# Chapter 22: Theory of Rotodynamic Machine¶

## Example 22.1, Page 779¶

In :
from __future__ import division
import math

#Initializing  the  variables
Q  =  5;
R1  =  1.5/2;
R2  =  2/2;
w  =  18;
rho  =  1000;
rhoA  =  1.2;
Hth  =  0.017;
g=9.81;

#Calculations
A  =  math.pi*(R2**2-R1**2);
Vf  =  Q/A;
Ut  =  w*R2;
Uh  =  w*R1;
B1t  =  math.atan(Vf/Ut);
B1h  =  math.atan(Vf/Uh);
E  =  Hth*rho/rhoA;
def  Beta(u):
y  =  math.atan(Vf/(u-E*g/u));
return y
B2t  =  Beta(Ut);
B2h  =  Beta(Uh);

print "At tip (in degrees) :",round(B1t*180/math.pi,1),"\nAt Hub (in degrees) :",round(B1h*180/math.pi,1)
print "At tip (in degrees):",round(B2t*180/math.pi,1),"\nAt Hub(in degrees) :",round(B2h*180/math.pi,1)

!----Blade Inlet Angles----!
At tip (in degrees) : 11.4
At Hub (in degrees) : 15.1

At tip (in degrees): 19.5
At Hub(in degrees) : 48.6


## Example 22.2, Page 793¶

In :
from __future__ import division
import math

#Initializing  the  variables
D  =  0.1;
t  =  15*10**-3;
Q  =  8.5/3600;
N  =  750/60;
B2  =  25*math.pi/180;                                                                #  Beta  2  ind  degrees
g  =  9.81;
z  =  16;

#Calculations
A  =  round(math.pi*D*t,5);
V_f2  =  round(Q/A,3);
U2  =  round(math.pi*N*D,3);
V_w2  =  round(U2  -  V_f2/math.tan(B2),1);
Hth  =  round(U2*V_w2/g,2);
Sf  =  round(1 - math.pi*math.sin(B2)/(z*(1-(V_f2/U2)/math.tan(B2))),3);
H  =  round(Sf*Hth,2);

print "Part (a) - Head developed (m): ",Hth
print "Part (b) - Head developed (m): ",H

Part (a) - Head developed (m):  1.16
Part (b) - Head developed (m):  1.03


## Example 22.3, Page 797¶

In :
from __future__ import division
import math

#Initializing  the  variables
Ma  =  0.6;
Cl  =  0.6;
tByC  =  0.035;                                                      #  Thickness  to  chord  ratio
cByC  =  0.015;                                                      #  Camber  to  chord  ratio
x  =  3;                                                                    #  Angle  of  incidence

#Calculations
lamda  =  1/(1-Ma**2)**0.5;
Cl#  =  lamda*Cl;
tByC1  =  tByC*lamda;
cByC1  =  cByC*lamda;
Cl1  =  Cl*lamda**2;
Ae  =  x*lamda;
print "____Geometric Characterstics____\n"
print "Thickness to chord ratio      :",tByC1
print "Camber to chord ratio         :",cByC1
print "Lift Coefficient              :",Cl1
print "angle of incidence (Degrees)  :",Ae

____Geometric Characterstics____

Thickness to chord ratio      : 0.04375
Camber to chord ratio         : 0.01875
Lift Coefficient              : 0.9375
angle of incidence (Degrees)  : 3.75