Chapter 2 : Similarity

Example 2.1 Page No : 23

In [1]:
	
#initialisation of variables
r= 4.
l1= 4 	#units long axis
l2= 10 	#units long axis
	
#CALCULATIONS
sxy= (4/r)
sxy1= l1**2
sxy2= l2**2
	
#RESULTS
print  'x**2+4*y**2 = %.f '%(sxy)
print  ' x**2+4*y**2 = %.f '%(sxy1)
print  ' x**2+4*y**2 = %.f '%(sxy2)

x**2+4*y**2 = 1 
 x**2+4*y**2 = 16 
 x**2+4*y**2 = 100

Example 2.3 Page No : 29

In [1]:
import math

#initialisation of variables
vo= 10 	#ft/sec
a= 0.5 	#ft**-1
b= 1 	#ft
x= -2 	#ft
y= 2 	#ft
b1= 2
a1= 3./5 	#ft
	
#CALCULATIONS
Vx= vo/(a*x**2+b)
Vy= -2*a*b*vo*x*y/(a*x**2+b)**2
V= math.sqrt(Vx**2+Vy**2)
fx= -2*a*b**2*vo**2*x/(a*x**2+b)**3
fy= 2*a*b**2*vo**2*y*(b-a*x**2)/(a*x**2+b)**4
f= math.sqrt(fx**2+fy**2)
r= b1**2/a1
f1= f*r
	
#RESULTS
print  'Vx = %.2f ft/sec'%(Vx)
print  ' Vy = %.2f ft/sec'%(Vy)
print  ' V = %.2f ft/sec'%(V)
print  ' fx = %.2f ft/sec**2'%(fx)
print  ' fy = %.2f ft/sec**2'%(fy)
print  ' f = %.2f ft/sec**2'%(f)
print  ' r = %.2f in the present case'%(r)
print  ' f1 = %.2f ft/sec**2'%(f1)

Vx = 3.33 ft/sec
 Vy = 4.44 ft/sec
 V = 5.56 ft/sec
 fx = 7.41 ft/sec**2
 fy = -2.47 ft/sec**2
 f = 7.81 ft/sec**2
 r = 6.67 in the present case
 f1 = 52.05 ft/sec**2

Example 2.4 Page No : 36

In [3]:
	
#initialisation of variables
r= 1./5
b1= 2 	#ft
a1= 3./5 	#ft
	
#CALCULATIONS
r= (a1*b1)**2*r
	
#RESULTS
print  'ratio of resultant forces acting on coorresponding fluid elements = %.3f '%(r)

ratio of resultant forces acting on coorresponding fluid elements = 0.288

Example 2.5 Page No : 44

In [2]:
	
#initialisation of variables
vos= 70. 	#ft/sec
as1= 78. 	#ft density
am= 72. 	#ft wind-tunnel
ls1= 6. 	#ft strut section
lm= 2.  	#ft length
um= 386. 	#ft/sec
us= 372. 	#ft/sec
dm= 0.4
	
#CALCULATIONS
vom= vos*as1*ls1*um/(am*lm*us)
Ds= dm*(am/as1)*(us/um)**2
	
#RESULTS
print  'Air speed = %.f ft/sec'%(vom)
print  ' Ds = %.3f lbf'%(Ds)

Air speed = 236 ft/sec
 Ds = 0.343 lbf

Example 2.6 Page No : 45

In [3]:
	
#initialisation of variables
vom= 236. 	#ft/sec
as1= 0.072 	#ft
am = 62.4 	#ft density of water
ls1= 2. 	#ft
lm= 8. 	#ft
um= 248. 	#ft/sec  viscosity
us= 3.86 	#ft/sec
Pm= 0.4/3.3
	
#CALCULATIONS
voh= vom*as1*ls1*um/(am*lm*us)
Ds= Pm*(as1/am)*(um/us)**2*(ls1/lm)*(lm-ls1)
	
#RESULTS
print  'Air speed = %.2f ft/sec'%(voh)
print  ' Drag force = %.3f lbf'%(Ds)

# note : rounding off error

Air speed = 4.37 ft/sec
 Drag force = 0.866 lbf

Example 2.7 Page No : 51

In [4]:
import math 
	
#initialisation of variables
To1= 540. 	#R temperature
po3= 12.6 	#lbf/in**2
l3= 3.   	#ft
po1= 14.7 	#lbf/in**2 pressure
l1= 1.   	#ft
vo1= 500. 	#ft/sec velocity
r= 0.83
P1= 1.   	#lbf/in**2 turbine blade
	
#CALCULATIONS
To3= To1*(po3*l3/(po1*l1))**r
Vo3= vo1*math.sqrt(To3/To1)
P3= P1*po3*l3/(po1*l1)
	
#RESULTS
print  'To3 = %.f R'%(To3)
print  ' Vo3 = %.f ft/sec'%(Vo3)
print  ' P3 = %.2f lbf/ft'%(P3)

# note : book answers are not accurate.

To3 = 1183 R
 Vo3 = 740 ft/sec
 P3 = 2.57 lbf/ft