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FLUID MECHANICS - CASE STUDY

    Introduction


Schematic of Experiment Set #1
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Schematic of Experiment Set #2
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In a laboratory, two sets of experiments are conducted to measure the steady velocity in a funnel. The first set of the experimental data is collected at fixed locations, as shown in the figure. The measured velocities are:

Sensor Location A B C
Velocity (V), cm/s 5.2 5.6 5.5
Sensor Location D E F
Velocity (V), cm/s 11.5 12.4 11.7
Sensor Location G H I
Velocity (V), cm/s 40.0 50.5 39.5

The second set of the experimental data is obtained by following three different fluid particles. As the fluid particle travels along its path, the velocity and its location (with respect to the origin, point O) are measured randomly:

Fluid Particle #1
Location (r), m 0.25 0.18 0.07
Velocity (V), cm/s 8.1 15.5 101.8
Fluid Particle #2
Location (r), m 0.30 0.25 0.19
Velocity (V), cm/s 5.7 7.8 14.0
Fluid Particle #3
Location (r), m 0.21 0.17 0.10
Velocity (V), cm/s 11.0 16.9 50.0

Assume that the velocity is inversely proportional to the square of the location r (see figures). Students are asked to find a correlation to describe the velocity field.

     
    Questions

   

Identify which viewpoint (Eulerian or Lagrangian) is used for the experiment. Also, find a correlation for the velocity.

     
    Approach

   
  • Determine the correlation based on the average value of the collected experimental data.
  • The flow is steady. Hence, it is not a function of time.
  • The flow is assumed to be a function of the location r only.