Chapter 10 : Steady Flow in Pipes and Channels

Example 10.1.1 page no : 269

In [1]:
import math 
#initialisation of variables
Q= 450. 			#ft**3/sec
k= 0.5
i= 1./2000
C= 105. 			#ft**1/2/sec
			
#CALCULATIONS
d= (((Q*math.sqrt(2./i))/(2*math.sqrt(1+k**2-k)*C))**(2./5))*(5.41/7.55)
b= d/2.
s= d*math.sqrt(1+k**2.)
			
#RESULTS
print  ' vertical= %.2f ft'%(d)
print  '  horizontal= %.2f ft'%(s)

 vertical= 5.41 ft
  horizontal= 6.05 ft

Example 10.2.2 page no : 275

In [5]:
import math 

#initialisation of variables

d= 6. 			#ft
C= 95. 			#ft**0.5/sec
i= 1./800
m= 1.705 			#ft
a= 15.16
g= 32.2 			#ft**2/sec
alpha = 15.30      # degree			

#CALCULATIONS
theta = int(180 + 2*alpha)
A= ((d/2)**2./2)*(((theta*math.pi)/180)+math.sin(math.radians(2*a)))
u= C*math.sqrt(m*i)
Q= A*u
f= (2*g)/C**2.
			
#RESULTS
print  ' rate of volumetric flow= %.1f ft**3/sec'%(Q)
print  '  resistance factor= %.5f '%(f)

 rate of volumetric flow= 82.3 ft**3/sec
  resistance factor= 0.00714

Example 10.3.1 page no : 277

In [5]:
import math 
#initialisation of variables

m= 6. 			#lb/sec
w= 62.3			#lb/ft**3
s= 0.9
l= 2500. 			#ft
u= 0.115
r= 8. 			#ft
g= 32.2 			#ft/sec**2

#CALCULATIONS
uc = round(2300*u/.25 * 1/(s*w),1)
v = round(m/(s*w) * 1./(math.pi/4 *1./16),2)
p1p2 = (r*u)/math.pi * l * 64**2 * 6 /(s*w*g)
dp= 8.*u*l*r**4*m/(math.pi*s*w*g)
P= m*dp/(s*w*550.)
			
#RESULTS
print  ' Critical Velocity is = %.1f ft/sec'%uc
print  ' Actual Velocity is = %.2f ft/sec'%v
print  ' Power required= %.f h.p'%(P)

# Note : Answers may vary because of rounding error. Please calculate manually.

 Critical Velocity is = 18.9 ft/sec
 Actual Velocity is = 2.18 ft/sec
 Power required= 2 h.p

Example 10.4.1 page no: 282

In [22]:
import math 
#initialisation of variables
p= 0.0024 			#slug/ft**3
u= 10. 			#ft/sec
v= 3.75*10**-7 			#slug
d= 0.25			#in
u1= 100. 			#ft/sec
			
#CALCULATIONS
R= round(u*d*p/(12.*v),-1)
f= round(16./R,3)
F1= f*p*u**2*math.pi*d/(2*12.)
R1= R*10.
f1= 0.0791/R1**0.25
F2= f1*p*u1**2*math.pi*d/(2*12*10.)
C= F2/F1
			
#RESULTS
print  '  Raynolds number = %.0f'%R
print  '  resistance coefficient = %.2f '%(f)
print  '  Drag force per foot length = %.2e lbf/ft'%(F1)
print  '  Ratio of skin-friction drag forces per ft  = %.2f '%(C)

  Raynolds number = 1330
  resistance coefficient = 0.01 
  Drag force per foot length = 9.42e-05 lbf/ft
  Ratio of skin-friction drag forces per ft  = 6.14

Example 10.4.2 pageno : 283

In [25]:
import math 
#initialisation of variables

Q= 0.7			#ft**3/sec
a= 16.
n= 0.65
P= 5. 			#h.p
l= 3000. 			#ft
g= 32.2 			#ft**2/sec 
d= 0.85 			#gm/cc
d1= 0.5 			#ft
			
#CALCULATIONS
u= Q*a/math.pi
u1= n*P*550.*g/(8*math.pi*u**2*l)
v= u1/d
R= round(u*d1*30.5**2/1.05,-1)
			
#RESULTS
print "Coefficient of viscosity is = %.2f ft/sec"%u
print  ' Reynolds number= %.f '%(R)

Coefficient of viscosity is = 3.57 ft/sec
 Reynolds number= 1580

Example 10.4.3 page no : 285

In [27]:
import math 			
#initialisation of variables

u1= 80. 			#ft/sec
c= 62.
s= 0.25
l= 11. 			#ft
w= 62.3 			#lb/ft**3
u1= 80. 			#ft/sec
d= 2. 			#lbf/in**2
			
#CALCULATIONS
u= u1*c/(l*w*s)
P= ((u1/u)**2)*s*d*144./(l*w)
			
#RESULTS
print  ' water velocity = %.2f ft/sec'%(u)
print  ' w pressure drop = %.3f lbf/ft**2 per ft length'%(P)

 water velocity = 28.95 ft/sec
 w pressure drop = 0.802 lbf/ft**2 per ft length