1.3. Integration with Boundary Conditions

Try these first

1. 1.

   What equation defines shear stress in a turbulent flow?

   Hint

   Identify the relationship between shear stress and friction velocity.

2. 2.

   What is the value of u* if τ₀ = 153.6 N/m² and ρ = 1000 kg/m³?

   Hint

   Remember to apply the square root function.

3. 3.

   What is the relationship between shear stress, velocity, and density in turbulent flow?

   • τ = ρu²
   • τ = ρu*²
   • τ = ρu/2

   Hint

   Think about how density influences shear stress in fluid flow.

4. 4.

   True or False: The logarithmic velocity profile can only be derived for laminar flows.

   • True
   • False

   Hint

   Recall the characteristics of laminar versus turbulent profiles.

5. 5.

   A fluid with a shear stress of 200 N/m² and density of 800 kg/m³ flows through a pipe. Determine u*, the friction velocity, and classify if the boundary is smooth or rough if k is given as 5 mm.

   Hint

   Ensure to check the kinematic viscosity beforehand.

6. 6.

   In a turbulent flow within a circular pipe, if the radius is halved, how does this affect τ and u_max assuming constant flow rate?

   Hint

   Consider conservation of flow equation and continuity as you derive.