In [1]:

```
from __future__ import division
from math import tan, pi
#input data
b1=60#The angle made by the relative velocity vector at exit in degree
db=30#The turning angle in degree
dCx=100#The change in the tangential velocities in m/s
DR=0.5#Degree of reaction
N=36000#The speed of the compressor in rpm
D=0.14#Mean blade diameter in m
P1=2#Inlet pressure in bar
T1=330#Inlet temperature in K
b=0.02#Blade height in m
R=287#The universal gas constant in J/kg.K
Cp=1.005#The specific heat of air at constant pressure in kJ/kg.K
r=1.4#The ratio of specific heats of air
#calculations
b2=b1-db#The angle made by the relative velocity vector at entry in degree
a1=b2#Air flow angle at exit in degree as DR=0.5
U=(3.1415*D*N)/60#The blade mean speed in m/s
T2=((U*dCx)/(Cp*1000))+T1#The exit air temperature in K
P2=P1*(T2/T1)**(r/(r-1))#The exit air pressure in bar
dP=P2-P1#The pressure rise in bar
Ca=(2*U*DR)/(tan(b2*pi/180)+tan(b1*pi/180))#The axial velocity in m/s
A1=3.1415*D*b#The inlet flow area in m**2
d1=(P1*10**5)/(R*T1)#The inlet air density in kg/m**3
m=d1*A1*Ca#The amount of air handled in kg/s
W=m*Cp*(T2-T1)#The power developed in kW
#output
print '(a)Air flow angle at exit is %3i degree\n(b)The pressure rise is %3.2f bar\n(c)The amount of air handled is %3.2f kg/s\n(d)The power developed is %3.1f kW'%(a1,dP,m,W)
# The answer in the textbook is not correct.
```

In [2]:

```
from math import log10
#input data
P01=1#Atmospheric pressure at inlet in bar
T01=291#Atmospheric temperature at inlet in K
T02=438#Total head temperature in delivery pipe in K
P02=3.5#Total head pressure in delivery pipe in bar
P2=3#Staic pressure in delivery pipe in bar
R=287#The universal gas constant in J/kg.K
Cp=1005#The specific heat of air at constant pressure in J/kg.K
r=1.4#The ratio of specific heats of air
#calculations
T02s=T01*(P02/P01)**((r-1)/r)#Total isentropic head temperature in delivery pipe in K
nc=(T02s-T01)/(T02-T01)#Total head isentropic efficiency
np=((log10(P02/P01))/((r/(r-1))*(log10(T02/T01))))#Polytropic efficiency
T2=T02*(P2/P02)**((r-1)/r)#Static temperature in delivery pipe in K
C2=(2*Cp*(T02-T2))**(1/2)#The air velocity in delivery pipe in m/s
#output
print '(a)Total head isentropic efficiency is %0.1f %%\n(b)Polytropic efficiency %0.1f %%\n(c)The air velocity in delivery pipe is %3.2f m/s'%(nc*100,np*100,C2)
```

In [3]:

```
from math import atan, degrees
#input data
N=8#Number of stages
Po=6#Overall pressure ratio
T01=293#Temperature of air at inlet in K
nc=0.9#Overall isentropic efficiency
DR=0.5#Degree of reaction
U=188#Mean blade speed in m/s
Ca=100#Constant axial velocity in m/s
R=287#The universal gas constant in J/kg.K
Cp=1005#The specific heat of air at constant pressure in J/kg.K
r=1.4#The ratio of specific heats of air
#calculations
T0n1s=T01*(Po)**((r-1)/r)#The isentropic temperature of air leaving compressor stage in K
T0n1=((T0n1s-T01)/nc)+T01#The temperature of air leaving compressor stage in K
dta2ta1=(Cp*(T0n1-T01))/(N*U*Ca)#The difference between tan angles of air exit and inlet
sta1tb1=U/Ca#The sum of tan of angles of air inlet and the angle made by the relative velocity
b1=degrees(atan((dta2ta1+sta1tb1)/2))#The angle made by the relative velocity vector at exit in degree as the DR=1 then a2=b1
a1=degrees(atan(tan(b1*pi/180)-dta2ta1))#Air flow angle at exit in degree
W=Cp*(T0n1-T01)*10**-3#Power required per kg of air/s in kW
#output
print '(a)Power required is %3.2f kW\n(b)\n (1)Air flow angle at exit is %.f degree \n (2)The angle made by the relative velocity vector at exit is %.f degree'%(W,a1,b1)
```

