Chapter 6 : Fluid Mechanics and Hydraulic Machines

Example 6.1 Page No : 116

In [1]:
# Variables
Rn = 1700.
v = 0.744*(10**-4)
d = 0.05

# Calculations 
V = (Rn*v)/d
Vmax = 2*V
x = 0.00625
r = (d/2)-x
V1 = Vmax*(1-(2*r/d)**2)

# Results 
print "velocity at the point 6.25 mm from the wall in m/sec",V1

velocity at the point 6.25 mm from the wall in m/sec 2.2134

Example 6.2 Page No : 117

In [2]:
import math

# Variables
d = 0.3
p = 787.
v = 1.6*(10**-6)
Rn = 2000.

# Calculations 
V = Rn*v/d
a = math.pi*d*d/4
Q = a*V

# Results 
print "maximum flow rate for which the flow is maximium %.3e"%Q,"m**3/s"

maximum flow rate for which the flow is maximium 7.540e-04 m**3/s

Example 6.3 Page No : 118

In [5]:
# Variables
vd = 8*(10**-3)*0.1
p = 996.

# Calculations 
vk = vd/p

# Results 
print "kinematic vismath.cosity in m2/sec %.3e"%vk

kinematic vismath.cosity in m2/sec 8.032e-07

Example 6.4 Page No : 118

In [3]:
import math

# Variables
u = 1.5/98.1
s = 0.81
d = 0.14
Q = 0.03
g = 9.81

# Calculations 
p = s*1000/g
a = math.pi*d*d/4
V = Q/a
Rn = V*p*d/u

# Results 
print "Rn less than 2000, flow is laminar",round(Rn,2)

Rn less than 2000, flow is laminar 1473.32

Example 6.5 Page No : 119

In [7]:
# Variables
d = 0.2
Q = 0.088
l = 5.
vd = 0.01
p = 1000.

# Calculations 
v = vd/(p*10)
a = 3.142*d*d/4
g = 9.81
V = Q/a
Re = V*d/v
f = 0.0018+(0.092/(3*(Re**0.5)))
Hf = (4*f*l*V*V)/(d*2*g)

# Results 
print "head lost due to friction in m",round(Hf,5)

head lost due to friction in m 0.0736

Example 6.6 Page No : 120

In [5]:
import math

# Variables
s = 0.75
d = 0.2
l = 1000.
Q = 3/60.
f = 0.01
a = math.pi*d*d/4
V = Q/a
g = 9.81

# Calculations 
Hf = (4*f*l*V*V)/(d*2*g)
w = g*s*1000
dp = w*Hf

# Results 
print "pressure drop along its entire lenght in N/m2 %.2f"%dp

pressure drop along its entire lenght in N/m2 189977.22

Example 6.7 Page No : 121

In [9]:
# Variables
d = 0.3
g = 9.81
l = 400
Q = 0.3
f = 0.032

# Calculations 
a = 3.142*d*d/4
V = Q/a
Lentrance = (0.5*V*V)/(2*g)
Hf = (4*f*l*V*V)/(d*2*g)
Lexit = (V*V)/(2*g)
Totalloss = Lentrance+Hf+Lexit

# Results 
print "diffrenc in elevation in m",round(Totalloss,2)

 diffrenc in elevation in m 158.02

Example 6.8 Page No : 112

In [10]:
# Variables
l = 40.
l1 = 20.
l2 = 20.
d1 = 0.15
d2 = 0.3
H = 8.
f = 0.01

# Calculations 
h1 = (2*d2*d2)/(d1*d1)
h2 = 4*f*l1*16/d1
h3 = 9
h4 = 4*f*l2/d2
g = 9.81
ht = h1+h2+h3+h4+1
V2 = (H*2*g/ht)**0.5
a2 = 3.142*d2*d2/4
Q = V2*a2

# Results 
print "rate of low in litres/sec",round((Q*1000),0)

 

rate of low in litres/sec 86.0

Example 6.9 Page No : 124

In [11]:
# Variables
l = 2000.
d = 0.2
V = 0.8
f = 0.01
g = 9.81

# Calculations 
hf = (4*f*l*V*V)/(d*2*g)

# Results 
print "Head loss due to friction in pipeline",round(hf,4)

Head loss due to friction in pipeline 13.0479

Example 6.10 Page No : 124

In [9]:
import math

# Variables
d1 = 0.15
d2 = 0.1
Q = 0.03
a1 = math.pi*d1*d1/4
a2 = math.pi*d2*d2/4
V1 = Q/a1
V2 = Q/a2
c = 0.6
g = 9.81

# Calculations 
dz = (V2*V2/(2*g))-(V1*V1/(2*g))+(V2*V2/(2*g))*((1/c-1)**2)
w = 9810
dp = dz*w

# Results 
print "pressure loss across the contraction in N/m2",round(dp,1)

# note : rounding off error

pressure loss across the contraction in N/m2 9096.4

Example 6.11 Page No : 125

In [11]:
import math

# Variables
d1 = 0.5
d2 = 0.25
p1 = 103005.
p2 = 67689.
p3 = p2
w = 9810.
g = 9.81
c = 0.65

# Calculations and Results
z = 1-(1./16)+((1/c-1)**2)
dp = p1-p2
v2 = ((dp*2*g)/(w*z))**0.5
a2 = math.pi*d2*d2/4
Q = v2*a2
print "rate of flow in m3/sec",round((Q*1000),2)

