Chapter 4 : Flow Through Orifices

Example 4.2 Page No : 83

In [1]:
# Variables
q = 0.0982
d = 0.12
H = 10.
x = 4.5
y = 0.54
g = 9.81

# Calculations 
Vth = (2*g*H)**0.5
a = 3.142*d*d/4
Qth = Vth*a
Cd = q/Qth
Cv = ((x*x)/(4*y*H))**0.5
Cc = Cd/Cv

# Results 
print "Cd ,Cv, Cc  of the orifice",round(Cd,4),round(Cv,3),round(Cc,2)

Cd ,Cv, Cc  of the orifice 0.6198 0.968 0.64

Example 4.3 Page No : 83

In [2]:
# Variables
D = 0.1
d = 0.05
q = 0.02
A = 3.142*D*D/4
g = 9.81
w = 9810.
p = 58.86*1000

# Calculations 
v = q/A
Vh = (v*v)/(2*g)
Ph = p/w
Th = Ph+Vh
a = 3.142*d*d/4
Cd = q/(a*((2*g*Th)**0.5))

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

co-efficient of discharge 0.914

Example 4.4 Page No : 85

In [3]:
# Variables
Cd = 0.6
H1 = 3.
H2 = 4.
b = 2.

# Calculations 
g = 9.81
Q = (2*Cd*b*((2*g)**0.5)*((H2*H2*H2)**0.5-(H1*H1*H1)**0.5))/3
q1 = Q*1000

# Results 
print "dischsrge flow rate in litres/sec",round(q1,1)

dischsrge flow rate in litres/sec 9935.6

Example 4.5 Page No : 85

In [4]:
# Variables
b = 0.75
H1 = 2.25
H2 = 2.5
H = 0.5
g = 9.81
Cd = 0.62

# Calculations 
Q = Cd*b*(H2-H1)*((2*g*H)**0.5)
Q1 = Q*1000

# Results 
print "discherge through the orifice in litres/sec",round(Q1,1)

discherge through the orifice in litres/sec 364.1

Example 4.6 Page No : 86

In [5]:
# Variables
b = 2.
d = 3.
H1 = 4.
H2 = 7.

# Calculations 
H = 0.8+H1
Cd = 0.62
g = 9.81
Q1 = (2*Cd*b*((2*g)**0.5)*((H*H*H)**0.5-(H1*H1*H1)**0.5))/3
Q2 = Cd*b*(H2-H)*((2*g*H)**0.5)
Q = Q1+Q2
q = Q*1000

# Results 
print "Discharge in litres/sec",round(q,3)

Discharge in litres/sec 35687.468

Example 4.7 Page No : 87

In [6]:
# Variables
l = 20.
b = 10.
a = l*b
H1 = 1.5
Cd = 0.62
H2 = 0
T = 5.*60
n = 4.
g = 9.81

# Calculations 
a1 = (2*a*((H1**0.5)-(H2**0.5)))/(Cd*T*((2*g)**0.5))
d = ((4*a1)/(3.142*n))**0.5
d1 = d*100

# Results 
print "diameter of the orifice in cm",round(d1,1)

diameter of the orifice in cm 43.5

Example 4.8 Page No : 88

In [7]:
# Variables
l1 = 10.
b1 = 5.
l2 = 5.
b2 = 2.5
a1 = l1*b1
a2 = l2*b2
d = 0.2
a = 3.142*d*d/4
H1 = 4.
g = 9.81
q = 25.
Cd = 0.62

# Calculations 
h1 = q/a1
h2 = q/a2
H2 = H1-h1-h2
T = (2*a1*a2*((H1)**0.5-(H2)**0.5))/(a*Cd*(a1+a2)*((2*g)**0.5))

# Results 
print "time taken to flow 25 m3 in sec",round(T,1)

time taken to flow 25 m3 in sec 179.7

Example 4.9 Page No : 89

In [2]:
import math

# Variables
Cd = 0.8
D = 2.
r = 1.
H1 = 2.
d = 0.1
a = math.pi*d*d/4
l = 8.
g = 9.81

# Calculations 
T = (4*l*((2*r)**1.5-(2*r-H1)**1.5))/(3*Cd*a*((2*g)**0.5))

# Results 
print "time taken for emptying the boiler in min",round((T/60),1)

# note : rounding off error.

time taken for emptying the boiler in min 18.1

Example 4.10 Page No : 89

In [10]:
# Variables
r = 5.
h1 = 5.
d = 0.08
a = 0.005
h2 = h1-2

# Calculations 
Cd = 0.6
g = 9.81
z = ((2*r*((h1**1.5)-(h2**1.5)))/3)-((((h1**2.5)-(h2**2.5)))/5)
T = (z*2*3.142)/(Cd*a*((2*g)**0.5))

# Results 
print "time in seconds to lower the level by 2m",round(T,0)

time in seconds to lower the level by 2m 5620.0
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