Chapter 4 : Energy Considerations in Steady Flow

Example 4.1 Page No : 93

In [3]:
import math 
	
#Initialization of variables
d = 1.26    #specific gravity
d = 24.  	#in
d2 = 60.    #cm
Q = 25. 	#cfs
Q2 = 700. 	#L/s
dout = 12. 	#in
dout2 = 30./100 	#m
z = 3. 	    #ft
z2 = 1. 	#m
P1 = 45. 	#psi
P2 = 300. 	#kN/m**2
gamma = 9.81 	#kN/m**3
	
#calculations
V1 = d/math.pi
V2 = d*4/math.pi
pf = (P1*144/(1.26*62.4) + (V1**2)/64.4 - V2**2 /64.4 +z)*1.26*62.4/144
V1 = Q2/1000/(math.pi*dout2**2)
V2 = 4*V1
p2f = ((P2/(1.26*gamma)) + V1**2 /(2*gamma) -V2**2 /(2*gamma) +z2)*1.26*gamma

#Results
print " English units"
print " Pressure at point 2  =  %.1f psi "%(pf)
print " \n SI Units"
print " Pressure at point 2  =  %.d kN/m**2 "%(p2f)

 English units
 Pressure at point 2  =  39.2 psi 
 
 SI Units
 Pressure at point 2  =  254 kN/m**2

Example 4.2 Page No : 94

In [2]:
import math 
	
#Initialization of variables
h = 20.    	#m
c = 4187. 	#N m /(kg K)
g = 9.81
	
#calculations
dT = g*h/c
	
#Results
print "Increase in temperature of water  =  %.3f K"%(dT)

Increase in temperature of water  =  0.047 K

Example 4.3 Page No : 96

In [4]:
	
#Initialization of variables
sg = 1.26  #specific gravity of liquid
sg2 = 1.26 #
HP = 22.
HP2 = 16.
	
#calculations
hp = HP*550/(sg*62.4) 	#divide by Q
Q = 14.2 	#cfs
print "In English units, By trial Q =  %.1f cfs"%(Q)
hp2 = HP2*1000/(sg2*9.81)
Q2 = 0.42 	#m**3/s
print " In SI units, By trial Q =  %.2f m**3/s"%(Q2)

In English units, By trial Q =  14.2 cfs
 In SI units, By trial Q =  0.42 m**3/s

Example 4.4 Page No : 96

In [5]:
	
#Initialization of variables
g = 9810. 	#N/m**3
Q = 10 	    #m**3/s
H = 20 	    #m
	
#calculations
Rate = g*Q*H/1000
	
#Results
print "Rate of energy loss  =  %d kW"%(Rate-2)

Rate of energy loss  =  1960 kW

Example 4.5 Page No : 98

In [6]:
import math 
	
#Initialization of variables
s = 0.86
P2 = 3.8 	#pressure - psia
Patm = 26.8 	#atmospheric pressure - Hg
SPatm = 29.9 	#in of Hg
psi = 14.7 	#psia
	
#calculations
Pa = Patm*psi/SPatm
Pcrit = -(Pa-P2)*144/(s*62.4)
Q = math.sqrt((-Pcrit+ 10*144/(s*62.4))*64.4*math.pi**2 /(-1/2.25**2 + 1/0.25**2 ))
	
#Results
print "Max. theoretical flow  =  %.1f cfs"%(Q)

Max. theoretical flow  =  45.7 cfs

Example 4.6 Page No : 104

In [7]:
import math 
	
#Initialization of variables
z = 3.       	#ft
s = 0.82
	
#calculations
ua = math.sqrt(z*2*32.2)
ub = math.sqrt(2*32.2*(-2*(1-s) +ua**2 /(2*32.2)))
	
#Results
print "Velocity at B =  %.1f fps"%(ub)

Velocity at B =  13.0 fps

Example 4.7 Page No : 108

In [5]:
import math 
	
#Initialization of variables
d = 3.   	#in
x1 = 0.5**2
x2 = 0.75**2
z = 80.  	#ft
z3 = 10. 	#ft
	
#calculations
print ("Using Bernoullis theorem")
v3 = 29.7 	#fps
Q = math.pi /4 *(d/12)**2 *v3
hls = 5*(x1*v3)**2 /(2*32.2)
hld = 12*(x2*v3)**2 /(2*32.2)
	
#Results
print "Head loss in suction pipe  =  %.1f ft"%(hls)
print " Head loss in discharge pipe  =  %.1f ft"%(hld)
print " Flow rate  =  %.2f cfs"%(Q)

Using Bernoullis theorem
Head loss in suction pipe  =  4.3 ft
 Head loss in discharge pipe  =  52.0 ft
 Flow rate  =  1.46 cfs

Example 4.8 Page No : 109

In [9]:
import math 
	
#Initialization of variables
z1 = 2.
z2 = 0.8
	
#calculations
print ("From equation of continuity, z1*v1 = z2*v2")
V1 =  math.sqrt((z2-z1)*2*9.81/(1-z1**2 /z2**2))
V2 = z1*V1/z2
Q = z1*1*V1
	
#Results
print "Flow rate  =  %.2f m**3/s"%(Q)

From equation of continuity, z1*v1 = z2*v2
Flow rate  =  4.24 m**3/s

Example 4.9 Page No : 113

In [1]:
import math 
	
#Initialization of variables
theta = 30. 	#degrees
z = 10.     	#ft
x = 60.  	    #ft
	
#calculations
V = math.sqrt((0.5*32.2*69.3**2)/((x-math.sin(math.radians(theta)) *69.3)))
	
#Results
print "velocity  =  %.0f fps"%(V)

# rounding off error

velocity  =  55 fps

Example 4.10 Page No : 119

In [11]:
import math 
	
#Initialization of variables
V = 60. 	#fps
theta = 15. #degrees
ra = 6/12. 	#ft
rb = 8/12. 	#ft
B = 1.5/12 	#ft
	
#calculations
Vra = V*math.sin(math.radians(theta))
Q = 2* math.pi*ra*B*Vra
Vratio = ra/rb
Vb = Vratio*V
flow = (V**2 - Vb**2)/(2*32.2)
	
#Results
print "Flow rate  =  %.2f cfs"%(Q)
print " Velocity at b  =  %d fps"%(Vb)
print " Pressure head  =  %.1f ft"%(flow)

Flow rate  =  6.10 cfs
 Velocity at b  =  45 fps
 Pressure head  =  24.5 ft