Chapter 9 : Potential Flow

Example 9.4 Page No : 339

In [2]:
import math 
			
#Initialization of variables
k = 1.5
r = 40. 	    		#cm
theta = 45. 			#degrees
			
#calculations
vr =  -2*k*r*math.cos(math.radians(2*theta))
vt =  2*k*r*math.sin(math.radians(2*theta))
			
#results
print "velocity in radial direction  =  %d cm/s"%(vr)
print " velcoity in angular direction  =  %d cm/s"%(vt)

velocity in radial direction  =  0 cm/s
 velcoity in angular direction  =  120 cm/s

Example 9.14 Page No : 371

In [1]:
import math 
			
#Initialization of variables
T = 4.5                 #m^2/s
a = 0.6                 #diameter - m
u = 5. 		        	#velocity - m/s
rho = 1000. 			#kg/m**3
			
#calculations
sint = 0.5*(1- T/(2*math.pi*a*u))
theta =  math.degrees(math.asin((sint)))
dp =  0.5*rho*u**2 *(1 - (2 + T/(2*math.pi*a*u))**2)
			
#results
print "Angle  =  %.1f or %.1f degrees"%(theta,180-theta)
print " Min guage pressure  =  %.2f kN/m**2"%(dp/1000)

#The answer in textbook is wrong. please check

Angle  =  22.4 or 157.6 degrees
 Min guage pressure  =  -50.15 kN/m**2

Example 9.15 Page No : 371

In [4]:
import math 
			
#Initialization of variables
T = 6*math.pi
r = 1./3
			
#calculations
vab = T/(4*math.pi)
vba =  T/(2*math.pi)
w = vab/r
			
#results
print "rate of rotation  =  %.1f rad/s"%(w)
print "speed of A by B  =  %.1f m/s"%(vab)
print "speed of B by A  =  %.1f m/s"%(vba)

rate of rotation  =  4.5 rad/s
speed of A by B  =  1.5 m/s
speed of B by A  =  3.0 m/s