# Chapter 13 : Fluid Flow about Immersed Objects¶

## Example 13.1 Page No : 502¶

In [3]:
import math

# variables
b = 50.;		#ft
c = 7.;		    #ft
CL = 0.6;		#lift coefficient
CD = 0.05;		#drag coefficient
alpha = 7.;		#degrees
V = round(150/0.681818);		#coverting mph to fps
H = 10000.;		#ft
rho = 0.001756;		#slug/cuft

# calculations
D = CD*b*c*rho*0.5*V**2;
hp = D*V/550;
L = CL*b*c*rho*0.5*V**2;
mu = 3.534*10**-7;		#lb-sec/sqft
R = V*c*rho/mu;
a = math.sqrt(1.4*32.2*53.3*(23.4+459.6));
M = V/a;

# results
print 'hp = %.f hp, L = %.2f lb, R = %d, M = %.3f'%(hp,L,round(R,-4),M);

# note : answer is different because of rounding off error

hp = 297 hp, L = 8923.99 lb, R = 7650000, M = 0.204


## Example 13.2 Page No : 511¶

In [13]:
import math

# variables
l = 5.;		#ft
d = 0.5;		#ft
v = 1.;		#fps
T = 60.;		#degreeF
D = 0.04;		#lb
k = 1./64;		#model scale

# calculations
nu = 0.00001217;
R = round(v*l/nu,-4);
Cf1 = 0.0020;
Cf2 = 0.0052;
Dx1 = round(2*Cf1*l*d*1.938*0.5*v**2,4);
Dx2 = round(2*Cf2*l*d*1.938*0.5*v**2,3)
delta1 = round(l*5.20/math.sqrt(R),2);
delta2 = l*0.38/(R**0.2);
V_0 = math.sqrt((v**2 /l)*(l*(1/k)));
R_p = V_0*l*(1/k)/nu;
Cf = 0.00185;
Dx = 2*Cf*l*d*(1/k)**2 *1.938*0.5*V_0**2;
Dw = D-Dx2;
Dw_p = (1/k)**2 *d*l*V_0**2 *Dw/(l*d);
D = round(Dw_p + Dx,-1);

# results
print 'Total drag of the prototype = %d lb'%(D);

Total drag of the prototype = 6280 lb


## Example 13.3 Page No : 524¶

In [3]:
import math

# variables
c = 6.;		#ft
b = 36.;		#ft
AR1 = 6.;		#aspect ratio
Cd = 0.0543;		#drag coefficient
Cl = 0.960;		#lift coefficient
alpha1 = 7.2;		#degrees
AR2 = 8.;

# calculations
#for aspect ratio = 8
CL = 0.960;		#negligible change of lift coefficient
#for aspect ratio = 6
C_Di = Cl**2 /(math.pi*AR1);
#for aspect ratio = infinity
C_D0 = Cd - C_Di;
#for AR = 8
C_D = C_D0 + Cl**2 /(math.pi*AR2);
#for AR = 6
alpha_i = (180/math.pi)*Cl/(math.pi*AR1);
#for AR = infinty
alpha_0 = alpha1 - alpha_i;
#for AR = 8
alpha = alpha_0 + Cl/(AR2*math.pi) *(360/(2*math.pi));

# results
print 'Lift coefficient = %.3f (negligible change of lift coefficient)'%(CL);  #incorrect answer in the textbook
print 'Drag coefficient = %.4f'%(C_D);
print 'Angle of attack = %.1f degress'%(alpha);

Lift coefficient = 0.960 (negligible change of lift coefficient)
Drag coefficient = 0.0421
Angle of attack = 6.5 degress