1. Turbulent Pipe Flow

Try these first

1. 1.

   What is turbulent flow?

   Hint

   Think of water flowing rapidly with swirls and eddies.

2. 2.

   Define the term friction velocity.

   Hint

   How does wall friction relate to flow speed?

3. 3.

   What does the term 'turbulent flow' refer to?

   • Regular flow
   • Chaotic and irregular flow
   • Steady flow

   Hint

   Think about how turbulent flow looks visually.

4. 4.

   True or False: The equation for average velocity in rough and smooth pipes differs.

   • True
   • False

   Hint

   Reflect on the concept we discussed regarding equations for various piped conditions.

5. 5.

   Given a pipe radius of R = 0.5 m, find the maximum and average velocity if the profile defined is $u(r) = u_{max}(1 - \frac{r}{R})^{\frac{1}{7}}$ with $u_{max} = 10 m/s.$

   Hint

   Break it down by simplifying the integration process and referencing the derived formulas.

6. 6.

   Explain why the wall shear stress cannot be calculated using the power law velocity profile at the boundary, and provide a mathematical basis for your reasoning.

   Hint

   Investigate the implications of derivatives as you approach the pipe's wall in calculations.