15.2.2. Dimensions of Fluid Mechanics Properties

Try these first

1. 1.

   What is dimensional analysis?

   Hint

   Consider its use in checking equations.

2. 2.

   Name the three types of similarities discussed.

   Hint

   Think about model constructions and fluid movement.

3. 3.

   What does dimensional analysis help verify?

   • The equations are dimensionless
   • The equations are dimensionally homogeneous
   • The equations are always correct

   Hint

   It relates to consistency in physics.

4. 4.

   True or False: Geometric similarity requires identical forces in models and prototypes.

   • True
   • False

   Hint

   Consider what geometric similarity really pertains to.

5. 5.

   A model of a river dam is tested in a lab where the flow rate is reduced by a factor of 100. What should be the scaling factors for length and discharge to maintain similarity?

   Hint

   Remember scaling laws for hydrodynamic similarity.

6. 6.

   Explain how to validate Bernoulli's equation dimensionally using an example from a fluid flow situation.

   Hint

   Focus on units for pressure (Pa), velocity (m/s), and height (m).