In [4]:

```
#input data
W=4.5#Power absorbed by the compressor in MW
m=20#Amount of air delivered in kg/s
P01=1#Stagnation pressure of air at inlet in bar
T01=288#Stagnation temperature of air at inlet in K
np=0.9#Polytropic efficiency of compressor
dT0=20#Temperature rise in first stage in K
R=287#The universal gas constant in J/kg.K
Cp=1.005#The specific heat of air at constant pressure in kJ/kg.K
r=1.4#The ratio of specific heats of air
#calculations
T02=T01+dT0#Stagnation temperature of air at outlet in K
T0n1=((W*10**3)/(m*Cp))+T01#The temperature of air leaving compressor stage in K
P0n1=P01*(T0n1/T01)**((np*r)/(r-1))#Pressure at compressor outlet in bar
P1=(T02/T01)**((np*r)/(r-1))#The pressure ratio at the first stage
N=((log10(P0n1/P01)/log10(P1)))#Number of stages
T0n1T01=(P0n1/P01)**((r-1)/(np*r))#The temperature ratio at the first stage
T0n1sT01=(P0n1/P01)**((r-1)/r)#The isentropic temperature ratio at the first stage
nc=((T0n1sT01-1)/(T0n1T01-1))#The overall isentropic efficiency
#output
print '(a)Pressure at compressor outlet is %3.2f bar\n(b)Number of stages is %3.f\n(c)The overall isentropic efficiency is %0.1f %%'%(P0n1,N,nc*100)
```

In [5]:

```
from math import log
#input data
DR=0.5#Degree of reaction
b1=44#Blade inlet angle in degree
b2=13#Blade outlet angle in degree
Po=5#The pressure ratio produced by the compressor
nc=0.87#The overall isentropic efficiency
T01=290#Inlet temperature in K
U=180#Mean blade speed in m/s
l=0.85#Work input factor
R=0.287#The universal gas constant in kJ/kg.K
Cp=1005#The specific heat of air at constant pressure in J/kg.K
r=1.4#The ratio of specific heats of air
#calculations
a2=b1#Air flow angle at entry in degree as DR=0.5
a1=b2#Air flow angle at exit in degree as DR=0.5
T0n1s=T01*(Po)**((r-1)/r)#The isentropic temperature of air leaving compressor stage in K
T0n1=((T0n1s-T01)/nc)+T01#The temperature of air leaving compressor stage in K
Ca=U/(tan(b2*pi/180)+tan(b1*pi/180))#The axial velocity in m/s
N=((Cp*(T0n1-T01))/(l*U*Ca*(tan(a2*pi/180)-tan(a1*pi/180))))#The number of stages
ds=(Cp*(10**-3)*log(T0n1/T01))-(R*log(Po))#Change in entropy in kJ/kg.K
#output
print '(a)The number of stages are %3.f\n(b)The change in entropy is %3.3f kJ/kg-K'%(N,ds)
```

In [6]:

```
#input data
D=0.6#Mean diameter of compressor in m
N=15000#Running speed of the compressor in rpm
dT=30#Actual overall temperature raise in K
PR=1.3#Pressure ratio of all stages
m=57#Mass flow rate of air in kg/s
nm=0.86#Mechanical efficiency
T1=308#Initial temperature in K
T2=328#Temperature at rotor exit in K
r=1.4#The ratio of specific heats of air
Cp=1.005#The specific heat of air at constant pressure in kJ/kg.K
#calculations
W=m*Cp*dT#Work done in kW
P=W/nm#Power required in kW
ns=((T1*((PR**((r-1)/r))-1))/(dT))#Stage efficiency
R=(T2-T1)/(dT)#Reaction ratio
#output
print '(a)Power required to drive the compressor is %3.3f kW\n(b)The stage efficiency is %0.2f %%\n(c)The degree of reaction is %3.2f'%(P,ns*100,R)
```

