Chapter 9 : Forces on bodies immersed in fluids

example 9.1 pageno : 166

In [1]:
import math 

# Initialization of Variable
rho = 1.2
mu = 1.85/100000
pi = 3.1428
d = 3.
v = 50.*1000/3600

#calculation part 1
Re = d*rho*v/mu

#from chart of drag coeff. vs Re
Cd = 0.2                    #coeff. of drag
Ad = pi*d**2/4.             #projected area
Fd = Ad*Cd*rho*v**2/2.
print  "The drag force on sphere in N",Fd 

#part 2
v = 2.
l = 0.25
Re = l*v*rho/mu
zi = 4*pi*(l**3*3./4/pi)**(2/3.)/6./l**2            #sphericity

#using graph
Cd = 2.
Ad = l**2
Fd = Ad*Cd*rho*v**2/2.
print  "The drag force on cube in N",Fd 

The drag force on sphere in N 163.6875
The drag force on cube in N 0.3

example 9.2 page no : 168

In [2]:
import math 

# Initialization of Variable
rho = 1.2
mu = 1.85/100000
pi = 3.1428
g = 9.81
d = 1.38
t = 0.1                 #thickness
v = 30*1000/3600.
T = 26.2                #Tension
m = 0.51                #mass
theta = 60.*pi/180.

#calculation
Fd = T*math.cos(theta)
print "Drag force in N: %.4f"% Fd
A = pi*d**2/4.
Ad = A*math.cos(theta)              #area component to drag
Cd = 2*Fd/Ad/rho/v**2               #coeff of drag
print  "The drag coefficient: %.4f"% Cd 
Fg = m*g                            #force of gravity
Fb = rho*pi*d**2/4.*t*g              #buoyant force
Fl = Fg-Fb+T*math.sin(theta)
print "The lift force in N : %.4f"%Fl
Al = A*math.sin(theta)
Cl = 2*Fl/Al/rho/v**2
print "The coefficient of lift: %.4f"%Cl 

Drag force in N: 13.0909
The drag coefficient: 0.4202
The lift force in N : 25.9368
The coefficient of lift: 0.4803

example 9.3 page no : 171

In [3]:
import math 

# Initialization of Variable
rhog = 1200.            #density of glycerol
mu = 1.45
pi = 3.1428
g = 9.81
rhos = 2280.             #density of sphere
v = 0.04                #terminal velocity
a = 2*mu*g*(rhos-rhog)/v**3./3./rhog**2         #a = Cd/2/Re

#using graph of Cd/2/Re vs Re
Re = 0.32
d = Re*mu/v/rhog
print  "Diameter of sphere in (m): %.4f"%d 

Diameter of sphere in (m): 0.0097

example 9.4 page no : 173

In [5]:
import math 

# Initialization of Variable
rhoa = 1.218            #density of air
mu = 1.73/100000
pi = 3.1428
g = 9.81
rhog = 1200.
rhop = 2280.            #density of polythene
d = 0.0034              #diameter
a = 4*d**3*(rhop-rhoa)*rhoa*g/3/mu**2       #a = Cd*Re**2

#using graph of Cd*Re**2 vs Re
Re = 2200.
v = Re*mu/d/rhog
print  "The terminal velocity in (m/s) %f"%v 

The terminal velocity in (m/s) 0.009328

example 9.6 page no : 177

In [7]:
import math 

# Initialization of Variable
pi = 3.1428
rho = 825
mu = 1.21
g = 9.81
l = 0.02
de = 0.02           #dia exterior
di = 0.012          #dia interior

# Initialization of Variable
rho = 998.              #density of water
mu = 1.25/1000          #viscosity of water
w = 100.                #mass of water
pi = 3.1428
g = 9.81
rhog = 2280.            #density of glass
wg = 60.                #mass of glass
d = 45.*10**-6           #diameter of glass sphere

#claculation
rhom = (w+wg)/(w/rho+wg/rhog)       #density of mixure
e = w/rho/(w/rho+wg/rhog)           #volume fraction of watter

#using charts
zi = math.exp(-4.19*(1.-e))

K = d*(g*rho*(rhog-rho)*zi**2/mu**2)**(1./3)        #stoke's law coeff.
print K
if K<3.3:
    print "settling occurs in stoke-s law range"
    U = g*d**2*e*zi*(rhog-rhom)/18/mu
    print "settling velocity in m/s: %f"%U
else:
    print "settling does not occurs in stoke-s law range"

0.504080734813
settling occurs in stoke-s law range
settling velocity in m/s: 0.000297

example 9.7 page no : 180

In [9]:
import math 
from numpy import linspace


# Initialization of Variable
rhog = 1200.            #density of glycerol
mu = 1.45               #viscosity of glycerol
pi = 3.1428
g = 9.81
rhos = 2280.            #density of sphere
d = 8/1000.
s = 0.
uf = 0.8*0.026

#calculation
def intre():
    s = 0.
    u = linspace(0,uf,1000)
    for i in range(0,1000):
        y = ((pi/6*d**3*rhos*g-pi*d**3/6*rhog*g-0.5*pi*d**2/4*24*mu/d/rhog*rhog*u[i])/pi*6/d**3/rhos)**(-1)*uf/1000
        s = s+y
    a = s
    return a

t = intre()
print "Time taken by particle to reach 80%% of its velocity in (s): %f"%t

Time taken by particle to reach 80% of its velocity in (s): 0.009020
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