10.4.3. Deriving Velocity Distributions

Try these first

1. 1.

   What do the Navier-Stokes equations describe?

   Hint

   Think about fluid motion in various contexts.

2. 2.

   What is the continuity equation?

   Hint

   Think about how mass would behave in a flowing fluid.

3. 3.

   What do the Navier-Stokes equations account for in fluid mechanics?

   • Viscosity
   • Density
   • Pressure

   Hint

   Think about the factors impacting how fluids move.

4. 4.

   True or False: The velocity potential function is used only in rotational flows.

   • True
   • False

   Hint

   Consider what types of flow allow for potential functions.

5. 5.

   Consider a fluid flowing between two plates, both fixed, under a pressure gradient. If the pressure difference across the length of one meter is known, how would you calculate the flow rate?

   Hint

   Remember to use the velocity distribution relevant to pressure-driven flow.

6. 6.

   Derive the shear stress acting on the plate when fluid flows due to a pressure gradient. What parameters do you need to consider?

   Hint

   Focus on the definition of shear stress and how it relates to viscosity.