In [7]:

```
#input data
Pr=2#The pressure ratio of first stage
P1=1.01#The inlet pressure in bar
T1=303#The inlet temperature in K
nc=0.83#Overall efficency of the compressor
pi=0.47#The flow coefficient
dCxCa=0.5#Ratio of change of whirl velocity to axial velocity
D=0.5#Mean diameter in m
r=1.4#The ratio of specific heats of air
Cp=1005#The specific heat of air at constant pressure in J/kg.K
#calculations
dT=T1*((Pr**((r-1)/r))-1)/nc#The Actual overall temperature raise in K
dCx=dCxCa*pi#The change of whirl velocity in m/s
U=(dT*Cp/dCx)**(1/2)#The mean blade speed in m/s
N=(U*60)/(3.1415*D)#Speed at which compressor runs in rpm
Cx2=(U+(dCx*U))/2#The whirl velocity at exit in m/s
Cx1=U-Cx2#The whirl velocity at entry in m/s
Ca=pi*U#The axial velocity in m/s
C1=((Ca**2)+(Cx1**2))**(1/2)#The inlet absolute velocity of air in m/s
#output
print '(a)The compressor speed is %3i rpm\n(b)The absolute velocity of air is %3.2f m/s'%(N,C1)
```

In [8]:

```
from math import acos, asin, sin,cos, sqrt, degrees, pi, atan, tan
from __future__ import division
#input data
N=9000#The rotational speed in rpm
dT0=20#The stagnation temperature rise in K
DhDt=0.6#The hub to tip ratio
l=0.94#The work donee factor
ns=0.9#The isentropic efficiency of the stage
C1=150#Inlet velocity in m/s
P01=1#The ambient pressure in bar
T01=300#The ambient temperature in K
Mr1=0.92#Mach number relative to tip
R=287#The universal gas constant in J/kg.K
Cp=1005#The specific heat of air at constant pressure in kJ/kg.K
r=1.4#The ratio of specific heats of air
g=9.81#Acceleration due to gravity in m/s**2
#calculations
T1=T01-((C1**2)/(2*Cp))#The inlet temperature in K
W1=Mr1*sqrt(r*R*T1)#The relative velocity at entry in m/s
b11=degrees(acos((C1)/(W1)))#The inlet rotor angle at tip in degree
Ut=W1*sin(b11*pi/180)#Tip speed in m/s
rt=(Ut*60)/(2*3.1415*N)#The tip radius in m
b12=degrees(atan((tan(b11*pi/180)))-((Cp*dT0)/(l*Ut*C1)))#The outlet rotor angle at tip in degree
P1=P01*(T1/T01)**(r/(r-1))#The inlet pressure in bar
d1=(P1*10**5)/(R*T1)#The density of air at the entry in kg/m**3
Dt=2*rt#The tip diameter in m
Dh=DhDt*(Dt)#The hub diameter in m
A1=(3.141/4)*((Dt**2)-(Dh**2))#The area of cross section at the entry in m**2
rm=((Dt/2)+(Dh/2))/2#The mean radius in m
h=((Dt/2)-(Dh/2))#The height of the blade in m
A=2*3.1415*rm*h#The area of the cross section in m**2
m=d1*A*C1#The mass flow rate in kg/s
P03P01=(1+((ns*dT0)/T01))**(r/(r-1))#The stagnation pressure ratio
P=m*Cp*dT0*10**-3#The power required in kW
Uh=(3.1415*Dh*N)/60#The hub speed in m/s
b21=degrees(atan(Uh/C1))#The rotor air angle at entry in degree
b22=degrees(atan(tan(b21*pi/180)-((Cp*dT0)/(l*Uh*C1))))#The rotor air angle at exit in degree
#output
print '(a)\n (1)The tip radius is %3.3f m\n (2)The rotor entry angle at tip section is %3.1f degree\n (3)The rotor exit angle at tip section is %3.2f degree\n(b)Mass flow entering the stage is %3.3f kg/s\n(c)\n (1)The stagnation pressure ratio is %3.3f\n (2)The power required is %3.2f kW\n(d)\n (1)The rotor air angle at entry is %3.2f degree\n (2)The rotor air angle at exit is %3.2f degree'%(rt,b11,b12,m,P03P01,P,b21,b22)
#the answer in the textbook is not correct.
```

