Chapter 7 : Fluid Resistance¶
Example 7.1 Page no 245¶
In [1]:
# Is the flow laminar or turbulent
from math import *
from __future__ import division
# Given
nu1 = 0.804*10**-6 # viscosity in m**2/s
V = 0.3 # velocity in m/s
D = 0.02 # diameter in m/s
# for water
rho = 995.7 # density in kg/m**3
# for gylcerine
mu = 8620*10**-4 # viscosity in Ns/m**2
S = 1.26 # specific gravity
nu2 = mu/(S*rho) # viscosity of glycerine in Ns/m**2
# Solution
R1 = V*D/nu1
print "Reynolds number for water =",round(R1,0)
print "R > 2000 the flow is turbulent for water"
print "\n"
R2 = V*D/nu2
print "Reynolds number for glycerine =",round(R2,1)
print "R < 2000 the flow is laminar for glycerine"
Example 7.2 Page no 248¶
In [2]:
# Eddy Viscosity; mixing length ; turbulence constant
from math import *
from __future__ import division
from scipy import *
import numpy as np
from sympy import *
y = Symbol('y')
d = 0.0175 # diameter in m
s = 0.3 # shear stress at a distance in m
tau = 103 # shear stress in Pa
rho = 1000 # density in kg/m**3
#y = 0.3
# solution
Up = diff(8.5+0.7*log(y),y)
print Up
Up = (0.7/0.3) # for y = 0.3
k = sqrt(tau/(rho*s**2*Up**2))
print "Turbulence constant = ",round(k,2)
Ml = k*s*100 # mixing length
print "Mixing length = ",round(Ml,1),"cm"
Eta = rho*(Ml/100)**2*Up
print "Eddy viscosity =",round(Eta,1),"Nm/s**2"
Example 7.3 Page no 256¶
In [3]:
# PLot boundary layer distribution and total drag on the plate
from math import *
from __future__ import division
from pylab import plt
from numpy import *
from scipy import *
from sympy import *
import matplotlib.pyplot as plt
# Given
# for glycerine
S = 1.26 # specific gravity
mu = 0.862 # dynamic viscosity in Ns/m**2
rho = S *1000 # density in kg/m**3
K2 = 0.332
V=1 # velocity in m/s
# Solution
# from blasius equation
x = [0,0.1,0.5,1.0,2.0];
d = 0.1307*np.sqrt(x)*100
tauo = K2*rho*V**2/(sqrt(1462)*np.sqrt(x))
#plt.figure()
plt.plot(x, d, 'r')
plt.xlabel('x(m)')
plt.ylabel('delta(cm),tauo(N/m**2)')
#plt.title('delta v/s x')
#plt.legend('d')
plt.plot(x, tauo, 'b')
plt.xlabel('x')
#plt.ylabel('tauo(N/m**2)')
#plt.title('tauo v/s x(m)')
plt.legend('d''t')
plt.show()
Example 7.4 page no 260¶
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# Sketch the boundary layer and drag on the plate
import numpy as np
from math import *
from __future__ import division
import matplotlib.pyplot as plt
from numpy import sqrt
# Given
rho = 1.197 # air density in kg/m**3
mu = 18.22*10**-6 # viscosity in Ns/m**2
l = 5 # length of the plate
V = 8 # velocity in m/s
Rec = 5*10**5 # crictical reynolds number
l1 = 0.951 # length from 0 to 0.951
l2 = 5.0 # length from 0 to 5
l3 = 0.951 # length from 0 to 0.951
# Solution
X = Rec/525576
x = [0,0.1,0.3,0.6,0.951];
d = 0.0069*np.sqrt(x)*100
plt.figure()
plt.plot(x, d, 'r')
plt.xlabel('x(m)')
plt.ylabel('delta(cm)')
plt.title('delta v/s x')
plt.legend('L')
plt.show()
X1 = [0.951,1.5,2.0,2.5,3.0,4.0,5.0]
Dt = 0.0265*np.power(X1,(4/5))*100
plt.figure()
plt.plot(X1, Dt, 'g')
plt.xlabel('x(m)')
plt.ylabel('delta(cm)')
plt.title('delta v/s x')
plt.legend('T')
plt.show()
Td = 0.664*sqrt(mu*rho*V**3*l1)+0.036*rho*V**2*l2*(mu/(rho*V*l2))**0.2-0.036*rho*V**2*l3*(mu/(rho*V*l3))**0.2
print "Total Drag = ",round(Td,3),"N"
Example 7.5 Page no 270¶
In [6]:
# Determine drag on the sphere
from math import *
from pylab import plt
from __future__ import division
# Given
d = 0.01 # doameter of sphere in m
v = 0.05 # velocity in m/s
S = 1.26 # specific gravity
mu = 0.826 # kinematic viscosity in Ns/m**2
rho = S*1000 # density
# Solution
R = rho*v*d/mu
# for the above rho
Cd = 35
Fd = 0.5*Cd*rho*v**2*pi*d**2/4
print "Drag on the sphere = ",round(Fd,4),"N"
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