Ch 3. Fluid Kinematics Multimedia Engineering Fluids FlowDescriptions Steady &Unsteady Streamlines,Streaklines Velocity &Acceleration IrrotationalFlow
 Chapter 1. Basics 2. Fluid Statics 3. Kinematics 4. Laws (Integral) 5. Laws (Diff.) 6. Modeling/Similitude 7. Inviscid 8. Viscous 9. External Flow 10. Open-Channel Appendix Basic Math Units Basic Equations Water/Air Tables Sections Search eBooks Dynamics Fluids Math Mechanics Statics Thermodynamics Author(s): Chean Chin Ngo Kurt Gramoll ©Kurt Gramoll

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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