# Chapter 11 : Forces on Immersed Bodies¶

## Example 11.1 Page No : 413¶

In [1]:
import math

#Initialization of variables
d = 1.2     		    	#diameter - m
w = 1.  	    		    #m
U = 60.*1000/3600 			#speed - m/s
nu = 1.5e-5      			#m**2/s
Cd = 0.4
rho = 1.22 		        	#kg/m**3

#calculations
Rn = U*d/nu
A = d*w
Fd =  Cd*0.5*rho*U**2 *A
M =  0.5*Fd

#results
print "Bending moment  =  %.2f h**2 N m"%(M)

Bending moment  =  40.67 h**2 N m


## Example 11.2 Page No : 415¶

In [2]:
import math

#Initialization of variables
d = 0.006 			#diameter - m
U = 0.01 			#m/s
gaml = 8000. 		#specific weight - N/m**3
gams = 7.9*10**3 *9.81
mu = 13.9

#calculations
mu =  d**2 /18 *(gams - gaml)/U
RN =  U*d*(gaml/9.81) /mu

#results
print "Viscosity of oil  =  %.1f Ns /m**2"%(mu)
print "Reynolds number of motion is = %.3f"%RN

# rounding off error. please check.

Viscosity of oil  =  13.9 Ns /m**2
Reynolds number of motion is = 0.004


## Example 11.3 Page No : 416¶

In [3]:
import math

#Initialization of variables
s = 2.7
gamw = 9810. 			#N/m**3
mu = 0.001  			#Ns/m**2
d = 0.15*10**-3 			#m
rho = 1000. 			#kg/m**3

#calculations
gams = s*gamw
U =  d**2 *(gams-gamw)/(18*mu)
RN =  U*d*rho/mu
Cd  =  (1+ 3./16 *RN)**0.5 *(24/RN)
U22  =  4./3 *d*(gams-gamw) /(Cd*rho)
U2 = math.sqrt(U22)

#results
print "Settling velocity of sand in case 1   =  %.2f m/s"%(U)
print " Settling velocity of sand in case 2  =  %.4f m/s"%(U2)
#The answer is a bit different due to rounding off error.

Settling velocity of sand in case 1   =  0.02 m/s
Settling velocity of sand in case 2  =  0.0186 m/s


## Example 11.4 Page No : 417¶

In [4]:
import math

#Initialization of variables
A = 2.           			#area - m**2
U = 100*1000./3600 			#speed-m/s
Cd = 0.32
rho = 1.24

#calculations
Fd =  Cd*0.5*rho*U**2 *A
P =  Fd*U

#results
print "Power required  =  %.1f kW"%(P/1000)

Power required  =  8.5 kW


## Example 11.5 Page No : 417¶

In [6]:
import math

#Initialization of variables
ratio = 0.15

#calculations
VU =  (1/(1-ratio))**(1./3)
percent =  (VU-1)*100

#results
print "percent increase in speed  =  %.1f %%"%(percent)

percent increase in speed  =  5.6 %


## Example 11.6 Page No : 419¶

In [4]:
import math
from sympy import Symbol,solve

#Initialization of variables
U = 50.*1000/3600 			#speed - m/s
cd1 = 0.34
cd2 = 1.33

#calculations
print ("On solving for both convex and concave surfaces,")
w = Symbol("w")
ans = solve(1.98*(13.98 - 0.25*w) - (13.88 + 0.25*w))
w = ans[0]
N = w/(2*math.pi) *60

#results
print "rotational speed  =  %.1f rpm"%(N)

# note : value of w is slightly different because of sympy inbuilt method solve. but it is very accurate.

On solving for both convex and concave surfaces,
rotational speed  =  176.9 rpm