# Chapter 10 : Hydraulic Prime Movers¶

## Example 10.1 Page No : 188¶

In [1]:
import math

#initialisation of variables
v= 231. 	#ft/sec
g= 32.2 	#ft/sec**2
vc= 0.97
r= 0.47
p= 85.  	#per cent
A= 170. 	#degrees
p1= 88. 	#per cent
l= 950. 	#ft

#CALCULATIONS
H= v**2/(vc**2*2*g)
u= r*v
vr= v-u
vr1= p*vr/100
W= u*(v-w1)/g
he= W*100/H
W1= p1*W/100
oe= W1*100/l

#RESULTS
print  'hydraulic efficiency = %.f percent'%(he)
print  ' overall efficiency = %.1f percent'%(oe)

hydraulic efficiency = 86 percent
overall efficiency = 70.2 percent


## Example 10.2 Page No : 189¶

In [2]:
import math

#initialisation of variables
d= 1.    	#in
v= 95.   	#ft/sec
F= 173.2 	#lb
A= 163.  	#degrees
H= 500.  	#ft
Cv= 0.97
d1= 1.33 	#ft
r= 0.47
w= 62.4 	#lb/ft**3
g= 32.2 	#ft/sec**2

#CALCULATIONS
Q= w*math.pi*v/(144*4)
v1= Cv*math.sqrt(2*g*H)
W= v1*w*d**2*math.pi/(4*144)
N= 60*r*v1/(math.pi*d1)
Ns= N*whp**0.5/H**1.25

#RESULTS
print  'specific speed = %.2f r.p.m'%(Ns)

specific speed = 4.75 r.p.m


## Example 10.4 Page No : 192¶

In [1]:
import math

#initialisation of variables
D= 2. 	#ft
f= 0.005
l= 10000. 	#ft
g= 32.2 	#ft/sec**2
H= 1000. 	#ft
w= 62.4 	#lb/ft**3

#CALCULATIONS
d= (2*D**5/(f*l))**0.25
v= math.sqrt(8*g*H*D**5/(f*l*d**4+4*D**5))
HP= w*math.pi*d**2*v**3/(2*g*550*4)
Q= math.pi*d**2*(HP/67)/4

#RESULTS
print  'Quantity flowing = %.f cusecs'%(Q)

# rounding off error

Quantity flowing = 185 cusecs


## Example 10.5 Page No : 193¶

In [4]:
import math

#initialisation of variables
pl= 122.5 	# ft
Hw= 1225 	#ft
g= 32.2 	#ft/sec**2
Cd= 0.98
Cd1= 0.45
N= 500. 	#r.p.m
P= 6800. 	#h.p
n= 0.86
w= 62.4 	#lb/ft**2
l= 5450. 	#ft
f= 0.005
A= 18.   	#ft**2

#CALCULATIONS
Ah= Hw-pl
js= Cd*math.sqrt(2*g*Ah)
bs= Cd1*js
D= bs*60*2/(N*2*math.pi)
a=  P*2*g*550*144/(n*w*js**3*2)
vp= math.sqrt(pl*2*g/(4*f*l))
dp= (js*2*4*A/(math.pi*144*vp))**(2./3)
dp=2.495 	#ft

#RESULTS
print  'diameter of bucket circle D = %.1f ft'%(D)
print  ' area of jet = %.f in**2'%(a)
print  ' diameter of pipe = %.1f ft'%(dp)

diameter of bucket circle D = 4.5 ft
area of jet = 18 in**2
diameter of pipe = 2.5 ft


## Example 10.6 Page No : 194¶

In [13]:
import math

#initialisation of variables
u= 10.*math.pi 	#ft/sec
u1= 5.*math.pi 	#ft/sec
a= 20. 	#degrees
A= 300. 	#r.p.m
v= 10. 	#ft/sec
g= 32.2 	#ft/sec**2
wi= 2. 	#ft
d= 6. 	#in
w1= 62.4 	#lb/ft**3

#CALCULATIONS
a1= math.degrees(math.atan((v/(u-w))))
b= math.degrees(math.atan((v/u1)))
W= u*w/g
A1= math.pi*wi*d/12
Q= A1*v
WHP= W*Q*w1/550

#RESULTS
print  'Blade angle at inlet is given by = %.2f degrees'%(a1)
print  ' Blade angle at inlet is given by = %.2f degrees'%(b)
print  ' Water horse power = %.1f h.p'%(WHP)

# rounding off error

Blade angle at inlet is given by = 68.49 degrees
Blade angle at inlet is given by = 32.48 degrees
Water horse power = 95.5 h.p


## Example 10.7 Page No : 196¶

In [7]:
import math

#initialisation of variables
g= 32.2 	#ft/sec**2
H= 100. 	#ft
a= 25. 	#degrees
a1= 20. 	#degrees
r1= 9./8
r2= 0.2
u= 6.63 	#ft/sec
w= 62.4 	#lb/ft**3
h1= 34. 	#ft
h2= 100. 	#ft
r= 0.1