In [9]:

```
#input data
Ur=150#The blade root velocity in m/s
Um=200#The mean velocity in m/s
Ut=250#The tip velocity in m/s
dT0=20#The total change in temperature in K
Ca=150#The axial velocity in m/s
l=0.93#The work done factor
Rm=0.5#Reaction at mean radius
R=287#The universal gas constant in J/kg.K
Cp=1005#The specific heat of air at constant pressure in J/kg.K
r=1.4#The ratio of specific heats of air
#calculations
dtb1tb2=((Cp*dT0)/(l*Um*Ca))#The difference between the tangent angles of blade angles at mean
atb1tb2=((2*Rm*Um)/(Ca))#The sum of the tangent angles of blade angles at mean
b1m=degrees(atan((atb1tb2+dtb1tb2)/2))#The inlet blade angle in degree at mean
a2m=b1m#The exit air angle in degree as the Reaction at mean radius is 0.5
b2m=degrees(atan(tan(b1m*pi/180)-dtb1tb2))#The exit blade angle in degree at mean
a1m=b2m#The inlet air angle in degree as the reaction at mean radius is 0.5
rmrh=Um/Ur#The ratio of radii of mean and root velocities at hub
a1h=degrees(atan(tan(a1m*pi/180)*(rmrh)))#The inlet air angle in degree at hub
b1h=degrees(atan((Ur/Ca)-(tan(a1h*pi/180))))#The inlet blade angle in degree at hub
a2h=degrees(atan(tan(a2m*pi/180)*(rmrh)))#The outlet air angle in degree at hub
b2h=degrees(atan((Ur/Ca)-(tan(a2h*pi/180))))#The outlet blade angle in degree at hub
Rh=((Ca*(tan(b1h*pi/180)+tan(b2h*pi/180)))/(2*Ur))#The degree of reaction at the hub
rmrt=Um/Ut#The ratio of radii of mean and tip velocities at tip
a1t=degrees(atan(tan(a1m)*(rmrt)))#The inlet air angle in degree at tip
b1t=degrees(atan((Ut/Ca)-(tan(a1t*pi/180))))#The inlet blade angle in degree at tip
a2t=degrees(atan(tan(a2m)*(rmrt)))#The outlet air angle in degree at tip
b2t=degrees(atan((Ut/Ca)-(tan(a2t*pi/180))))#The outlet blade angle in degree at tip
Rt=((Ca*(tan(b1t*pi/180)+tan(b2t*pi/180)))/(2*Ut))#The degree of reaction at tip
#output
print '(a)At the mean\n (1)The inlet blade angle is %3.2f degree\n (2)The inlet air angle is %3.2f degree\n (3)The outlet blade angle is %3.2f degree\n (4)The outlet air angle is %3.2f degree\n (5)Degree of reaction is %3.1f \n(b)At the root\n (1)The inlet blade angle is %3.2f degree\n (2)The inlet air angle is %3.2f degree\n (3)The outlet blade angle is %3.2f degree\n (4)The outlet air angle is %3.2f degree\n (5)Degree of reaction is %3.3f\n(c)At the tip\n (1)The inlet blade angle is %3.2f degree\n (2)The inlet air angle is %3.2f degree\n (3)The outlet blade angle is %3.2f degree\n (4)The outlet air angle is %3.2f degree\n (5)Degree of reaction is %3.3f\n'%(b1m,a1m,b2m,a2m,Rm,b1h,a1h,b2h,a2h,Rh,b1t,a1t,b2t,a2t,Rt)
#the answer in the textbook is not correct.
```

