Chapter 3 : Hydrodynamics

Example 3.1 Page No : 39

In [1]:
import math 

#initialisation of variables
# points
hob= 34. 	#ft
hoc= 5. 	#ft
hoa= 50. 	#ft

hod= 80. 	#ft height
g= 32.2 	#ft/sec**2

# sectional areas
A= 2.1 	#in**2
A1= 4.8 	#in**2
A2= 9.6 	#in**2

#CALCULATIONS
v= math.sqrt(2*g*(hod-hoc))
Q= v*A/144
va= v*A/A1
vb= v*A/A2
Va= va**2/(2*g)
Vb= vb**2/(2*g)
r= hob+hod-hoa-(va**2/(2*g))
r1=hob+hod-hob-(vb**2/(2*g))

#RESULTS
print  'Discharge = %.2f cuses'%(Q) 
print  ' Velocity head at A = %.2f ft-lb/lb'%(Va)
print  ' Velocity head at B = %.2f ft-lb/lb'%(Vb)
print  ' Pressure head at A = %.2f ft-lb/lb'%(r) 
print  ' Pressure head at B = %.2f ft-lb/lb'%(r1) 

Discharge = 1.01 cuses
 Velocity head at A = 14.36 ft-lb/lb
 Velocity head at B = 3.59 ft-lb/lb
 Pressure head at A = 49.64 ft-lb/lb
 Pressure head at B = 76.41 ft-lb/lb

Example 3.2 Page No : 40

In [2]:
import math 

#initialisation of variables
w= 62.4 	#lb/ft**3
P= 1.7  	#lb/in**2 pressure
d1= 6. 	    #in diameters
d2= 3. 	    #in diameters
hab= 8. 	#ft
Q= 0.75 	#cuses
sm= 13.6    # gravity
g= 32.2 	#ft/sec**2

#CALCULATIONS
dP= P*144/w
va= Q*(d1/d2)**4/math.pi
k= -(((d1/d2)**4-1)-((-dP+hab)*2*g/va**2))
h= (-dP+hab)*12/(sm-1)

#RESULTS
print  'k = %.f '%(k)
print  'height difference = %.2f in'%(h) 

k = 3 
height difference = 3.88 in

Example 3.3 Page No : 42

In [3]:
import math 

#initialisation of variables
h= 20. 	    #ft pressure head
Q= 4.81 	#cuses 
C= 1.
g= 32.2 	#ft/sec**2
d= 10.   	#indiameter

#CALCULATIONS
d= ((Q*4*144/(d**2*math.pi))**2*100**2/((Q*4*144/(d**2*math.pi))**2+2*g*h))**0.25

#RESULTS
print  'Smallest Diameter = %.1f in'%(d)

Smallest Diameter = 4.9 in

Example 3.4 Page No : 43

In [4]:
import math 

#initialisation of variables
d= 1./3 	#ft
g= 32.2 	#ft/sec**2
d1= 4. 	    #in
d2= 1.6 	#in diameter

# guage readings
h1= 5.7 	#ft
h2= -1.9 	#ft

Q= 0.3  	#cuses
H1= 34. 	#ft height of water
H2= 19. 	#ft
H3= 7. 	    #ft
H4= 9.2 	#ft
h3= 2.9 	#ft
h4= 3.9 	#ft
Et= 54. 	#ft-lb/lb

#CALCULATIONS
v1= math.sqrt(2*g*(h1-h2)/((d1/d2)**4-1))
Q1= math.pi*v1*d**2/4
k= Q/Q1
P= (H1+H2)*H3/H4
P1= P-h3
r= P+h1-h2-h4
V= v1**2/(2*g)
E= r+V
dE= Et-E

#RESULTS
print  'Coefficienct of venturi meter = %.4f '%(k)
print  ' Pressure of venturi throat = %.2f ft of water'%(P1)
print  ' Loss in energy = %.1f ft-lb/lb'%(dE)

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

Coefficienct of venturi meter = 0.9587 
 Pressure of venturi throat = 37.43 ft of water
 Loss in energy = 9.8 ft-lb/lb
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