Chapter 10 : Centrifugal Pump

Example 10.1 Page No : 210

In [11]:
import math 

# Variables
N = 900./60
x1 = 90.
D1 = 0.2
D2 = 0.4
n = 0.7
g = 9.81
u1 = math.pi*D1*N
u2 = 2*u1 			# as D2 = 2D1
y1 = 20.

# Calculations 
Vf1 = u1*math.tan(math.radians(y1))
Vr1 = Vf1/math.sin(math.radians(y1))
Vf2 = Vf1
Vr2 = Vr1
x = (Vr2*Vr2-Vf1*Vf1)**0.5
Vw2 = u2-x
B1 = 0.02
Q = math.pi*D1*B1*Vf1
H = Vw2*u2/g
w = 9810
P = (w*Q*Vw2*u2)/(g*1000)
inputpower = (w*Q*H)/(1000*n)
print "discharge through the pump %.4f litre/s \
\nheat developed %f m \
\npower in Kw at outlet %.3f \
\ninput power if overall efficiency is 70%% : %.4f kW" \
%(Q*1000,H,P,inputpower)

# note : rounding off error

discharge through the pump 43.1069 litre/s 
heat developed 18.109366 m 
power in Kw at outlet 7.658 
input power if overall efficiency is 70% : 10.9401 kW

Example 10.2 Page No : 212

In [2]:
# Variables
Hs = 2.
Hd = 20.
Hfs = 1.
Hfd = 5.
Q = 1./60
N = 1450./60
ds = 0.1
dd = ds
n = 0.75
g = 9.81
w = 9810.

# Calculations 
a = 3.142*ds*ds/4
Vs = Q/a
Vd = Vs
Ht = Hs+Hd+Hfs+Hfd+(Vs*Vs/(2*g))+(Vd*Vd/(2*g))
Pi = (w*Q*Ht)/(n*1000)
Ns = ((N*(Q**0.5))/(Ht**0.75))*60

# Results 
print "total head developed by the pump,power input to the pump,specific speed of pump in r.p.m",round(Ht,4),round(Pi,5),round(Ns,3)

total head developed by the pump,power input to the pump,specific speed of pump in r.p.m 28.4589 6.20404 15.192

Example 10.3 Page No : 213

In [3]:
import math 

# Variables
d2 = 0.6
Q = 20./60
N = 1400./60
V1 = 2.8
g = 9.81
y2 = 30.
w = 9810.
Vf1 = V1
Vf2 = V1

# Calculations 
u2 = 3.142*d2*N
x = Vf2/math.radians(math.tan(y2))
Vw2 = u2-x
Hm = Vw2*u2/g
P = (w*Q*Hm)/1000

# Results 
print "head developed, pump power",round(Hm,4),round(P,4)

head developed, pump power 309.5484 1012.2231

Example 10.4 Page No : 214

In [4]:
# Variables
N = 1450./60
N1 = 1650./60
H = 12.
P = 6.

# Calculations 
H1 = H*((N1/N)**2)
P1 = P*((N1/N)**3)

# Results 
print "head developed and power required if pump runs at 1650 r.p.m",round(H1,4),round(P1,4)

head developed and power required if pump runs at 1650 r.p.m 15.5386 8.841

Example 10.5 Page No : 215

In [6]:
# Variables
Q = 0.03
Hs = 18.
d = 0.1
l = 90.
n = 0.8
w = 9810.
a = 3.142*d*d/4
f = 0.04
g = 9.81

# Calculations 
Vd = Q/a
H1 = (4*f*l*Vd*Vd)/(d*2*g)+(Vd*Vd/(2*g))
Hm = Hs+H1
P = (w*Q*Hm)/(n*1000)

# Results 
print "power required to drive the pump",round(P,3),"kW"

power required to drive the pump 46.279 kW

Example 10.6 Page No : 216

In [6]:
# Variables
Q = 0.04
Hm = 30.
n = 0.75
w = 9810.

# Calculations 
p = w*Q*Hm/1000
P = p/n

# Results 
print "output power of the pump,power required to drive the motor",p,P

output power of the pump,power required to drive the motor 11.772 15.696

Example 10.7 Page No : 216

In [7]:
# Variables
Q = 1.8/60
d = 0.1
n = 0.72
Hs = 20.
w = 9810.
Hl = 8.

# Calculations 
Hm = Hs+Hl
p = (w*Hm*Q)/1000
P = p/n
print "water power required to the pump,power required to run the pump",p,P

water power required to the pump,power required to run the pump 8.2404 11.445

Example 10.8 Page No : 217

In [12]:
import math 

# Variables
d2 = 0.6
Q = 15./60
N = 1450./60
V1 = 2.6
g = 9.81
y2 = 30.
w = 9810.
Vf1 = V1
Vf2 = V1

# Calculations 
u2 = math.pi*d2*N
x = Vf2/math.tan(math.radians(y2))
Vw2 = u2-x
Hm = Vw2*u2/g
P = (w*Q*Hm)/1000

# Results 
print "head developed, pump power",round(Hm,4),round(P,4)

head developed, pump power 190.6161 467.4859

Example 10.9 Page No : 217

In [8]:
# Variables
Q = 0.05
p = 392.4*1000
n = 0.65
s = 0.8
w1 = 9810.

