Chapter 6 : Equations of Motion for a Fluid Element

Example 6.1.1 page no : 127

In [1]:
#initialisation of variables

F= 100. 		#lbf
a= 20. 			#ft/sec**2
			
#CALCULATIONS
m= F*32.2/a
			
#RESULTS
print  ' mass of the body = %.f lb'%(m)

 mass of the body = 161 lb

Example 6.1.2 Page no : 127

In [2]:
#initialisation of variables

m= 5. 			#lb
a= 200. 			#cm/sec**2
			
#CALCULATIONS
F= m*a/(32.2*30.5)
			
#RESULTS
print  ' Force on the body = %.2f lbf'%(F)

 Force on the body = 1.02 lbf

Example 6.1.3 page no : 128

In [3]:
#initialisation of variables

m= 1. 			#gm
g= 327. 		#cm/sec**2
			
#CALCULATIONS
F=m*g/981.
			
#RESULTS
print  ' Force on the body = %.2f gf'%(F)

 Force on the body = 0.33 gf

Example 6.2.1 page no : 129

In [4]:
#initialisation of variables

w= 0.0764 			#lbf/ft**3
u= 88. 			#ft/sec
g= 32.2 			#ft/sec**2
			
#CALCULATIONS
q= w*u**2./(2*g)
			
#RESULTS
print  ' dynamic pressure of air = %.2f lbf/ft**2'%(q)

 dynamic pressure of air = 9.19 lbf/ft**2

Example 6.3.1 page no: 132

In [6]:
    
#initialisation of variables

p= 60. 			#lbf/in**2
w= 62.4 			#lbf/ft**3
l= 1. 			#ft
g= 32.2 			#ft/sec**2
			
#CALCULATIONS
i= p*144./(w*l)
a= i*g
			
#RESULTS
print  'accelaration of fluid = %.f ft/sec**2'%(a)
print 'Answer in book is wrong please check manually.'

accelaration of fluid = 4458 ft/sec**2
Answer in book is wrong please check manually.

Example 6.3.2 page no : 133

In [7]:
#initialisation of variables
import math 
import numpy

w= 60. 			#re/min
d= 1. 			#ft
g= 32.2 		#ft/sec**2
			
#CALCULATIONS
a= w**2.*d*4.*math.pi**2./(2.*60**2)
i= a/g
o= math.degrees(numpy.arctan(i))
			
#RESULTS
print  'slope ofthe free surface = %.1f degrees'%(o)

slope ofthe free surface = 31.5 degrees

Example 6.3.3 page no : 134

In [9]:
#initialisation of variables
import math 

H= 50. 			#ft
l= 200. 			#ft
g= 32.2 			#ft/sec**2
			
#CALCU;ATIONS
i= H/l
a= i*g
			
#RESULTS
print  'accelaration = %.2f ft/sec**2'%(a)

accelaration = 8.05 ft/sec**2

Example 6.7.2 page no :145

In [10]:
#initialisation of variables
import math 

g= 32.2 			#ft/sec**2
h= 12. 			#in
r= 10. 			#in
			
#CALCULATIONS
w= math.sqrt(2*g*(r/12)*(12/r)**2)*(60/(2*math.pi))
P= h+(r/4.)
			
#RESULTS
print  'speed of rotation = %.f rev/min'%(w)
print  ' maximum pressure head = %.1f in of water'%(P)

speed of rotation = 84 rev/min
 maximum pressure head = 14.5 in of water

Example 6.8.1 page no : 147

In [11]:
#initialisation of variables
import math 

l= 6. 			#ft
g= 32.2 			#ft/sec**2
			
#CALCULATIONS
T= 2*math.pi*math.sqrt(l/g)
			
#RESULTS
print  'natural period ofthe system = %.2f sec'%(T)

natural period ofthe system = 2.71 sec

Example 6.8.2 page no : 151

In [12]:
#initialisation of variables
import math 

l= 6. 			#ft
g= 32.2 		#ft/sec**2
l1= 6. 			#ft
l2= 6. 			#ft
l3= 34.			#ft
			
#CALCULATIONS
a= -((l1+l2-l3)/l)*g
w= math.sqrt(a/4.5)*(60/(2*math.pi))
			
#RESULTS
print  'maximum speed = %.1f cycles/min'%(w)

maximum speed = 48.9 cycles/min