Chapter 8 : Similitude and Dimensional Analysis

Example 8.1 Page No : 266

In [1]:
		

# variables
Tw = 32.;		# degreeF
d1 = 3.;		# in
v = 10.;		#fps
delp = 2.;		#psi
h1 = 30.;		# ft
Tb = 68.;		#degreeF
d2 = 1.;		#in
h2 = 10.;		#ft

# calculations 
V = v*(d1/12)*0.0000137/((d2/12)*0.88*0.0000375);
del_p = delp/h2**2 *0.88*V**2;

# results 
print 'V = %.2f fps del_p = %.2f psi'%(V,del_p);

V = 12.45 fps del_p = 2.73 psi

Example 8.2 Page No : 266

In [3]:
import math 
		
# variables
l = 400.;		# ft
h = 10.;		#ft
v = 30.;		# fps
D = 2.;		#lb

# calculations 
V = math.sqrt((v**2 /l)*h);
D_p = (D/V**2) *(v**2)*(l**2)/h**2;

# results 
print 'V = %.2f fps Prototype drag = %d lb'%(V,D_p);

V = 4.74 fps Prototype drag = 128000 lb

Example 8.3 Page No : 266

In [1]:
		
# variables
G = 20000.;		#cfs
k = 1./15;

# calculations 
Q_m = G*(k)**(2+ 1./2);

# results 
print 'Qm = %.f cfs'%(Q_m);

Qm = 23 cfs

Example 8.4 Page No : 266

In [6]:
import math 
		
# variables
k = 1./10;
v = 3000.;		#fps
h = 15000.;		#altitude
T = 68.;		# degreeF
am = 870.;		#fps
ap = 1057.;		#fps

# calculations 
Vm = v*(am/ap);
rho_m = v*(1/k)*0.001495*0.031/(0.033*Vm);
p_m = 32.2*rho_m*34.9*(T+460)/(144);

# results 
print 'Vm = %d fps p_m = %d psia'%(Vm,p_m);

#rounding-off errors

Vm = 2469 fps p_m = 70 psia