,pi,psil,W)
# Answer in the textbook is not accurate.
```

In [17]:

```
from math import sin, pi
#Ex Page
#input data
P0=100#Initial pressure of steam in bar
T0=773#Initial temperature of steam in K
D=1#Turbine diameter in m
N=3000#Speed of turbine in rpm
m=100#Mass flow rate of steam in kg/s
a1=70#Exit angle of the first stage nozzle in degree
ns1=0.78#Stage efficiency of first stage
ns2=ns1#Stage efficiency of second stage
#calculations
U=(pi*D*N)/60#Mean blade speed in m/s
C1=(2*U)/sin(a1*pi/180)#Velocity of steam at exit from nozzle in m/s
b11=degrees(atan(tan(a1*pi/180)/2))#Inlet angle of the rotor blade in degree
b21=b11#Outlet angle of the rotor blade in degree
b12=b21#Inlet angle of the rotor blade in second stage in degree
b22=b12#Outlet angle of the rotor blade in second stage in degree
W=4*m*U**2*10**-6#Total work done in both the stages in MW
dh02=2*U**2*10**-3#Change in enthalpy in first stage of turbine in kJ/kg
dh02s=(dh02/ns1)#Change in enthalpy isentropically of turine first stage in kJ/kg
print 'The values of enthalpy and specific volume are taken from the mollier chart at inlet and exit conditions respectively'
h0=3370#Enthalpy at beginning of first stage in kJ/kg
h2=h0-dh02#Enthalpy at the end of first stage in kJ/kg
h2s=h0-dh02s#Isentropic enthalpy at the end of first stage in kJ/kg
v2=0.041#Specific volume at the end of first stage in m**3/kg
dh24=2*U**2*10**-3#Change in enthalpy in second stage of turbine in kJ/kg
dh24s=dh24/ns2#Change in enthalpy isentropically of turine second stage in kJ/kg
h4=h2-dh24#Enthalpy at beginning of second stage in kJ/kg
h4s=h2-dh24s#Isentropic enthalpy at the end of second stage in kJ/kg
v4=0.05#Specific volume at the end of second stage in m**3/kg
Ca=C1*cos(a1*pi/180)#Axial velocity in m/s
h1r=(m*v2)/(3.1415*D*Ca)#Blade height at first stage rotor exit in m
h2r=(m*v4)/(3.1415*D*Ca)#Blade height at second stage rotor exit in m
#output
print '\n\n(a)rotor blade angles\n Inlet angle of the rotor blade is %3.2f degree\n Outlet angle of the rotor blade is %3.2f degree\n Inlet angle of the rotor blade in second stage is %3.2f degres\n Outlet angle of the rotor blade in second stage is %3.2f degree\n(b)Total work done or Power developed in both the stages is %3.2f MW\n(c)final state of steam\n Enthalpy at beginning of first stage is %3i kJ/kg\n Enthalpy at the end of first stage is %3.2f kJ/kg\n Isentropic enthalpy at the end of first stage is %3.2f kJ/kg\n Specific volume at the end of first stage is %3.3f m**3/kg\n Enthalpy at beginning of second stage is %3.1f kJ/kg\n Isentropic enthalpy at the end of second stage is %3.2f kJ/kg\n Specific volume at the end of second stage is %3.2f m**3/kg\n(d)blade height\n Blade height at first stage rotor exit is %3.4f m\n Blade height at second stage rotor exit is %3.4f m'%(b11,b21,b12,b22,W,h0,h2,h2s,v2,h4,h4s,v4,h1r,h2r)
```

In [18]:

