Chapter 3 : Flow of Fluids

Example 3.1 Page No : 62

In [2]:
import math

# Variables
d1 = 0.3
d2 = 0.1
z1 = 6.
z2 = 3.
p1 = 200.*1000
q1 = 0.07
a1 = math.pi*d1*d1/4
a2 = math.pi*d2*d2/4
v1 = q1/a1
v2 = q1/a2
w = 9810.
g = 9.81

# Calculations 
#applying bernoulli equation
p2 = ((z1-z2)+(((v1**2)-(v2**2))/(2*g))+(p1/w))*w

# Results 
print "pressure at point B in N/m2",round(p2,2),"N/m**2"

# note : rounding off error.

pressure at point B in N/m2 190202.44 N/m**2

Example 3.2 Page No : 63

In [6]:
import math

# Variables
d1 = 1.
d2 = 0.5
q = 0.1
p1 = 70.*1000
l = 60.
z2 = 0.
z1 = l/20
a1 = math.pi*d1*d1/4
a2 = math.pi*d2*d2/4
v1 = q/a1
v2 = q/a2
w = 9810.
g = 9.91

# Calculations 
# applying bernoulli equation
p2 = ((z1-z2)+(((v1**2)-(v2**2))/(2*g))+(p1/w))*w

# Results 
print "presssure at lower end in N/m2 %d"%round(p2,3),"N/m**2"

# note : rounding off error.

presssure at lower end in N/m2 99309 N/m**2

Example 3.3 Page No : 64

In [9]:
import math

d1 = 0.2
d2 = 0.1
l = 4.
x = 30.
p1 = 392.4*1000
q = 0.035
z1 = 0

# Calculations 
z2 = l*math.sin(math.radians(x))
a1 = math.pi*d1*d1/4
a2 = math.pi*d2*d2/4
v1 = q/a1
v2 = q/a2
w = 9810.
g = 9.81
p2 = ((z1-z2)+(((v1**2)-(v2**2))/(2*g))+(p1/w))*w

# Results 
print "pressure intensity at outlet in N/m2",round(p2,2),"N/m**2"

# note : rounding off error.

pressure intensity at outlet in N/m2 363471.12 N/m**2

Example 3.4 Page No : 65

In [4]:
# Variables
d1 = 0.2
d2 = 0.1
d3 = 0.15
v1 = 4
g = 9.81

# Calculations 
vh1 = (v1**2)/(2*g)
a1 = 3.142*d1*d1/4
a2 = 3.142*d2*d2/4
a3 = 3.142*d3*d3/4
v2 = (a1*v1)/a2
vh2 = (v2**2)/(2*g)
v3 = (a1*v1)/a3
vh3 = (v3**2)/(2*g)
q = a1*v1
mf = q*1000

# Results 
print "velocity head at point 1",round(vh1,3),"m"
print "velocity head at point 2",round(vh2,3),"m"
print "velocity head at point 3",round(vh3,3),"m"
print "mass flow rate in kg/sec",mf

velocity head at point 1 0.815 m
velocity head at point 2 13.048 m
velocity head at point 3 2.577 m
mass flow rate in kg/sec 125.68

Example 3.5 Page No : 66

In [5]:
# Variables
d1 = 0.2
d2 = 0.5
p1 = 98.1*1000
p2 = 58.86*1000
q = 0.2
z1 = 0
z2 = 4.
g = 9.81
s = 0.87

# Calculations 
a1 = 3.142*d1*d1/4
a2 = 3.142*d2*d2/4
v1 = q/a1
v2 = q/a2
w = 9810
ph1 = p1/(w*s)
ph2 = p2/(w*s)
vh1 = (v1**2)/(2*g)
vh2 = (v2**2)/(2*g)
th1 = vh1+ph1+z1
th2 = vh2+ph2+z2
tl = th1-th2

# Results 
print "loss of head in m,flow from 1 to 2",round(tl,3),"m"

loss of head in m,flow from 1 to 2 2.61 m

Example 3.6 Page No : 67

In [6]:
# Variables
d1 = 0.3
d2 = 0.15
a1 = 3.142*d1*d1/4
a2 = 3.142*d2*d2/4
H = 0.18
Cd = 0.85
s2 = 13.6
s1 = 1.
w = 9810.

