2. Calculation of Average Velocity

Try these first

1. 1.

   Define average velocity in pipe flow.

   Hint

   Think about the flow rate and area involved.

2. 2.

   What does the symbol 'u_star' represent?

   Hint

   Recall its significance in flow characterization.

3. 3.

   What is the equation for average velocity in smooth pipes?

   • u - V_average = 5.75 log_10(y/R) + 3.75
   • V_average = 5.75u + 3.75y
   • u = V_average * R

   Hint

   Recall the derivation we did in class!

4. 4.

   True or False: The average velocity in rough pipes differs from smooth pipes.

   • True
   • False

   Hint

   Think about the generalization of the equations.

5. 5.

   Calculate the average velocity in a pipe of radius R given u(r) = u_max * (1 - (r/R)^(1/8)). Show your work.

   Hint

   Use substitution as shown in previous examples.

6. 6.

   Discuss the wall shear stress calculation for a power law profile. Explain any issues faced.

   Hint

   Consider the behavior of velocity as it approaches the edges.