```
#input data
P0=100#Initial pressure of steam in bar
T0=773#Initial temperature of steam in K
D=1#Turbine diameter in m
N=3000#Speed of turbine in rpm
m=100#Mass flow rate of steam in kg/s
a1=70#Exit angle of the first stage nozzle in degree
ns=0.65#Stage efficiency of first stage
#calculations
U=(3.1415*D*N)/60#Mean blade speed in m/s
C1=(4*U)/sin(a1*pi/180)#Velocity of steam at exit from nozzle in m/s
Ca=C1*cos(a1*pi/180)#Axial velocity in m/s
Wx1=3*U#Inlet whirl velocity in m/s
b11=degrees(atan(Wx1/Ca))#Inlet angle of the rotor blade in degree
b21=b11#Outlet angle of the rotor blade in degree
C2=Ca#Velocity of steam at exit from stage in m/s
b22=degrees(atan(U/Ca))#Outlet angle of the rotor blade in degree
b12=b22#Inlet angle of the rotor blade in in degree
W=m*8*U**2*10**-6#Total work done or power developed in MW
print 'The values of enthalpy and specific volume are taken from the mollier chart at inlet and exit conditions respectively'
h0=3370#Enthalpy at beginning of stage in kJ/kg
dh04=(W*10**3)/m#Change in enthalpy of turbine in kJ/kg
dh04s=dh04/ns#Change in enthalpy isentropically of turine in kJ/kg
h4=h0-dh04#Enthalpy at beginning of stage in kJ/kg
h4s=h0-dh04s#Isentropic enthalpy at the end of stage in kJ/kg
v4=0.105#Specific volume at the end of stage in m**3/kg
h=(m*v4)/(3.1415*D*Ca)#Rotor blade height in m
print '\n\n(a)rotor blade angles\n Inlet angle of the rotor blade is %3.2f degree\n Outlet angle of the rotor blade is %3.2f degree\n Inlet angle of the rotor blade in second stage is %3.2f degres\n Outlet angle of the rotor blade in second stage is %3.2f degree\n(b)Total work done or Power developed in both the stages is %3.2f MW\n(c)final state of steam\n Enthalpy at beginning of first stage is %3i kJ/kg\n Enthalpy at beginning of stage is %3.1f kJ/kg\n Isentropic enthalpy at the end of stage is %3.2f kJ/kg\n Specific volume at the end of stage is %3.3f m**3/kg\n(d)rotor blade height is %3.4f m'%(b11,b21,b12,b22,W,h0,h4,h4s,v4,h)
```

In [19]:

```
#input data
a1=(90-30)#Nozzle angle in axial direction in degree
Ca=180#Axial velocity in m/s
U=280#Rotor blade speed in m/s
R=0.25#Degree of reaction
#calculations
Cx1=Ca*tan(a1*pi/180)#Velocity of whirl at inlet in m/s
b1=degrees(atan((Cx1-U)/Ca))#Blade angle at inlet in degree
b2=a1#Blade angle at exit in degree as degree of reaction is 0.5
#output
print '(a)Blade angle at inlet is %3i degree\n(b)Blade angle at exit is %3i degree'%(b1,b2)
```

In [20]:

```
#input data
R=0.5#Degree of reaction
ns=0.85#Stage efficiency
P0=800#Inlet pressure of hot gas in kPa
T0=900#Inlet temperature of hot gas in K
U=160#Blade speed in m/s
m=75#Mass flow rate of hot gas in kg/s
a1=70#Absolute air angle at first stage nozzle exit in degree
#calculations
C1=U/sin(a1*pi/180)#Velocity of steam at exit from nozzle in m/s
Ca=C1*cos(a1*pi/180)#Axial velocity of hot gas in m/s
C2=Ca#Velocity of steam at exit from stage in m/s
b1=0#Blade angle at inlet in degree as Wx1=0
a2=b1#Stator exit angle in degree as degree of reaction is 0.5
b2=a1#Blade angle at outlet in degree as degree of reaction is 0.5
Cx2=0#Velocity of whirl at outlet in m/s
Cx1=U#Velocity of whirl at inlet in m/s
W=m*U*(Cx1+Cx2)*10**-6#Power developed in MW
Wm=W*10**3/m#Work done per unit mass flow rate in kJ/kg
dhs=Wm/ns#Isentropic enthalpy drop in kJ/kg
#output
print '(a)Rotor blade angles\n Absolute air angle at first stage nozzle exit is %3i degree\n Blade angle at outlet is %3i degree\n Blade angle at inlet is %3i degree\n Stator exit angle is %3i degree\n(b)Power developed is %3.2f MW\n(c)Isentropic enthalpy drop is %3.2f kJ/kg'%(a1,b2,b1,a2,W,dhs)
```

In [21]:

```
from __future__ import division
from math import pi
#input data
b1m=46#Rotor blade angle at entry at mean section in degree
b2m=75#Rotor blade angle at exit at mean section in degree
a1m=75#Nozzle angle at exit at mean section in degree
DhDt=0.6#Hub to tip ratio
N=7500#Mean rotor speed in rpm
Dh=0.45#Hub diameter in m
#calculations
R=0.5#Degree of reaction as a1m=b2m
a2m=b1m#Stator angle at exit at mean section in degree
Dm=(Dh+(Dh/DhDt))/2#Mean diameter of turbine at mean section in m
Um=(pi*DhDt*N)/60#Mean blade speed in m/s
Ca=Um/(tan(a1m*pi/180)-tan(b1m*pi/180))#Axial velocity in m/s
fi=Ca/Um#Flow coefficient
psil=fi*(tan(b1m*pi/180)+tan(b2m*pi/180))#Blade loading coefficient
a1h=degrees(atan(tan(a1m*pi/180)*((Dm/2)/(Dh/2))))#Nozzle angle at inlet at root section in degree
Uh=(3.14*Dh*N)/60#Blade speed at root section in m/s
b1h=degrees(atan(tan(a1h*pi/180)-(Uh/Ca)))#Rotor blade angle at entry at root section in degree
a2h=degrees(atan(tan(a2m*pi/180)*((Dm/2)/(Dh/2))))#Stator angle at exit at root section in degree
b2h=degrees(atan((Uh/Ca)+tan(a2h*pi/180)))#Rotor blade angle at exit at root section in degree
pih=Ca/Uh#Flow coefficient at root section
Rh=(pih/2)*(tan(b2h*pi/180)-tan(b1h*pi/180))#Degree of reaction at root section
psilh=pih*(tan(b1h*pi/180)+tan(b2h*pi/180))#Blade loading coefficient at root section
#output
print 'Mean section\n (a)Degree of reaction is %3.1f\n (b)Blade loading coefficient is %3.2f\nRoot section (a)Degree of reaction is %3.2f\n (b)Blade loading coefficient is %3.2f'%(R,psil,Rh,psilh)
```

In [22]:

```
#input data
T00=973#Total head inlet temperature in K
P00=4.5#Total head inlet pressure in bar
P2=1.6#Static head outlet pressure in bar
m=20#Gas flow rate in kg/s
a1=(90-28)#Nozzle outlet angle measured perpendicular to blade velocity in degree
Dmh=10#Mean blade diameter to blade height ratio
NLC=0.1#Nozzle loss coefficient
Cp=1155.6#Specific heat of gas at a constant pressure in kJ/kg
R=289#Gas constant in J/kg
r=1.333#Ratio of specific heats of gas
#calculations
T2ss=T00*(P2/P00)**((r-1)/r)#Isentropic temperature at outlet in mid section in K here T00=T01
T1s=T2ss#Isentropic temperature at inlet at mid section in K
C1m=(2*Cp*(T00-T1s)/1.1)**(1/2)#Velocity of steam at exit from nozzle at mid section in m/s
T1=T00-((C1m**2)/(2*Cp))#Gas temperature at mid section in K
d=(P2*10**5)/(R*T1)#Density of gas in kg/m**3
Rg=(Cp*(r-1)/r)#Gas constant of the gas in kJ/kg
Ca=C1m*cos(a1*pi/180)#Axial velocity in m/s
h=((m/(d*Ca))*(1/(Dmh*3.1415)))**(1/2)#Hub height in m
Dm=Dmh*h#Mean blade diameter in m
Dh=Dm-h#Hub diameter in m
a1h=degrees(atan(((Dm/2)/(Dh/2))*tan(a1*pi/180)))#Discharge angle at hub in degree
C1h=Ca/cos(a1h*pi/180)#Gas velocity at hub section in m/s
T1h=T00-((C1h**2)/(2*Cp))#Gas temperature at hub in K here T01=T00
Dt=Dm+h#Tip diameter in m
a1t=degrees(atan(((Dm/2)/(Dt/2))*tan(a1*pi/180)))#Gas discharge angle at tip in degree
C1t=Ca/cos(a1t)#Gas velocity at tip in m/s
T1t=T00-((C1t**2)/(2*Cp))#Gas temperature in K here T00=T01
#output
print '(a)At mid section\n Gas velocity is %3.1f m/s\n Gas temperature is %3.1f K\n Gas discharge angle is %3i degree\n(b)At hub section\n Gas velocity is %3.1f m/s\n Gas temperature is %3.2f K\n Gas discharge angle is %3.2f degree\n(c)At tip section\n Gas velocity is %3.1f m/s\n Gas temperature is %3.2f K\n Gas discharge angle is %3.2f degree'%(C1m,T1,a1,C1h,T1h,a1h,C1t,T1t,a1t)
```

In [23]:

