4.1. Hydrodynamically Rough and Smooth Boundaries

Try these first

1. 1.

   Define shear stress in fluid dynamics.

   Hint

   Think about the forces acting on a wall.

2. 2.

   What is the significance of the viscous sublayer?

   Hint

   Consider how this relates to flow characteristics.

3. 3.

   What is the shear stress formula?

   • τ₀ = ρu*²
   • τ₀ = μdu/dy
   • τ₀ = P/A

   Hint

   Think of the relationship between stress and velocity.

4. 4.

   A smooth boundary has k/δ < 0.25. Is this true or false?

   • True
   • False

   Hint

   Recall the definitions we just talked about.

5. 5.

   A pipe flowing with oil has surface irregularities height k = 0.2 mm, τ₀ = 3 N/m², and ν = 0.005 Stokes. Classify the boundary and discuss the implications.

   Hint

   Remember to perform each calculation step by step.

6. 6.

   If the viscous sublayer is significantly thinner than the irregularities present, what is likely the effect on frictional losses in a system with turbulent flow?

   Hint

   Consider how turbulence affects energy loss.