Chapter 12 : Reaction Turbine

Example 12.1 Page No : 250

In [1]:
import math 

# Variables
D1 = 0.6
D2 = 0.3
x2 = 90.
B1 = 0.15
N = 300./60
x1 = 15.
Vf1 = 3.

# Calculations 
Vf2 = Vf1
u1 = math.pi*D1*N
u2 = math.pi*D2*N
Vw1 = Vf1/math.tan(math.radians(x1))
y1 = math.tan(math.radians(Vf1/(Vw1-u1)))
Q = math.pi*D1*B1*Vf1
w = 9810
g = 9.81
P = w*Q*Vw1*u1/(g*1000)

# Results 
print "blade angles, Power developed in Kw",round(y1,4),round(P,4)

blade angles, Power developed in Kw 0.0296 89.5063

Example 12.2 Page No : 251

In [2]:
# Variables
D1 = 1.
N = 200./60
B1 = 0.15
Vf1 = 3.
Vf2 = Vf1
x2 = 90.

# Calculations 
Q = 3.142*D1*B1*Vf1
u1 = 3.142*D1*N
Vw1 = u1
w = 9810
g = 9.81
P = (w*Q*Vw1*u1)/(g*1000)
H = (Vw1*u1/g)+(Vf2*Vf2/(2*g))
nh = Vw1*u1/(g*H)


# Results 
print "power developed in Kw,hydraulic efficiency",round(P,3),round((nh*100),0),"%"

power developed in Kw,hydraulic efficiency 155.092 96.0 %

Example 12.3 Page No : 253

In [6]:
import math 

# Variables
D1 = 0.75
D2 = 0.5
x1 = 20.
Vf1 = 3.
Vf2 = 3.
B1 = 0.15
N = 250./60

# Calculations 
u1 = math.pi*D1*N
u2 = math.pi*D2*N
Vw1 = Vf1/math.tan(math.radians(x1))
y1 = math.degrees(math.atan(Vf1/(u1-Vw1)))
y2 = math.degrees(math.atan(Vf2/u2))
Q = 3.142*D1*B1*Vf1
w = 9810
g = 9.81
P = w*Q*Vw1*u1/(g*1000)
H = (Vw1*u1/g)+(Vf2*Vf2/(2*g))
nh = Vw1*u1/(g*H)

# Results 
print "hydraulic efficiency : %.2f %% \
\npower developed in Kw : %.2f \
\nblade angle at inlet and outlet : %.3f and %.3f"%(nh*100,P,y1,y2)

# note : rounding off error.

hydraulic efficiency : 94.73 % 
power developed in Kw : 85.81 
blade angle at inlet and outlet : 62.300 and 24.625

Example 12.4 Page No : 254

In [9]:
import math 

# Variables
H = 150.
Q = 6.
N = 400./60
D1 = 1.2
x1 = 20.
x2 = 90.
B1 = 0.1

# Calculations 
u1 = math.pi*D1*N
Vf1 = Q/(math.pi*D1*B1)
Vw1 = Vf1/math.tan(math.radians(x1))
Vw2 = 0
w = 9810
g = 9.81
P = w*Q*Vw1*u1/(g*1000)

# Results 
print "whirl component at inlet and outlet m/s : %.5f and %d \
\npower developed in Kw : %.4f"%(round(Vw1,5),Vw2,round(P,4))

whirl component at inlet and outlet m/s : 43.72746 and 0 
power developed in Kw : 6593.9458

Example 12.5 Page No : 256

In [13]:
import math 

# Variables
D1 = 0.76
D2 = 0.5
x1 = 20.
Vf1 = 4.
Vf2 = Vf1
B1 = 0.15
N = 300./60

# Calculations 
u1 = math.pi*D1*N
u2 = math.pi*D2*N
Vw1 = Vf1/math.tan(math.radians(x1))
y1 = math.degrees(math.atan(Vf1/(u1-Vw1)))
y2 = math.degrees(math.atan(Vf2/u2))
Q = 3.142*D1*B1*Vf1
w = 9810.
g = 9.81
P = w*Q*Vw1*u1/(g*1000)

# Results 
print "blade angle at inlet and outlet : %.2f and %.2f \
\npower developed in Kw : %.2f"%(y1,y2,P)

blade angle at inlet and outlet : 76.66 and 26.99 
power developed in Kw : 187.97

Example 12.6 Page No : 257

In [16]:
import math 

# Variables
no = 0.8
P = 147.*1000
H = 10.
g = 9.81

# Calculations 
u1 = 0.95*(math.sqrt(2*g*H))
Vf1 = 0.3*(math.sqrt(2*g*H))
N = 160./60
Vw2 = 0
nh = (H-(0.2*H))/H
Vw1 = nh*g*H/u1
x1 = math.degrees(math.atan(Vf1/Vw1))
y1 = math.degrees(math.atan(Vf1/(u1-Vw1)))
D1 = u1/(math.pi*N)
w = 9810.
p = 147.*1000
Q = p/(w*H*no)
B1 = Q/(math.pi*D1*Vf1)

# Results 
print "guide blade angle : %.4f degrees \
\nwheel vane angle : %.4f degrees \
\ndiameter of wheel : %.7f m**3/s \
\nwidth of wheel at inlet in cm : %.2f"%(x1,y1,D1,B1*100)

# note : rounding off error.

guide blade angle : 35.4699 degrees 
wheel vane angle : 29.5604 degrees 
diameter of wheel : 1.5883803 m**3/s 
width of wheel at inlet in cm : 8.93

Example 12.7 Page No : 259

In [18]:
import math 

# Variables
sp = 25.*(10**6)
H = 40.
no = 0.9
P = 25.*1000
g = 9.81

# Calculations 
u1 = 2*(math.sqrt(2*g*H))
Vf1 = 0.6*(math.sqrt(2*g*H))
w = 9810
Q = sp/(w*no*H)
De = (Q*4/(math.pi*Vf1*(1-(0.35**2))))**0.5
Db = 0.35*De
N = u1*60/(math.pi*De)
Ns = N*(P**0.5)/(H**1.25)

# Results 
print "diameter of runner and boss : %.4f and %.4f m \
\nspeed and specific speed of runner in r.p.m : %.2f and %.2f "%(De,Db,N,Ns)

# note: rounding off error.

diameter of runner and boss : 2.4720 and 0.8652 m 
speed and specific speed of runner in r.p.m : 432.87 and 680.39

Example 12.8 Page No : 260

In [20]:
import math 

# Variables
D = 4.5
d = 2.
P = 20608.
N = 140./60
H = 22.
nh = 0.94
w = 9810.
g = 9.81
no = 0.85

# Calculations 
Q = P*1000/(w*no*H)
Vf1 = Q*4/(math.pi*((D**2)-(d**2)))
u1 = math.pi*D*N
Vw1 = nh*g*H/u1
x1 = math.degrees(math.atan(Vf1/Vw1))

# Results 
print "discharge through the turbine : %.4f m**3/s \
\nguide blade angle at inlet : %d degrees"%(Q,x1)

discharge through the turbine : 112.3376 m**3/s 
guide blade angle at inlet : 55 degrees
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