2. Problem Solving on Turbulent Flow

Try these first

1. 1.

   What is the shear stress at the pipe wall referred to?

   Hint

   Think about the definition of shear stress in fluid dynamics.

2. 2.

   Define the term 'Logarithmic Velocity Profile.'

   Hint

   Recall the equation involving ln(R/y).

3. 3.

   What does τ0 represent in turbulent flow?

   • The shear stress at the wall
   • The velocity at the center
   • The diameter of the pipe

   Hint

   Focus on the forces acting at the wall of the pipe.

4. 4.

   True or False: The viscous sublayer is characterized by a linear velocity profile.

   • True
   • False

   Hint

   Recall the definition of the viscous sublayer.

5. 5.

   Given a turbulent pipe flow with average velocities at the center and wall, derive the shear stress at the wall using the velocity defect law.

   Hint

   Utilize the logarithmic relationship to find u* before substituting.

6. 6.

   Calculate the type of boundary for a pipe if k = 0.2 mm and viscous sublayer is 0.8 mm.

   Hint

   Think about Nikuradse's experiments and their defined limits.