# Calculations 
Hw = p/w1
Hoil = p/(w1*s)
Pw = (w1*Q*Hw)/(n*1000)
Poil = (w1*s*Q*Hoil)/(n*1000)

# Results 
print "power in Kw to drive the pump with water and oil of s,p = 0.8",round(Poil,6),round(Pw,6)

power in Kw to drive the pump with water and oil of s,p = 0.8 30.184615 30.184615

Example 10.10 Page No : 218

In [15]:
import math 

# Variables
Q = 0.118
N = 1450./60
Hm = 25.
d2 = 0.25
B2 = 0.05
n = 0.75
g = 9.81

# Calculations 
u2 = math.pi*d2*N
Vf2 = Q/(math.pi*d2*B2)
Vw2 = g*Hm/(n*u2)
y2 = math.degrees(math.atan(Vf2/(u2-Vw2)))

# Results 
print "vane angle in degree at the outer nperiphery of the impeller",round(y2,2)

# note : rounding off error

vane angle in degree at the outer nperiphery of the impeller 59.75

Example 10.11 Page No : 219

In [18]:
import math 

# Variables
Hm = 14.5
N = 1000./60
y2 = 30.
d2 = 0.3
B2 = 0.05
g = 9.81
n = 0.95

# Calculations 
u2 = math.pi*d2*N
Vw2 = g*Hm/(n*u2)
Vf2 = (u2-Vw2)*math.tan(math.radians(y2))
Q = math.pi*d2*B2*Vf2

# Results 
print "discharge of pump in m3/sec if manometric efficiency if 95%% : %.3f litre/s"%(Q*1000)

discharge of pump in m3/sec if manometric efficiency if 95% : 168.024 litre/s

Example 10.12 Page No : 220

In [21]:
import math 

# Variables
d2 = 1.2
N = 200./60
Q = 1.88
Hm = 6.
y2 = 26.
g = 9.81
Vf2 = 2.5
d1 = 0.6
u2 = math.pi*d2*N

# Calculations 
Vw2 = u2-(Vf2/math.tan(math.radians(y2)))
n = g*Hm/(Vw2*u2)
z1 = (math.pi*d2/60)**2
z2 = (math.pi*d1/60)**2
N1 = (Hm*2*g/(z1-z2))**0.5

# Results 
print "least speed to start pump : %.3f r.p.m \
\nmanometric efficiency : %.2f %%"%(N1,(n*100))

least speed to start pump : 199.395 r.p.m 
manometric efficiency : 62.95 %

Example 10.13 Page No : 222

In [26]:
import math 

# Variables
Q = 0.125
Hm = 25.
N = 660./60
d2 = 0.6
d1 = d2*0.5
a = 0.06
y2 = 45.
g = 9.81

# Calculations 
u2 = math.pi*d2*N
u1 = u2*0.5
Vf2 = Q/a
Vw2 = u2-(Vf2/math.tan(math.radians(y2)))
n = g*Hm/(Vw2*u2)
Vf1 = Q/(a)
y1 = math.degrees(math.atan(Vf1/u1))

# Results 
print "manometric efficiency %.2f %% \
\nvane angle at inlet : %.2f degrees"%((n*100),y1)

# note : rounding off error.

manometric efficiency 63.42 % 
vane angle at inlet : 11.36 degrees

Example 10.14 Page No : 223

In [28]:
import math 

# Variables
n = 3.
d2 = 0.4
B2 = 0.02
y2 = 45.
da = 0.1
nm = 0.9
w = 9810.
no = 0.8
g = 9.81
N = 1000./60
Q = 0.05

# Calculations 
Vf2 = Q/(math.pi*d2*nm*B2)
u2 = math.pi*d2*N
Vw2 = u2-(Vf2/math.tan(math.radians(y2)))
Hm = nm*Vw2*u2/g
Ht = n*Hm
P = w*Q*Ht/1000
Ps = P/no

# Results 
print "shaft power in Kw %.2f"%Ps

shaft power in Kw 66.21

Example 10.15 Page No : 225

In [12]:
# Variables
n = 6.
Q = 0.12
p = 5003.1*1000
N = 1450./60
w = 9810.

# Calculations 
Ht = p/w
h = Ht/n
Ns = (N*(Q**0.5)/(h**0.75))*60

# Results 
print "radial impeller would be selected",round(Ns,2)

radial impeller would be selected 17.94

Example 10.16 Page No : 225

In [13]:
import math 

# Variables
sg = 1.08
w = 9810.*sg
Q = 0.3
H = 12.
no = 0.75

# Calculations 
P = w*Q*H/(no*1000)
p = w*H

# Results 
print "power in Kw required by the pump,pressure developed by the pump in  N/m2",round(P,3),p

power in Kw required by the pump,pressure developed by the pump in  N/m2 50.855 127137.6

Example 10.17 Page No : 226

In [14]:
# Variables
d1 = 0.3
N1 = 2000./60
Q1 = 3.
Hm1 = 30.
Q2 = 5.
N2 = 1500./60
Ht = 200.

# Calculations 
Hm2 = ((N2/N1)*((Q2/Q1)**0.5)*(Hm1**0.75))**1.3333
n = Ht/Hm2
d2 = ((Hm2/Hm1)**0.5)*(N1/N2)*d1

# Results 
print "number of stages and diameter of each impeller in cm",round(n,3),round((d2*100),2)

number of stages and diameter of each impeller in cm 6.96 39.15
In [ ]: