10.5. Lec 31: Approximate Solutions of Navier-Stokes Equation: Boundary Layer Approximation

Try these first

1. 1.

   What is a boundary layer in fluid mechanics?

   Hint

   Think about flow near any solid object.

2. 2.

   What conditions must be satisfied to utilize the boundary layer approximation?

   Hint

   Remember the acronym SIV.

3. 3.

   What is the purpose of approximating the Navier-Stokes equations?

   • To simplify calculations
   • To increase complexity
   • To ignore fluid behavior

   Hint

   Think about why simplifications are necessary.

4. 4.

   True or False: A boundary layer only forms in turbulent flow.

   • True
   • False

   Hint

   Consider where viscosity plays a role.

5. 5.

   Derive an expression for velocity distribution in water flow between two plates moving at different velocities. Assume a linear velocity profile at the boundary. Discuss how pressure gradient affects this profile.

   Hint

   Focus on integrating the simplified Navier-Stokes equations under the right assumptions.

6. 6.

   Given a flat plate with a known flow velocity and viscosity, calculate the thickness of the boundary layer. Discuss the factors affecting its thickness.

   Hint

   Consider how viscosity relates to flow resistance over the boundary layer.