1.4. Power Law Velocity Profile

Try these first

1. 1.

   What is the significance of the Reynolds number in fluid flow?

   Hint

   Think about flow conditions and types.

2. 2.

   What does the power law velocity profile express?

   Hint

   Recall the formula we discussed.

3. 3.

   What is the equation for the power law velocity profile in smooth pipes?

   • u = u_max (1 - r/R)^(1/7)
   • u/u_max = (y/R)^(1/n)
   • u = 5.75 log(y/R)

   Hint

   Recall how we express velocity profile for laminar and turbulent cases.

4. 4.

   True or False: The average velocity is the same for smooth and rough pipes.

   • True
   • False

   Hint

   Consider the observations we made during discussion.

5. 5.

   Given a power law velocity profile u(r) = u_max (1 - r/R)^(1/5), calculate the average velocity in terms of u_max.

   Hint

   Look closely at the integration limits and how to apply the formula!

6. 6.

   For a specific Reynolds number, if the power law exponent n increases from 5 to 10, assess how this affects the velocity gradient near the walls.

   Hint

   Consider the relationship between n and flow turbulence.