In [10]:

```
#input data
Uh=150#The blade root velocity in m/s
Um=200#The mean velocity in m/s
Ut=250#The tip velocity in m/s
dT0=20#The total change in temperature in K
Ca1m=150#The axial velocity in m/s
l=0.93#The work done factor
Rm=0.5#Reaction at mean radius
N=9000#Rotational speed in rpm
R=287#The universal gas constant in J/kg.K
Cp=1005#The specific heat of air at constant pressure in J/kg.K
r=1.4#The ratio of specific heats of air
#calculations
dtb1tb2=((Cp*dT0)/(l*Um*Ca1m))#The difference between the tangent angles of blade angles at mean
atb1tb2=((2*Rm*Um)/(Ca1m))#The sum of the tangent angles of blade angles at mean
b1m=degrees(atan((atb1tb2+dtb1tb2)/2))#The inlet blade angle in degree at mean
a2m=b1m#The exit air angle in degree as the Reaction at mean radius is 0.5
b2m=degrees(atan(tan(pi/180*b1m)-dtb1tb2))#The exit blade angle in degree at mean
a1m=b2m#The inlet air angle in degree as the reaction at mean radius is 0.5
Dh=(Uh*60)/(3.141*N)#Hub diameter in m
Dm=(Um*60)/(3.141*N)#Mean diameter in m
Cx1m=Ca1m*tan(pi/180*a1m)#The whirl velocity at inlet at mean in m/s
Cx2m=Ca1m*tan(pi/180*a2m)#The whirl velocity at exit at mean in m/s
Cx1h=(Cx1m*(Dh/2)/(Dm/2))#The whirl velocity at inlet at hub in m/s
Cx2h=(Cx2m*(Dh/2)/(Dm/2))#The whirl velocity at exit at hub in m/s
K1=(Ca1m**2)+(2*(Cx1m**2))#Sectional velocity in m/s
Ca1h=((K1)-(2*(Cx1h**2)))**(1/2)#The axial velocity at hub inlet in (m/s)**2
w=(2*3.141*N)/60#Angular velocity of blade in rad/s
K2=(Ca1m**2)+(2*(Cx2m**2))-(2*((Cx2h/(Dh/2))-(Cx1m/(Dm/2))))*(w*(Dm/2)**(2))#Sectional velocity in (m/s)**2
Ca2h=(K2-(2*Cx2h**2)+(2*((Cx2h/(Dh/2))-(Cx1h/(Dh/2))))*(w*(Dh/2)**(2)))**(1/2)#Axial velocity at hub outlet in m/s
a1h=degrees(atan(Cx1h/Ca1h))#Air angle at inlet in hub in degree
b1h=degrees(atan((Uh-Cx1h)/Ca1h))#Blade angle at inlet in hub in degree
a2h=degrees(atan(Cx2h/Ca2h))#Air angle at exit in hub in degree
b2h=degrees(atan((Uh-Cx2h)/Ca2h))#Blade angle at exit in hub in degree
W1=Ca1h/cos(pi/180*b1h)#Relative velocity at entry in hub in m/s
W2=Ca2h/cos(pi/180*b2h)#Relative velocity at exit in hub in m/s
Rh=((W1**2)-(W2**2))/(2*Uh*(Cx2h-Cx1h))#The degree of reaction at hub
Dt=(Ut*60)/(3.141*N)#Tip diameter in m
Cx1t=(Cx1m*(Dt/2)/(Dm/2))#The whirl velocity at inlet at tip in m/s
Cx2t=(Cx2m*(Dt/2)/(Dm/2))#The whirl velocity at exit at tip in m/s
Ca1t=(K1-(2*Cx1t**2))**(1/2)#Axial velocity at tip inlet in m/s
Ca2t=(K2-(2*Cx2t**2)+(2*((Cx2t/(Dt/2))-(Cx1t/(Dt/2))))*(w*(Dt/2)**(2)))**(1/2)#Axial velocity at tip outlet in m/s
a1t=degrees(atan(Cx1t/Ca1t))#Air angle at inlet in tip in degree
b1t=degrees(atan((Ut-Cx1t)/Ca1t))#Blade angle at inlet in tip in degree
a2t=degrees(atan(Cx2t/Ca2t))#Air angle at exit in tip in degree
b2t=degrees(atan((Ut-Cx2t)/Ca2t))#Blade angle at exit in tip in degree
W1=Ca1t/cos(pi/180*b1t)#Relative velocity at entry in tip in m/s
W2=Ca2t/cos(pi/180*b2t)#Relative velocity at exit in tip in m/s
Rt=((W1**2)-(W2**2))/(2*Ut*(Cx2t-Cx1t))#The degree of reaction at tip
#output
print '(a)At the mean\n (1)The inlet blade angle is %3.2f degree\n (2)The inlet air angle is %3.2f degree\n (3)The outlet blade angle is %3.2f degree\n (4)The outlet air angle is %3.2f degree\n (5)Degree of reaction is %3.1f \n(b)At the root\n (1)The inlet blade angle is %3.2f degree\n (2)The inlet air angle is %3.1f degree\n (3)The outlet blade angle is %3.1f degree\n (4)The outlet air angle is %3.1f degree\n (5)Degree of reaction is %3.1f\n(c)At the tip\n (1)The inlet blade angle is %3.2f degree\n (2)The inlet air angle is %3.2f degree\n (3)The outlet blade angle is %3.2f degree\n (4)The outlet air angle is %3.2f degree\n (5)Degree of reaction is %3.1f\n'%(b1m,a1m,b2m,a2m,Rm,b1h,a1h,b2h,a2h,Rh,b1t,a1t,b2t,a2t,Rt)
# the answer in the textbook is not correct.
```

