8.4.2. Local and Convective Acceleration Components

Try these first

1. 1.

   Define local acceleration in your own words.

   Hint

   Think of how a single point in a flow changes speed.

2. 2.

   What is convective acceleration and how is it different from local acceleration?

   Hint

   Consider motion through different speed areas.

3. 3.

   What defines local acceleration?

   • Change in velocity over time
   • Change in position over time
   • Change in velocity due to motion

   Hint

   Reflect on how speed changes with time at fixed points.

4. 4.

   True or False: Convective acceleration is solely dependent on time changes.

   • True
   • False

   Hint

   Consider the movement of fluid particles across different areas.

5. 5.

   Given the velocity profile V(x,y,z) = (3y^2 - z, -2x + z, 5x + 4y), calculate the local and convective acceleration at the point (2, 1, 3).

   Hint

   Use partial derivatives with respect to each spatial component.

6. 6.

   A fluid flows through a pipe with varying cross-sections. Explain how local and convective acceleration would change when moving from a wide section to a narrow section.

   Hint

   Think about how velocity must adapt as forced through a smaller area.