1.2. Assumptions for Small Values of y

Try these first

1. 1.

   What is assumed about shear stress τ at small values of 'y'?

   Hint

   Think about the conditions near the pipe wall.

2. 2.

   What type of velocity profile is derived from the small 'y' assumptions?

   Hint

   Consider how the velocity changes with distance.

3. 3.

   What is τ₀ in the context of turbulent flow?

   • Variable shear stress
   • Constant shear stress at the wall
   • Average shear stress throughout the pipe

   Hint

   Think about constant values for very close proximity.

4. 4.

   True or False: The velocity profile for turbulent flow is linear close to the wall.

   • True
   • False

   Hint

   Analyze the nature of turbulent flow profiles.

5. 5.

   Consider an idealized pipe with a radius of 0.1 m where the centerline velocity is 5 m/s. Calculate the required shear stress at the wall if the velocity at a distance 0.01 m from the wall is known to be 4.5 m/s.

   Hint

   Use u_max and the velocity defect formula.

6. 6.

   A turbulent flow pipe has a surface roughness height of 0.2 mm and the velocity defect observed is 2 m/s. Estimate the effects of different layers on the flow profile.

   Hint

   Analyze the characteristics of each flow layer in relation to surface roughness.