1.3. Observation on Velocity Difference

Try these first

1. 1.

   Define average velocity in fluid dynamics.

   Hint

   Think about how flow rate and area are related.

2. 2.

   What is frictional velocity?

   Hint

   Remember, it relates to the drag experienced by the flow.

3. 3.

   What does the variable 'u' represent in turbulent flow?

   • Average flow velocity
   • Instantaneous local velocity
   • Frictional velocity

   Hint

   Think about how local conditions differ in a turbulent flow.

4. 4.

   True or False: The difference in velocity at a point is the same for both smooth and rough pipes.

   • True
   • False

   Hint

   Reflect on the key findings from our equations on velocity.

5. 5.

   Given a turbulent flow with a measured maximum velocity of 8 m/s and a frictional velocity of 3 m/s, determine the difference in velocity at 0.25 m from the wall of a pipe with radius 1 m. Use the derived logarithmic equation.

   Hint

   Focus on logarithmic properties when solving.

6. 6.

   If a power law velocity profile with n = 6 is given, derive an expression for the average velocity considering a pipe with radius R and radius r. Explain your steps.

   Hint

   Break down each step starting from the power law equation to simplifying the integral.