Chapter 13 : Hydraulic Power Transmission|

Example 13.1 Page No : 512

In [4]:
import math 
	
#initialisation of variables
nop= 0.88
nom= 0.88   # constant
Pm= 75.  	#hp
p= 3000. 	#lb/in**2 pressure
d= 54.5 	#lbm/ft**3 density
u= 1.05*10**-4  # viscosity
d1= 0.5 	#in
g= 32.2 	#ft/sec**2
	
#CALCULATIONS
nt= (7./11)*nop*nom
pp= Pm/nt
Q= nop*pp*550/(p*144)
Re= 4*d*Q/(math.pi*u*(d1/12)*g)
	
#RESULTS
print  ' ntrans = %.3f '%(nt)
print  ' Input power = %.f hp'%(pp)
print  ' Flow rate = %.3f ft**3/sec'%(Q)
print  ' Reynolds Number = %.1e '%(Re)

 ntrans = 0.493 
 Input power = 152 hp
 Flow rate = 0.171 ft**3/sec
 Reynolds Number = 8.4e+04

Example 13.2 Page No : 513

In [5]:
import math 
	
#initialisation of variables
lc= 0.25
a= 90.   	#degrees
p= 3000.     	#lb/in**2 pressure
g= 32.2 	#ft/sec**2
d1= 0.5 	#in
Q= 0.171 	#ft**3/sec
d= 54.5 	#lbm/ft**3 density
n1= 2. 
n2= 6.
lc1= 0.9
nop= 0.88
nom= 0.88
	
#CALCULATIONS
P1= 4*p*144/11
P2= 8*d*Q**2*(n1*lc+n2*lc1)/(math.pi**2*(d1/12)**4*g)
pt= P1+P2
dpm= (p*144-pt)
ntrans= nop*nom*dpm/(p*144)
	
#RESULTS
print  ' Frictional pressure drop = %.2e lbf/ft**2'%(P1) 
print  ' Extra Frictional pressure drop = %.2e lbf/ft**2'%(P2) 
print  ' Total pressure drop = %.2e lbf/ft**2'%(pt)
print  ' Motor pressure drop = %.2e lbf/ft**2'%(dpm)
print  ' Overall transmission coefficiency = %.3f'%(ntrans)

 Frictional pressure drop = 1.57e+05 lbf/ft**2
 Extra Frictional pressure drop = 7.85e+04 lbf/ft**2
 Total pressure drop = 2.36e+05 lbf/ft**2
 Motor pressure drop = 1.96e+05 lbf/ft**2
 Overall transmission coefficiency = 0.352

Example 13.3 Page No : 521

In [6]:
import math 
	
#initialisation of variables
bip= 135. 	#degrees inlet angle
bop= 150. 	#degrees outlet angle
bot= 140. 	#degrees turbine outlet angle
bos= 137. 	#degrees stator blade outlet angle
r= 1.8   
r1= 1.8    # ratio b1/b2
r2= 0.7    # ratio b1/b3
r3= 0.95   # ratio r3/r1
	
#CALCULATIONS
Vw2r2byVw1r1 = (1+(1/math.tan(math.radians(bip))/1/math.tan(math.radians(bos))))*r**2-r1*(1/math.tan(math.radians(bop))/1/math.tan(math.radians(bos)))
Vw3r3byVw1r1 = r2*r3**2*(1+(1/math.tan(math.radians(bip))/1/math.tan(math.radians(bos))))-(1/math.tan(math.radians(bot))/1/math.tan(math.radians(bos)))
CtbyCp = (Vw2r2byVw1r1-Vw3r3byVw1r1)/(Vw3r3byVw1r1-1)
	
#RESULTS
print  ' R1 = %.2f'%(Vw2r2byVw1r1) 
print  ' R2 = %.2f'%(Vw3r3byVw1r1) 
print  ' Torque ratio = %.2f'%(CtbyCp)

# rounding off error. please check. instead of cot, have used 1/tan. please check.

 R1 = 3.37
 R2 = 0.03
 Torque ratio = -3.45