```
from math import sin, cos, atan, tan, pi, degrees
#input data
a1=75#Nozzle air angle in degree
Rh=0#Degree of reaction
N=6000#Running speed of hub in rpm
Dh=0.45#Hub diameter in m
Df=0.75#Tip diameter in m
#calculations
Uh=(3.1415*Dh*N)/60#Hub speed in m/s
C1h=Uh/((sin(a1*pi/180))/2)#Velocity of steam at exit from nozzle in hub in m/s
Cah=C1h*cos(a1*pi/180)#Axial velocity at hub in m/s
Cx1h=C1h*sin(a1*pi/180)#Whirl component of velocity at inlet in hub in m/s
b1h=degrees(atan((Cx1h-Uh)/Cah))#Rotor blade angle at entry at hub section in degree
b2h=b1h#Rotor blade angle at exit at mean section in degree as zero reaction section
sopt=sin(a1*pi/180)/2#Blade to gas speed ratio at hub
rm=((Dh/2)+(Df/2))/2#Mean radius in m
rmrh=(rm/(Dh/2))**((sin(a1*pi/180))**2)#Ratio of inlet velocity at hub and mean for constant nozzle air angle at hub section
C1m=C1h/rmrh#Velocity of steam at exit from nozzle at mean section in m/s
Cx1m=Cx1h/rmrh#Velocity of whirl at inlet at mean section in m/s
Ca1m=Cah/rmrh#Axial velocity at mean section in m/s
Um=(3.1415*2*rm*N)/60#Mean blade speed in m/s
b1m=degrees(atan((Cx1m-Um)/Ca1m))#Rotor blade angle at entry at mean section in degree
b2m=degrees(atan(Um/Ca1m))#Rotor blade angle at exit at mean section in degree for axial exit Cx2=0
s=Um/C1m#Blade to gas ratio at mean
Rm=(Ca1m/(2*Um))*(tan(b2m*pi/180)-tan(b1m*pi/180))#Degree of reaction of mean section
rmrt=((rm)/(Df/2))**((sin(a1*pi/180))**2)#Ratio of inlet velocity at tip and mean for constant nozzle air angle at tip section
C1t=C1m*rmrt#Velocity of steam at exit from nozzle at tip section in m/s
Cx1t=Cx1m*rmrt#Velocity of whirl at inlet at tip section in m/s
Ca1t=Ca1m*rmrt#Axial velocity at tip section in m/s
Ut=(3.1415*Df*N)/60#Mean tip speed in m/s
b1t=degrees(atan((Cx1t-Ut)/Ca1t))#Rotor blade angle at entry at tip section in degree
b2t=degrees(atan(Ut/Ca1t))#Rotor blade angle at exit at tip section in degree for axial exit Cx2=0
st=Ut/C1t#Blade to gas ratio at tip
Rf=(Ca1t/(2*Ut))*(tan(b2t*pi/180)-tan(b1t*pi/180))#Degree of reaction of tip section
#output
print '(1)Hub section\n (a)\n Absolute air angle is %3.2f degree\n Relative air angle is %3.2f degree\n (b)Blade to gas speed ratio is %3.3f\n (c)Degree of reaction is %3i\n(2)Mean section\n (a)\n Absolute air angle is %3.2f degree\n Relative air angle is %3.2f degree\n (b)Blade to gas speed ratio is %3.3f\n (c)Degree of reaction is %3.3f\n(3)Tip section\n (a)\n Absolute air angle is %3.2f degree\n Relative air angle is %3.2f degree\n (b)Blade to gas speed ratio is %3.3f\n (c)Degree of reaction is %3.3f\n'%(b1h,b2h,sopt,Rh,b1m,b2m,s,Rm,b1t,b2t,st,Rf)
```