
FLUID MECHANICS  CASE STUDY SOLUTION



Since it is given that the velocity is inversely proportional
to the square of the location r, assume the correlation for velocity
has the following form:
V = c/r^{2}
where c is a constant which needs to be determined.




Schematic of Experiment Set #1
Correlation for Experiment Set #1 

For experiment set #1, the locations of the measurement points
are first determined (using the Pythagorean theorem):
Sensor Location 
A 
B 
C 
Location (r), m 
0.304 
0.300 
0.304 
Velocity (V), cm/s 
5.2 
5.6 
5.5 
c = Vr^{2}, m^{3}/s 
0.00481 
0.00504 
0.00508 
Sensor Location 
D 
E 
F 
Location (r), m 
0.206 
0.200 
0.206 
Velocity (V), cm/s 
11.5 
12.4 
11.7 
c = Vr^{2}, m^{3}/s 
0.00488 
0.00496 
0.00497 
Sensor Location 
G 
H 
I 
Location (r), m 
0.112 
0.100 
0.112 
Velocity (V), cm/s 
40.0 
50.5 
39.5 
c = Vr^{2}, m^{3}/s 
0.00502 
0.00505 
0.00495 
By taking the average of the calculated values for the constant c, it
is found that c is 0.00497, which is close to 0.005. The Eulerian viewpoint
is used in this experiment since the velocities are measured at fixed locations. 



Schematic of Experiment Set #2
Correlation for Experiment Set #2


For experiment set #2:
Fluid Particle #1 
Location (r), m 
0.25 
0.18 
0.07 
Velocity (V), cm/s 
8.1 
15.5 
101.8 
c = Vr^{2}, m^{3}/s 
0.00506 
0.00502 
0.00499 
Fluid Particle #2 
Location (r), m 
0.30 
0.25 
0.19 
Velocity (V), cm/s 
5.7 
7.8 
14.0 
c = Vr^{2}, m^{3}/s 
0.00513 
0.00488 
0.00505 
Fluid Particle #3 
Location (r), m 
0.21 
0.17 
0.10 
Velocity (V), cm/s 
11.0 
16.9 
50.0 
c = Vr^{2}, m^{3}/s 
0.00485 
0.00488 
0.00500 
The average value for the constant c is 0.00498, which is again close
to 0.005. Since the measurements in set #2 are taken by following individual
fluid particles, the flow field is determined using the Lagrangian viewpoint. 



