# Chapter 13 : Unsteady-Flow Problems¶

## Example 13.1 Page No : 449¶

In [1]:
import math

#Initialization of variables
ken = 0.5
kex = 0.2
f = 0.0018
l = 10. 	#ft
dia = 3. 	#in
z1 = 8.
z2 = 5.

#calculations
x1 = ken+kex+f*l*12/dia
t = 35.5*2/3 *(z1**(3./2) - z2**(3./2))

#Results
print "Time reqired  =  %.f s"%(t)

Time reqired  =  271 s


## Example 13.2 Page No : 451¶

In [2]:
import math

#Initialization of variables
print ("For steady state, dV/dt  = 0")
Q = 1600./449  #steady flow rate
A2 = 0.1963
g = 32.2
rp2 = 2000.  #speed of rotation - rpm

#calculations
V2 = Q/A2
hp1 = 32*V2**2 /(2*g) -50
hp2 = hp1*(rp2/1650)**2
hpf = 169. 	#ft
Q = 4.1 	#cfs

#Results
print "Steady state flow rate  =  %.2f cfs"%(Q)

For steady state, dV/dt  = 0
Steady state flow rate  =  4.10 cfs


## Example 13.3 Page No : 455¶

In [4]:
import math
from numpy import *

#Initialization of variables
kl = 0.5
f = 0.02
L = 15. 	#length - m
D = 0.1 	#ft
k = 3.5
g = 9.81
H = 2.	#ft

#calculations
k = kl+f*L/D
V0 = math.sqrt(2*g*H/(1+k))
Q = array([0.25, 0.5, 0.75])
V = V0*Q
Vfun = (2.95+V)/(2.95-V)
lnVfun = log(Vfun)
t = 1.129*lnVfun

print "ln        t,s"
#Results
for i in range(len(t)):
print "%.3f     %.3f"%(lnVfun[i],t[i])

print ("Similarly, it can be calculated for L = 150,1500 ft")

ln        t,s
0.511     0.577
1.100     1.242
1.949     2.201
Similarly, it can be calculated for L = 150,1500 ft


## Example 13.4 Page No : 462¶

In [6]:
import math

#Initialization of variables
Q = 30. 	#cfs
r = 2.  	#ft
cp = 3200.
rho = 1.94
Q2 = 10. 	#cfs
z = 300. 	#ft

#calculations
V = Q/(math.pi*r**2)
ph = rho*cp*V/144
phd = 4000/cp /(2*r) *ph
dV = (Q2-Q)/(math.pi*r**2)
dph = -rho*cp*dV/144
ph3 = rho*cp*V/3 /144
ph4 = ph3*z*2/cp

#Results
print "Water hammer pressure =  %.1f psi"%(ph)
print " Water hammer pressure in case 2 =  %.1f psi"%(phd)
print " Water hammer pressure in case 3 =  %.1f psi"%(dph)
print " Pressure at valve in case 4  =  %.1f psi"%(ph3)
print " Pressure at 300 ft from reservoir  =  %.2f psi"%(ph4)

Water hammer pressure =  102.9 psi
Water hammer pressure in case 2 =  32.2 psi
Water hammer pressure in case 3 =  68.6 psi
Pressure at valve in case 4  =  34.3 psi
Pressure at 300 ft from reservoir  =  6.43 psi