In [11]:

```
#input data
N=3600#Running speed of blower in rpm
Dt=0.2#The rotor tip diameter in m
Dh=0.125#The rotor hub diameter in m
P1=1.013#The atmospheric pressure in bar
T1=298#The atmospheric temperature in K
m=0.5#Mass flow rate of air in kg/s
db=20#The turning angle of the rotor in degree
b1=55#The inlet blade angle in degree
R=287#The universal gas constant in J/kg.K
nc=0.9#Total-to-total efficiency
P=0.25#Total pressure drop across the intake in cm of water
Cp=1005#The specific heat of air at constant pressure in J/kg.K
r=1.4#The ratio of specific heats of air
g=9.81#Acceleration due to gravity in m/s**2
ns=0.75#The stator efficiency
dw=1000#Density of water in kg/m**3
#calculations
d1=(P1*10**5)/(R*T1)#The density of air at inlet in kg/m**3
A=(3.141/4)*((Dt**2)-(Dh**2))#The area of flow in m**2
Ca=m/(d1*A)#The axial velocity of air in m/s
U=((3.141*(Dt+Dh)*N)/(2*60))#Mean rotor blade velocity in m/s
b2=b1-db#The outlet blade angle in degree
Cx2=U-(Ca*tan(pi/180*b2))#The whirl velocity at exit in m/s
Cx1=0#The whirl velocity at entry in m/s as flow at inlet is axial
dh0r=U*(Cx2-Cx1)#The actual total enthalpy rise across the rotor in J/kg
dh0sr=nc*dh0r#The isentropic total enthalpy rise across the rotor in J/kg
dP0r=(d1*dh0sr)*((10**-1)/(g))#The total pressure rise across the rotor in cm of water
P0=dP0r-P#Stagnation pressure at the rotor exit in cm of water
C2=((Ca**2)+(Cx2**2))**(1/2)#The absolute velocity at the exit in m/s
dPr=dP0r-((d1*((C2**2)-(Ca**2)))/2)*((10**-1)/g)#The static pressure across the rotor in cm of water
dhs=((C2**2)-(Ca**2))/2#The actual enthalpy change across the stator in J/kg
dhss=ns*dhs#The theoretical enthalpy change across the stator in J/kg
dPs=(d1*dhss)*((10**-1)/g)#The static pressure rise across the stator in cm of water
dP0s=-((dPs/((10**-1)/g))+((d1/2)*(Ca**2-C2**2)))*(10**-1/g)#The change in total pressure across the stator in cm of water
P03=P0-dP0s#Total pressure at stator inlet in cm of water
dh0ss=((dw*g*(P03/100))/d1)#Theoretical total enthalpy change across the stage in J/kg
ntt=dh0ss/dh0r#The overall total-to-total efiiciency
DR=dPr/(dPr+dPs)#The degree of reaction for the stage
#output
print '(a)Total pressure of air exit of rotor is %3.2f cm of water\n(b)The static pressure rise across the rotor is %3.2f cm of water\n(c)The static pressure rise across the stator os %3.2f cm of water\n(d)The change in total pressure across the stator is %3.2f cm of water\n(e)The overall total-to-total efficiency is %0.1f %%\n(f)The degree of reaction for the stage is %0.1f %%'%(P0,dPr,dPs,dP0s,ntt*100,DR*100)
```

