Chapter 3 : Kinematics of Fluid Motion

Example 3.1 Page No : 83

In [1]:
import math 

# variables
v_mag = 3.;
x = 8.;
y = 6.;

# calculations 
s = math.sqrt(x**2 + y**2);
v = v_mag*s;		# fps
a_t = v_mag*s*v_mag;		# ft/sec**2
a_r = 0;
a = math.sqrt(a_r**2 + a_t**2);

# results 
print 'v = %d fps  a = %d ft/sec**2'%(v,a);

v = 30 fps  a = 90 ft/sec**2

Example 3.2 Page No : 83

In [1]:
import math 

# variables
v = 5;		# fps
a_t = 0;

# calculations 
a_r = v**2 /2.;		# ft/sec**2

# results 
print 'Radial component of acceleration = %.1f ft/sec**2 \nTangential component of acceleration = %d '%(a_r,a_t);

Radial component of acceleration = 12.5 ft/sec**2 
Tangential component of acceleration = 0

Example 3.3 Page No : 85

In [4]:
import math 

# variables		
v = 5.;		# fps
r = 2.;
theta = 60.;		# degrees
x = 1.;
y = math.sqrt(3);
v_t = v;
v_r = 0;

# calculations 
u = -v*y/(math.sqrt(x**2 + y**2));
v = v*x/(math.sqrt(x**2 + y**2));
a_x = -50*x/8;
a_y = -50*y/8;
a_r = -v_t**2 /r;
a_t = v_r*v_t/r;

# results 
print 'u = %.2f fps, v = %.2f fps'%(u,v);
print ' v_r = %d, v_t = %d fps'%(v_r,v_t);
print ' a_x = %.2f ft/sec**2, a_y = %.2f ft/sec**2'%(a_x,a_y);
print ' a_r = %.1f ft/sec**2, a_t = %d'%(a_r,a_t);

u = -4.33 fps, v = 2.50 fps
 v_r = 0, v_t = 5 fps
 a_x = -6.25 ft/sec**2, a_y = -10.83 ft/sec**2
 a_r = -12.5 ft/sec**2, a_t = 0

Example 3.4 Page No : 88

In [2]:
import math 

# variables
w = 600.;		# pounds
l1 = 12.;		#inches
l2 = 8.;		#inches

# calculations 
Q = w/(62.4);
V_12 = Q/(0.25*math.pi*(l1/12)**2);
V_8 = Q/(0.25*math.pi*(l2/12)**2);

# results 
print 'Q = %.2f cfs'%(Q);
print 'V_12 = %.2f fps and V_8 = %.2f fps'%(V_12,V_8);

Q = 9.62 cfs
V_12 = 12.24 fps and V_8 = 27.55 fps

Example 3.5 Page No : 89

In [2]:
import math 
		
# variables
l = 12.;		# inches
W = 6.;		# pounds
w = 0.0624		# lb/cuft
l1 = 8.;		# inches
rho = 0.050;		# lb/cuft

# calculations 
Q_12 = W/w ;
Q_8 = W/rho ;
V_12 = Q_12/(0.25*math.pi*(l/12)**2);
V_8 = Q_8/(0.25*math.pi*(l1/12)**2);

# results 
print 'Q_12 = %.1f cfs, Q_8 = %d cfs'%(Q_12,Q_8);
print ' V_12 = %.1f fps, V_8 = %.f fps'%(V_12,V_8);

		

Q_12 = 96.2 cfs, Q_8 = 120 cfs
 V_12 = 122.4 fps, V_8 = 344 fps