Chapter 11 : Fluid Measurements

Example 11.1 Page No : 409

import math 
		
# variables
C_I = 0.98;		#coefficient of pitot tube
d = 3.;		#in

# calculations 
del_p = (d/12)*(13.55-0.88)/0.88;
v_c = C_I*math.sqrt(2*32.2*del_p);

# results 
print 'The velocity at the centerline of the pipe = %.1f fps'%(v_c);

The velocity at the centerline of the pipe = 14.9 fps

Example 11.2 Page No : 411

import math 
		
# variables
P = 25.;		#in. of mercury
p = 18.;		#in. of mercury
T = 150.;		#degreeF

# calculations 
k = P/p;
if k < (1.893) :
    V = math.sqrt(2*32.2*186.5*(T+460)*(1-(1/k)**0.286));

print 'The local velocity just upstream from the pitot static tube = %d fps'%(V);

The local velocity just upstream from the pitot static tube = 810 fps

Example 11.3 Page No : 411

import math 
		
# variables
P = 20.;		#in. of mercury
p = 5.;		#in. of mercury
T = 150.;		#degreeF

# calculations 
k = P/p;

if k >1.893:
    M_0 = 1.645;

V_0 = math.sqrt(2*32.2*186.5*(T+460)/(1+ (2*186.5)/(53.3*1.4*M_0**2)));

print 'The speed of this airplane = %d fps'%(round(V_0,-1));

		

The speed of this airplane = 1600 fps

Example 11.4 Page No : 420

import math 
		
# variables
b = 6.;		#in
d = 3.;		#in
p = 20.;		#psi
del_p = 6.;		#in. of mercury
p_bar = 14.70;		#psia
T = 60.;		#degreeF

# calculations 
k = (p + p_bar - b*(p_bar/29.92))/(p+p_bar);
gam1 = (p+p_bar)*144/53.3 /(T+460);
A2 = 0.0491;		#sqft
Y = 0.949;
Cv = 0.98;
G = Y*Cv*A2*gam1*math.sqrt(2*32.2*b*10*A2*144/gam1) /(math.sqrt(1-0.25**2));
Cv_true = 0.981;
G_true = G*Cv_true/Cv;

# results 
print 'G = %.2f lb/sec'%(G);

G = 3.31 lb/sec

Example 11.5 Page No : 422

import math 
		
# variables
d = 3.;		#in
l = 6.;		#in
h = 6.;		#in
T = 60.;		#degreeF

# calculations 
Cv= 0.99;
A1 = 0.25*math.pi*(d/12)**2;
Q = Cv*A1*math.sqrt(2*32.2*(h/12)*(13.55-1)) /(math.sqrt(1-0.25**2));
Cv_true = 0.988;
Q_true = Q*Cv_true/Cv;
h_L = 3.8;

# results 
print 'Q = %.3f cfs'%(Q);
print 'True Q = %.3f cfs'%(Q_true);
print 'Total head loss is about %.1f ft of water'%(h_L);

#there are small errors in the answer given in textbook

Q = 1.009 cfs
True Q = 1.007 cfs
Total head loss is about 3.8 ft of water