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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/r2

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 = Vr2, m3/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 = Vr2, m3/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 = Vr2, m3/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 = Vr2, m3/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 = Vr2, m3/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 = Vr2, m3/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.

     
   
 
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