1.6. Problem Solving: Average Velocity in Pipe

Try these first

1. 1.

   What is the definition of average velocity in fluid mechanics?

   Hint

   Consider how velocity changes across the area.

2. 2.

   What does the term frictional velocity refer to?

   Hint

   Think of forces acting on the fluid due to surface interaction.

3. 3.

   What does V_average represent?

   • The maximum velocity
   • The average velocity across a cross-section
   • The velocity at the center

   Hint

   Think about how averages are calculated.

4. 4.

   True or False: The power law velocity profile can calculate wall shear stress.

   • True
   • False

   Hint

   Consider the implications of infinite gradients at walls.

5. 5.

   A smooth pipe carries water with a given profile at different sections. If the max velocity at the center is 10 m/s, calculate the average velocity across various diameter sections.

   Hint

   Set your bounds for integration according to the sections' locations.

6. 6.

   Two pipes, one rough and one smooth, both have the same flow rate, analyze the average velocity and discuss what implications this has for engineering designs.

   Hint

   Look at the surface area impacts and friction factors.