3.3. Derivation of Strain Rates

Try these first

1. 1.

   Define the term 'Substantial Derivative'.

   Hint

   Think about the meaning of both spatial and temporal changes.

2. 2.

   What are kinematic properties of fluids?

   Hint

   Consider what happens to fluid movement.

3. 3.

   What does the substantial derivative capture?

   • Only local changes
   • Only convective changes
   • Both local and convective changes

   Hint

   Think of it as combining effects from space and time.

4. 4.

   True or False: Strain rates are independent of the fluid's motion.

   • True
   • False

   Hint

   Recall how movement affects deformation.

5. 5.

   A fluid element in a pipe changes shape under various velocities. Derive the expression for strain rates in this scenario.

   Hint

   Look for relationships between velocities and element deformation.

6. 6.

   In a rotating fluid, analyze the impact of angular velocity on strain rates. Write expressions for the resulting deformation.

   Hint

   Remember to incorporate the geometry of rotational motion.