Chapter 16 : Reaction Turbines

Example 16.2 Page No : 525

In [1]:
import math 
from sympy.functions.elementary.trigonometric import acot
	
#Initialization of variables
ns = 20. 
eta = 0.925
etah = 0.94
BD = 0.1
phie = 0.72
g = 32.2
alpha2 = 90. 	#degrees
	
#calculations
Cr = ns**2 /(67100*phie**2 *BD*eta)
c1cos = etah/(2*phie)
alpha = math.degrees(math.atan(Cr/c1cos))
C1 = Cr/math.sin(alpha)
#beta1 = 1/math.tan(math.radians((C1*math.cos(alpha) -phie)/(C1*math.sin(alpha))))
cotb1 = (0.653 - phie)/0.1243
beta1 = math.degrees(1./math.atan(cotb1))

#Results
print "Alpha  =  %.2f degrees"%(alpha)
print " Beta  =  %.2f degrees"%(beta1)
print ("part b")
h = 402.
n = 600. 	#rpm
bhp = 3600.
ns = n*math.sqrt(bhp) /h**(5./4)
D = 153.2*phie*math.sqrt(h) /n
B = BD*D
Dt = D*0.735
Ac = 0.95*math.pi*D*B
Vr = Cr*math.sqrt(2*g*h)
Q = Ac*Vr
	
#Results
print " Breadth =  %.3f ft"%(B)
print " depth D =  %.2f ft"%(D)
print " velocity Vr =  %d ft/s"%(Vr)
print " Flow rate Q =  %.1f cfs"%(Q)

# note : answers are slightly different because of rounding off error.

Alpha  =  10.78 degrees
 Beta  =  -115.90 degrees
part b
 Breadth =  0.369 ft
 depth D =  3.69 ft
 velocity Vr =  20 ft/s
 Flow rate Q =  81.1 cfs

Example 16.3 Page No : 527

In [6]:
	
#Initialization of variables
ns = 70. 
z1 = 10. 	#ft
z2 = 5000. 	#ft
	
#calculations
P1 = 12.2*144/62.4
P2 = 0.26*144/62.4
sigmac = 0.31
h = (P1-P2-z1)/sigmac
	
#Results
print "Max permissible head to assure against cavitation  =  %.f ft"%(h)

Max permissible head to assure against cavitation  =  57 ft

Example 16.4 Page No : 529

In [2]:
import math 
	
#Initialization of variables
Q = 600. 	#cfs
z = 350. 	#ft
eta = 0.9
	
#calculations
power = 62.4*Q*z*eta/550
rpm = 75.
n = 2.
ns = rpm*math.sqrt(power/n) /z**(5./4)
phi = 0.45
D = 153.3*math.sqrt(z) *phi/rpm
rpm2 = 600.
ns2 = rpm2*math.sqrt(power/n) /z**(5./4)
	
#Results
print "For two turbines, ns =  %.2f"%(ns)
print "For Francis turbines, ns =  %d "%(ns2)

For two turbines, ns =  5.13
For Francis turbines, ns =  41