8.4.2.1. Local Acceleration

Try these first

1. 1.

   Define local acceleration.

   Hint

   Focus on the aspect of time variation.

2. 2.

   What does convective acceleration account for?

   Hint

   Think about how velocity might change across positions in the fluid.

3. 3.

   What is the formula for Newton's second law?

   • F = ma
   • F = mv
   • F = ma²

   Hint

   Think about how force relates to mass and motion.

4. 4.

   Does convective acceleration depend on time?

   • True
   • False

   Hint

   Revisit the definitions of acceleration types for clarity.

5. 5.

   Given a fluid's velocity function v = 2xyi + (3z)j + (x^2)k, calculate the local acceleration at the point (2, 3, 4).

   Hint

   Remember to find partial derivatives followed by substitution.

6. 6.

   Analyze a scenario where a fluid's velocity changes spatially in a 3D grid. Formulate equations to demonstrate local and convective accelerations.

   Hint

   Focus on visualizing the fluid velocity to distinguish changes clearly.