Chapter 12: Incompressible Flow around a Body

Example 12.1, Page 399

In [1]:
from __future__ import division
import math


 #Initializing  the  variables
x  =35;
T  =  50;
m  =  1;
g  =9.81;
rho  =  1.2;
A  =  1.2;
U0  =  40*1000/3600;                                            #  Velocity  in  m/s

 #Calculations
L  =  T*math.sin(math.radians(x))+m*g;
D  =T*math.cos(math.radians(x));
Cl  =  2*L/(rho*U0**2*A);
Cd  =  2*D/(rho*U0**2*A);  

print "Lift Coefficient :",round(Cl,3)
print "Drag Coefficient :",round(Cd,3)

Lift Coefficient : 0.433
Drag Coefficient : 0.461

Example 12.2, Page 406

In [2]:
from __future__ import division
import math


 #Initializing  the  variables
Vp  =12;
lp  =  40;
lm  =  1;
As  =  2500;
Dm  =  32;
rhoP  =  1025;
rhoM  =  1000;
Ap  =  As;

 #Calculations
Am  =  As/40**2;
Vm  =  round(Vp*(lm/lp)**0.5,2);
Dfm  =  round(3.7*Vm**1.95*Am,1);
Rm  =  Dm  -  Dfm;
Rp  =  Rm  *(rhoP/rhoM)*(lp/lm)**2*(Vp/Vm)**2;
Dfp  =  2.9*Vp**1.8*Ap;
Dp  =  Rp  +  Dfp;

print "Expected total resistance (kN) :",round(Dp/1000,2)

Expected total resistance (kN) : 1407.07

Example 12.3, Page 410

In [3]:
from __future__ import division
import math


 #Initializing  the  variables
U0  =  80*1000/3600;
d  =  0.02;
rho  =1.2;
mu  =  1.7*10**-5;
A  =  0.02*500;                            #  Projected  area  of  wire
N  =  20;                                  #  No  of  cables

 #Calculations
Re  =  rho*U0*d/mu;
Cd  =  1.2                                 #  From  figure  12.10  for  given  Re;  
D  =  0.5*rho*Cd*A*U0**2
F  =  N*D;  
f  =    0.198*(U0/d)*(1-19.7/Re);

print "Total force on tower (kN) :",round(F/1000,2)
print "Frequency (Hz)            :",round(f,1)

Total force on tower (kN) : 71.11
Frequency (Hz)            : 219.9

Example 12.4, Page 415

In [4]:
from __future__ import division
import math


 #Initializing  the  variables
mu  =  0.03;
d  =  10**-3;
rhoP  =  1.1*10**3;
g  =  9.81;
rho0  =  0.9*10**3;
 #Calculations
B  =  18*mu/(d**2*rhoP);
t  =  round(4.60/B,4);
Vt  =  round(d**2*(rhoP  -  rho0)*g/(18*mu),5);
Re  =  rho0*Vt*d/mu;

print "Time taken by the particle take to reach 99 per cent of its terminal velocity (s):",t
print "\nReynolds No corrosponding to the velocity :",Re

Time taken by the particle take to reach 99 per cent of its terminal velocity (s): 0.0094

Reynolds No corrosponding to the velocity : 0.1089

Example 12.5, Page 417

In [5]:
from __future__ import division
import math


 #Initializing  the  variables
muO  =  0.0027;
Vt  =  3*10**-3;
rhoW  =  1000;
rhoP  =  2.4*rhoW;
rhoO  =  0.9*rhoW;
g  =  9.81;
muA  =  1.7*10**-5;
rhoA  =  1.3;

 #Calculations
d  =  (18*muO*Vt/(rhoP-rhoO)/g)**0.5;
Re  =  Vt*d*rhoO/muO;

 #Movement  of  particle  in  upward  direction
if(Re < 1):
    v  =  0.5;
    
    Re=5;       #  from  fig  12.15
    vt  =  muA*Re/(rhoA*d);
    u  =  vt+v;
    print "Velocity of air stream blowing vertically up (m/s) :",round(u,3) 
else:
    print "strokes law is not valid"

Velocity of air stream blowing vertically up (m/s) : 1.157

Example 12.6, Page 429

In [6]:
from __future__ import division
import math


 #Initializing  the  variables
c  =  2;
s  =  10;
rho  =  5.33;
rho_ellip  =  1.2;
D  =  400;
L  =  45000;
scale  =  20;
U_windTunnel  =  500;
U_proto  =  400*1000/3600;

 #Calculations
A  =  c*s;
U_model  =  U_windTunnel/scale;
Cd  =  D/(0.5*rho*U_model**2*A);
Cl  =  L/(0.5*rho_ellip*U_proto**2*A);          #  Considering  elliptical  Lift  model
Cdi  =  Cl**2/(math.pi*s/c);                    #  Aspect  Ratio  =    s/c  
Cdt  =  Cd  +  Cdi;
Dw  =  0.5*Cdt*rho_ellip*U_proto**2*A;
print "Total drag on full sized wing (kN) :",round(Dw/1000,2)

Total drag on full sized wing (kN) : 2.65