#CALCULATIONS
W= u*f**2/g
q= a*H*550/(10*W*w)
q1= q/w
A= q/f

#RESULTS
print  'f = %.1f ft/sec'%(f)
print  ' Work Done = %.1f ft-lb/lb'%(W)
print  ' Quantity flow = %.1f cusecs'%(q)
print  ' Area form guides = %.3f ft**2'%(A)
print  ' Pressure at entry of level = %.1f ft of water'%(dh)

#The answer is a bit different due to rounding off error in textbook

f = 20.2 ft/sec
Work Done = 83.9 ft-lb/lb
Quantity flow = 26.3 cusecs
Area form guides = 1.302 ft**2
Pressure at entry of level = 74.5 ft of water


## Example 10.8 Page No : 199¶

In [16]:
import math
#initialisation of variables
d= 8. 	#in
w= 2. 	#in
di= 12. 	#in
wi= 3. 	#in
a= 24. 	#degrees
p= 88. 	#per cent
a1= 85. 	#degrees
a2= 30. 	#degrees
p1= 94. 	#per cent
h= 180. 	#ft
d1= 18. 	#in
Cd= 0.92
g=32.2
n1= 111. 	#rpm

#calculations
r3= 2*r2/3
f= math.sqrt(g*h*(p/100.)/(r1*r2+r3*r4+(r5**2/2)))
A= r2*f/(d/12)
N= (A*60/(2*math.pi))-n1
W= (r1*r2+r3*r4)*f**2/g
Q= math.pi*(d1/12)*(w/12)*Cd*f*62.08
whp= W*Q/550
bhp= p1*whp/100

#RESULTS
print  'Speed = %.f rpm'%(N)
print  ' output horsepower = %.f hp'%(bhp)


Speed = 905 rpm
output horsepower = 369 hp


## Example 10.9 Page No : 201¶

In [1]:
import math

#initialisation of variables
N= 428.6 	#r.p.m
D= 5.    	#ft
w= 62.4 	#lb/ft**3
hp= 16800. 	#hp
Qw= 435. 	#cuses
g= 32.2 	#ft/sec**2
v= 32. 	#ft/sec
v1= 24. 	#f/sec
H= 200. 	#ft
lh1= 0.32 	#ft lb/lb

#CALCULATIONS
u= math.pi*D*N/60
W= hp*550/(Qw*w)
w= W*g/u
va= math.sqrt(w**2+v**2)
B= 180-b
vew= va**2/(2*g)
ve1w= v1**2/(2*g)
LH= H+vew-ve1w-W+lh1

#RESULTS
print  ' Absolute velocity at entry to runner = %.1f ft/sec'%(va)
print  ' Loss of head in runner = %.2f ft lb/lb'%(LH)

 Absolute velocity at entry to runner = 102.8 ft/sec
Loss of head in runner = 15.05 ft lb/lb


## Example 10.10 Page No : 203¶

In [2]:
import math

#initialisation of variables
A1= 25. 	#degrees
A2= 80. 	#degrees
H1= 100. 	#ft
H2= 13. 	#ft
g= 32.2 	#ft/sec**2
v= 8. 	#ft/sec
d= 3.5 	#in
de= 15.4 	#in
b= 1.5 	#in
w= 62.4 	#lb/ft**3

#CALCULATIONS
W= H1-H2-(v**2/(2*g))
V= d*u/7.7
r= math.degrees(math.atan(f/V))
N= 60*u*12/(math.pi*de)
Q= math.pi*de*f*b/144
HP= Q*w*W/550
Ns= N*math.sqrt(HP)/H1**1.25
di= math.sqrt(Q*4*144/(math.pi*f))

#RESULTS
print  'angle = %.f degrees'%(r)
print " Angular speed = %.1f rpm"%(Ns)
print  ' inlet diameter to draft tube = %.2f in'%(di)

angle = 48 degrees
Angular speed = 26.6 rpm
inlet diameter to draft tube = 9.61 in


## Example 10.12 Page No : 207¶

In [7]:
import math

#initialisation of variables
H= 82.1 	#ft
h= 90.   	#ft
k= 0.00646
k1= 0.00454
vd= 11.  	#ft/sec
P= 0.53 	#hp

#CALCULATIONS
Q= math.sqrt((1/k))*math.sqrt(h-H)
Qu= Q/math.sqrt(H)
Q1= math.sqrt(vd/k1)
hf= Q1**2*k
Qu1= Q1/math.sqrt(h-hf)
Pu= P*(h-hf)**1.5

#RESULTS
print  'Qu = %.2f cuses'%(Qu)
print  ' Q = %.1f cuses'%(Q1)
print  ' power Developed = %.f hp'%(Pu)

# rounding off error

Qu = 3.86 cuses
Q = 49.2 cuses
power Developed = 340 hp