# Calculations 
h = H*((s2/s1)-1)
g = 9.81
q = (Cd*a1*a2*((2*g*h)**0.5))/(((a1**2)-(a2**2))**0.5)
q1 = q*1000

# Results 
print "rate of flow in litres/sec",round(q1,2)

rate of flow in litres/sec 103.5

Example 3.7 Page No : 68

In [10]:
import math

# Variables
q = 0.1
d1 = 0.2
Cd = 0.9
H = 0.4
s1 = 1.
s2 = 13.6
g = 9.8

# Calculations 
h = H*((s2/s1)-1)
a1 = math.pi*d1*d1/4
z = 1+(((Cd*a1*((2*g*h)**0.5))/q)**2)
a2 = ((a1**2)/z)**0.5
d2 = (4*a2/3.1)**0.5

# Results 
print "diameter of throat in m",round(d2,3)
 
# note : rounding off error. 

diameter of throat in m 0.117

Example 3.8 Page No : 68

In [8]:
# Variables
q = 0.08
d1 = 0.3
d2 = 0.15
a1 = 3.142*d1*d1/4
a2 = 3.142*d2*d2/4
h = 1.5
g = 9.81

# Calculations 
z = (a1*a2*((2*g*h)**0.5))/(((a1**2)-(a2**2))**0.5)
Cd = q/z

# Results 
print "co-efficient of meter",round(Cd,3)

co-efficient of meter 0.808

Example 3.9 Page No : 69

In [11]:
# Variables
s2 = 13.6
s1 = 0.9
H = 0.25
h = H*((s2/s1)-1)
Cd = 0.98
w = 9810*s1
d1 = 0.3
d2 = 0.15

# Calculations 
a1 = 3.142*d1*d1/4
a2 = 3.142*d2*d2/4
dz = 0.3
g = 9.81
q = (Cd*a1*a2*((2*g*h)**0.5))/(((a1**2)-(a2**2))**0.5)
dp = (h+dz)*w

# Results 
print "discharge of the oil in m3/sec",round(q,4)
print "pressure diffrence in entrance and throat section ",dp,"N/m**2"

discharge of the oil in m3/sec 0.1488
pressure diffrence in entrance and throat section  33795.45 N/m**2

Example 3.10 Page No : 70

In [12]:
# Variables
H = 0.1
w = 9810.
sw = 12.

# Calculations 
h = H*(w/sw)
Cv = 0.96
g = 9.81
v = Cv*((2*g*h)**0.5)
v1 = v*18/5

# Results 
print "speed of the plane",round(v1,2),"Km/hr"

speed of the plane 138.41 Km/hr

Example 3.11 Page No : 71

In [11]:
import math

# Variables
d1 = 0.05
d2 = 0.025

# Calculations 
a1 = math.pi*d1*d1/4
a2 = math.pi*d2*d2/4
Cd = 0.94
g = 9.81
k = ((((a1**2)/(a2**2))-1)*(1-(Cd**2)))/(2*g*(a1**2)*(Cd**2))

# Results 
print "venturimeter constant m-5/s2",round(k,3)

venturimeter constant m-5/s2 26123.403

Example 3.12 Page No : 73

In [12]:
import math

# Variables
d0 = 0.05
d1 = 0.1
H = 0.09
s2 = 13.6
s1 = 1
g = 9.81

# Calculations 
h = H*((s2/s1)-1)
Cd = 0.65
a1 = math.pi*d1*d1/4
a0 = math.pi*d0*d0/4
q = (Cd*a1*a0*((2*g*h)**0.5))/(((a1**2)-(a0**2))**0.5)
q1 = q*(10**6)

# Results 
print "actual flow rate in cm3/sec",round(q1,3),"cm**3/s"

actual flow rate in cm3/sec 6217.469 cm**3/s
In [ ]: