10.1.1. Lec 30: The Navier-Stokes Equation III

Try these first

1. 1.

   What is the main purpose of velocity potential functions?

   Hint

   Think about how many scalar components we typically deal with in fluid flow.

2. 2.

   What are the key assumptions made when analyzing incompressible viscous flow?

   Hint

   Consider the flow direction and external forces acting on the fluid.

3. 3.

   What is the primary function of velocity potential functions?

   • To define pressure
   • To represent velocity fields in irrotational flows
   • To calculate mass flow rate

   Hint

   Think about reducing components for simplifying fluid velocity.

4. 4.

   Is the following statement true? Navier-Stokes equations can be approximated under certain conditions.

   • True
   • False

   Hint

   Recall how assumptions like irrotational flow can aid in simplifications.

5. 5.

   Using a scenario where water flows between a fixed and a moving plate, derive the expressions for shear stress and analyze the impact of varying velocities.

   Hint

   Integrate your solutions considering velocity profiles will provide shear values.

6. 6.

   Examine how flow around circular objects differs from flow past rectangular structures in terms of rotational effects.

   Hint

   Compare the designs to determine how shapes influence flow separation.