1.5. Limitations of Power Law Profiles

Try these first

1. 1.

   What does n represent in the power law velocity profile?

   Hint

   Think about how fluid mechanics relates to flow regimes.

2. 2.

   True or False: Power law profiles can predict wall shear stress.

   Hint

   Consider the implication of infinite gradients.

3. 3.

   What does the power law profile fail to predict at the center of a pipe?

   • Zero velocity
   • Zero slope
   • Maximum velocity

   Hint

   Think about what happens mathematically at that point.

4. 4.

   True or False: The difference in velocity profile remains the same for both smooth and rough pipes.

   • True
   • False

   Hint

   Reflect on the discussion about smooth and rough surfaces.

5. 5.

   Derive the average velocity for a turbulent flow profile given by u(r) = 2 * u_max * (1 - (r/R)^2). Discuss any changes from the power law derived result.

   Hint

   Set proper limits for r during the integration process.

6. 6.

   Discuss the design considerations needed when dealing with turbulent flows in pipes with varying smoothness.

   Hint

   Think beyond just velocity; consider entire flow behavior.