5. Further Problem Solving

Try these first

1. 1.

   What is shear stress?

   Hint

   Consider the force acting along the surface!

2. 2.

   List the four layers of turbulent flow.

   Hint

   Think about the flow's proximity to the boundary.

3. 3.

   What does τ not represent in turbulent flow?

   • Average velocity
   • Shear stress at the wall
   • Viscous force

   Hint

   Think about the definition of τ not and its significance.

4. 4.

   The viscous sublayer has a linear velocity profile.

   • True
   • False

   Hint

   Remember what characterizes this specific layer!

5. 5.

   A 0.1 m diameter pipe carries water at a velocity of 3 m/s. If the shear stress on the wall is given as 5 N/m², calculate the friction velocity and determine if the boundary is smooth, transitional, or rough using k = 0.1 mm.

   Hint

   Don’t forget to convert units appropriately and use known values for kinematic viscosity to find Re*.

6. 6.

   Calculate the velocity defect for water at a pipe wall using the velocity at the center and the velocity 1 cm from the wall. If the center velocity is 5 m/s and the velocity at 1 cm is 2.5 m/s, what is the defect?

   Hint

   Remember that the velocity defect measures the difference in velocities within the turbulent flow!