In [12]:

```
#input data
Q=2.5#The amount of air which fan takes in m**3/s
P1=1.02#The inlet pressure of air in bar
T1=315#The inlet temperature of air in K
dH=0.75#The pressure head delivered by axial flow fan in m W.G
T2=325#The delivery temperature of air in K
R=287#The universal gas constant in J/kg.K
Cp=1.005#The specific heat of air at constant pressure in kJ/kg.K
r=1.4#The ratio of specific heats of air
g=9.81#Acceleration due to gravity in m/s**2
#calculations
d=(P1*10**5)/(R*T1)#The density of air in kg/m**3
m=d*Q#The mass flow rate of air in kg/s
W=m*Cp*(T2-T1)#Power required to drive the fan in kW
dP=((10**3)*g*dH)/(10**5)#The overall pressure difference in bar
P2=P1+(dP)#The exit pressure in bar
nf=((T1*(((P2/P1)**((r-1)/r))-1))/(T2-T1))#Static fan efficiency
#output
print '(a)Mass flow rate through the fan is %3.2f kg/s\n(b)Power required to drive the fan is %3.2f kW\n(c)Static fan efficiency is %0.2f %%'%(m,W,nf*100)
```

In [13]:

```
#input data
b2=10#Rotor blade air angle at exit in degree
Dt=0.6#The tip diameter in m
Dh=0.3#The hub diameter in m
N=960#The speed of the fan in rpm
P=1#Power required by the fan in kW
pi=0.245#The flow coefficient
P1=1.02#The inlet pressure in bar
T1=316#The inlet temperature in K
R=287#The universal gas constant in J/kg.K
Cp=1.005#The specific heat of air at constant pressure in kJ/kg.K
r=1.4#The ratio of specific heats of air
g=9.81#Acceleration due to gravity in m/s**2
#calculations
A=(3.141/4)*((Dt**2)-(Dh**2))#Area of the fan at inlet in m**2
Dm=(Dt+Dh)/2#The mean rotor diameter in m
U=(3.141*Dm*N)/60#The mean blade speed in m/s
Ca=pi*U#The axial velocity in m/s
Q=A*Ca#The flow rate of air in m**3/s
d=(P1*10**5)/(R*T1)#Density of air in kg/m**3
dPst=((d*(U**2)*(1-((pi*tan(pi/180*b2))**2)))/2)*((10**5)/(g*(10**3)))*10**-5#Static pressure across the stage in m W.G
Wm=U*(U-(Ca*tan(pi/180*b2)))#Work done per unit mass in J/kg
m=d*Q#Mass flow rate in kg/s
W=m*Wm#Work done in W
no=W/(P*10**3)#Overall efficiency
#output
print '(a)THe flow rate is %3.3f m**3/s\n(b)Static pressure rise across the stage is %3.3f m W.G\n(c)The overall efficiency is %0.2f %%'%(Q,dPst,no*100)
# the answer for last part is not accurate.
```