v3 = v2
v1 = v3/4
v4 = v1
he = (v3-v4)**2/(2*g)
p4 = w*((p3/w)+((v3*v3-v4*v4)/(2*g))-he)
print "pressure at the 50 cm enlarge section in N/m2",round(p4,3)

# note : rouding off error.

rate of flow in m3/sec 372.37
pressure at the 50 cm enlarge section in N/m2 78478.522

Example 6.12 Page No : 127

In [15]:
# Variables
d = 0.04
v = 2.
dp = 20000.
l = 8.
w = 9810.

# Calculations 
u = (dp*d*d)/(32*l*v)

# Results 
print "viscosity of the flowing oil",u,"N/m**2"

viscosity of the flowing oil 0.0625 N/m**2

Example 6.13 Page No : 128

In [13]:
import math

# Variables
d = 0.25
l = 12.*1000
w = 9320.
i = 1./300
v = 20.*(10**-4)
a = math.pi*d*d/4
q = 0.015

# Calculations 
V = q/a
g = 9.81
Rn = V*d/v
f = 16/Rn
hf = (4*f*l*V*V)/(2*d*g)
H = hf+(i*l)
p = (w*q*H)/1000

# Results 
print "power required to pump the oil",round(p,4),"kW"

# note : rounding off error.

power required to pump the oil 59.1027 kW

Example 6.14 Page No : 129

In [17]:
# Variables
l = 600.
H = 160.
p = 1200.*1000
n = 0.85
f = 0.005

# Calculations 
hf = H/3
w = 9810
H1 = H-hf
q = p/(w*H1*n)
d = ((f*l*q*q)/(3*hf))**0.2


# Results 
print "minimium diameter of the pipe in cm",round((d*100),2)

minimium diameter of the pipe in cm 50.89

Example 6.15 Page No : 129

In [14]:
import math

# Variables
d = 0.25
l = 500.
a = math.pi*d*d/4
f = 0.006
q = 0.04
g = 9.81
p2 = 250.*1000

# Calculations 
V = q/a
hf = (4*f*l*V*V)/(d*2*g)
z1 = 0
z2 = 25
w = 9810
p1 = ((p2/w)+z2+hf)*w

# Results 
print "pressure at point A is N/m2",round(p1,2),"N/m**2"

pressure at point A is N/m2 511186.44 N/m**2

Example 6.16 Page No : 130

In [19]:
# Variables
q = 0.15/(2.5*60)
d = 0.03
p1 = 9810.
p2 = 6867.
l = 2.
w = 9810.

# Calculations 
hf = (p1-p2)/w
a = 3.142*d*d/4
V = q/a
g = 9.81
f = (hf*2*g*d)/(4*l*V*V)
C = V*((4*l)/(d*hf))**0.5

# Results 
print "darcy co-efficient",round(f,3)
print "Chezy formula",round(C,3)

darcy co-efficient 0.011
Chezy formula 42.173

Example 6.17 Page No : 131

In [20]:
# Variables
a = 90.
H1 = 10.
d = 0.15
l = 400.
H2 = 7.
g = 9.81
f = 0.008

# Calculations 
z = 3.142*d*d*((2*g)**0.5)
z1 = (1.5+(4*f*l/d))**0.5
T = (8*a*z1*(H1**0.5-H2**0.5))/z

# Results 
print "time to lower the level from 10m to 7m in hr",round((T/3600),4)

time to lower the level from 10m to 7m in hr 3.0742

Example 6.18 Page No : 132

In [15]:
import math

# Variables
q = 0.08
d1 = 0.25
d2 = 1.
l1 = 1500.
l2 = 1500.

# Calculations 
a1 = math.pi*d1*d1/4
a2 = math.pi*d2*d2/4
v2 = q*4/(math.pi*((1./32)+1))
v1 = v2*0.5
q1 = v1*a1
q2 = v2*a2

# Results 
print "disharge through  pipe in m3/sec",round((q2*1000),2),round((q1*1000),4)

disharge through  pipe in m3/sec 77.58 2.4242
In [ ]: