Chapter 23: Performance of Rotodynamic Machines¶
Example 23.1, Page 814¶
In [1]:
from __future__ import division
import math
from pylab import *
%matplotlib inline
#Initializing the variables
Q = []
for c in range(9):
Q.append(7*c)
H = [40, 40.6, 40.4, 39.3, 38, 33.6, 25.6, 14.5, 0];
n = [0, 41, 60, 74, 83, 83, 74, 51, 0];
N1 = 750;
N2 = 1450;
D1 = 0.5;
D2 = 0.35;
#Calculations
Q2=[]
H2=[]
for c in range(9):
Q2.append(Q[c]*(N2/N1)*(D2/D1)**3);
H2.append(H[c]*(N2/N1)**2*(D2/D1)**2);
plot(Q,H,label='H1')
plot(Q,n,label='n1')
plot(Q2,H2,'--',label='H2')
plot(Q2,n,'--',label='n2')
legend( loc='upper right', numpoints = 1 )
xlabel("Q (m3/s)");
ylabel("H (m of water) and n(percent)")
grid(True)
show()
Example 23.2, Page 831¶
In [2]:
from __future__ import division
import math
#Initializing the variables
n = 0.9;
g = 9.81;
D = 1.45;
N = 375/60;
H = 200; # Real height
x = 165; # Theta
P = 3750*10**3;
rho = 1000;
#Calculations
h = n*H; #Effective Head
v1 = (2*g*h)**0.5;
u = math.pi*D*N;
n_a = (2*u/v1**2)*(v1-u)*(1-n*math.cos(math.radians(x)));
P_b = P/n_a;
ppj = P_b/2; # Power per jet
d = (8*ppj/(rho*math.pi*v1**3))**0.5 ;
print "the efficiency of runner :",round(n_a,3)
print "Diameter of Jet (m) :",round(d,3)
Example 23.3, Page 834¶
In [3]:
from __future__ import division
import math
#Example 23.3
#Initializing the variables
g = 9.81;
H = 12;
n = 0.8;
w = 300*2*math.pi/60;
Q = 0.28;
#Calculations
V_f1 = 0.15*(2*g*H)**0.5;
V_f2 =V_f1;
V_w1 = (n*g*H)**0.5;
u1 = V_w1;
theta = math.atan(V_f1/u1);
u2 =0.5*u1;
B2 = math.atan(V_f2/u2);
r1 = u1/w;
b1 = Q/(V_f2*0.9*2*math.pi*r1); # vanes occupy 10 per cent of the circumference hence 0.9
b2 = 2*b1;
print "Guide vane angle (degree) :",round(theta*180/math.pi,2)
print "Vane angle at exit (degree) :",round(B2*180/math.pi,2)
print "Width of runner at inlet (mm) :",round(b1*1000,1)
print "Width of runner at exit (mm) :",round(b2*1000,1)
Example 23.4, Page 838¶
In [3]:
from __future__ import division
import math
import sympy
from sympy import solve,symbols
#Initializing the variables
H = 35;
g = 9.81;
D = 2;
N = 145/60;
z = 30*math.pi/180; # angle between vanes and direction of runner rotation
y = 28*math.pi/180; # angle between runner blades at the outlet.
#Calculations
H_net = 0.93*H ; # since 7% head is lost
v1 = (2*g*H_net)**0.5;
u = math.pi*N*D;
# from inlet velocity triangle
V_r1=14.3
## ash = cos(beta1+z)
ash = (V_r1**2+v1**2-u**2)/(2*V_r1*v1)
beta1=(z+math.acos(ash))*180/math.pi # in degrees
V_r2=(1-8/100)*V_r1 #8 % loss due to friction
V_w1= u + V_r1*math.cos(math.radians(beta1))
V_w2= u - V_r2*math.cos(y)
E = (u/g)*(V_w1 - V_w2);
n = E/H;
print "Blade angle at inlet :",round(beta1,1)
print "Efficiency (%) :",round(n*100)
Example 23.5, Page 844¶
In [5]:
from __future__ import division
import math
#Initializing the variables
s = 0.03;
P = 185*10**3;
rho = 0.86*10**3;
A = 2.8*10**-2;
N = 2250/60;
D = 0.46;
#Calculations
R0 = 0.46/2;
Ws_Wp = 1-s;
n = Ws_Wp;
Pf = s*P;
Q = (2*Pf*A**2/(3.5*rho))**(1/3);
Wp = 2*math.pi*N;
Ri = ((1/Ws_Wp)*(R0**2 -P/(rho*Q*Wp**2)))**0.5;# Modified equation for power transmission.
Di = 2*Ri;
T = P/(rho*Wp**3 *D**5);
print "Mean diameter (mm) :",round(Di*1000)
print "Torque Coefficient :",round(T,4)