In [14]:

```
#input data
b2=10#Rotor blade air angle at exit in degree
Dt=0.6#The tip diameter in m
Dh=0.3#The hub diameter in m
N=960#The speed of the fan in rpm
P=1#Power required by the fan in kW
pi=0.245#The flow coefficient
P1=1.02#The inlet pressure in bar
T1=316#The inlet temperature in K
R=287#The universal gas constant in J/kg.K
Cp=1.005#The specific heat of air at constant pressure in kJ/kg.K
r=1.4#The ratio of specific heats of air
g=9.81#Acceleration due to gravity in m/s**2
#calculations
A=(3.141/4)*((Dt**2)-(Dh**2))#Area of the fan at inlet in m**2
Dm=(Dt+Dh)/2#The mean rotor diameter in m
U=(3.141*Dm*N)/60#The mean blade speed in m/s
Ca=pi*U#The axial velocity in m/s
Q=A*Ca#The flow rate of air in m**3/s
d=(P1*10**5)/(R*T1)#Density of air in kg/m**3
b1=degrees(atan(U/Ca))#Rotor blade angle at entry in degree
dPst=((d*(U**2)*(1-((pi*tan(pi/180*b2))**2)))/2)#Static pressure rise across the stage in N/m**2
dPr=dPst#Static pressure rise across the rotor in N/m**2
Wm=U*(U-(Ca*tan(pi/180*b2)))#Work done per unit mass in J/kg
dP0st=d*Wm#Stagnation pressure of the stage in N/m**2
DR1=dPr/dP0st#Degree of reaction
DR2=(Ca/(2*U))*(tan(pi/180*b1)+tan(pi/180*b2))#Degree of reaction
#output
print '(a)Rotor blade angle at entry is %3.2f degree\n(b)Degree of reaction is %0.1f %%'%(b1,DR1*100)
# the answer for last part is not correct in the textbook.
```

In [15]:

```
#input data
m=3#Mass flow rate of air in kg/s
P1=100*10**3#The atmospheric pressure in Pa
T1=310#The atmospheric temperature in K
nb=0.8#The efficiency of the blower
nm=0.85#The mechanical efficiency
P=30#The power input in kW
R=287#The universal gas constant in J/kg.K
g=9.81#Acceleration due to gravity in m/s**2
dw=1000#Density of water in kg/m**3
#calculations
no=nb*nm#Overall efficiency of the blower
d=(P1)/(R*T1)#The density of the air in kg/m**3
dP=((no*P*10**3)/m)*d#The pressure developed in N/m**2
dH=((dP)/(g*dw))*(10**3)#The pressure developed in mm W.G
#output
print '(a)Overall efficiency of the blower is %3.2f\n(b)The pressure developed is %3.2f mm W.G'%(no,dH)
```

In [16]:

```
#input data
psi=0.4#Pressure coefficient
m=3.5#Mass flow rate of air in kg/s
N=750#The speed of fan in rpm
T1=308#The static temperature at the entry in K
Dh=0.26#The hub diameter in m
DhDt=1/3#The hub to tip ratio
P1=98.4*10**3#The static pressure at entry in Pa
nm=0.9#The mechanical efficiency
nf=0.79#Static fan efficiency
R=287#The universal gas constant in J/kg.K
Cp=1.005#The specific heat of air at constant pressure in kJ/kg.K
r=1.4#The ratio of specific heats of air
g=9.81#Acceleration due to gravity in m/s**2
dw=1000#Density of water in kg/m**3
#calculations
no=nm*nf#Overall efficiency
Dt=Dh/DhDt#The tip diameter in m
Dm=(Dt+Dh)/2#Mean rotor diameter in m
U=(3.141*Dm*N)/60#The mean blade speed in m/s
dPd=((U**2)/2)*psi#The ratio of change in pressure to density in J/kg
Wi=dPd*m#The ideal work in W
P=Wi/nm#The power required by the fan in W
d=P1/(R*T1)#The density of the air in kg/m**3
A=(3.141/4)*((Dt**2)-(Dh**2))#Area of cross section of the fan in m**2
Ca=m/(d*A)#The axial velocity of air in m/s
pi=Ca/U#The flow coefficient
tb1tb2=psi/(2*pi)#The difference between tangent angles of rotor inlet and exit angles
b2=degrees(atan((1-(dPd/U**2))/pi))#The exit rotor angle in degree
b1=degrees(atan((tan(b2*pi/180))+(tb1tb2)))#The inlet rotor angle in degree
dP=d*dPd#The pressure developed in N/m**2
dH=(dP/(dw*g))*10**3#Pressure developed in mm of W.G
#output
print '(a)The overall efficiency is %0.1f %%\n(b)The power required by the fan is %3.2f W\n(c)The flow coefficient is %3.2f\n(d)\n (1)The rotor inlet angle is %3.2f degree\n (2)The rotor exit angle is %3.2f degree\n(e)The pressure developed is %3.2f mm of W.G'%(no*100,P,pi,b1,b2,dH)
# the answer for part(d) is not correct in the textbook.
```