4.3.1. Velocity Divergence in Incompressible Flow

Try these first

1. 1.

   What is mass conservation?

   Hint

   Think about the implications of mass in any physical process.

2. 2.

   Define incompressible flow.

   Hint

   Consider how gases behave under pressure.

3. 3.

   What does mass conservation imply in fluid dynamics?

   • Mass can be created
   • Mass can be destroyed
   • Mass cannot be created or destroyed

   Hint

   Reflect on basic physics laws.

4. 4.

   True or False: Incompressible flow has a velocity divergence equal to zero.

   • True
   • False

   Hint

   Think about the definition of incompressibility.

5. 5.

   Consider a variable density fluid flowing through a passage. Develop the mass conservation equation while accounting for density changes across a control volume.

   Hint

   Apply the principles discussed for control volumes.

6. 6.

   In a cylindrical coordinate system, derive the divergence for a flow with a radial component and analyze its implications.

   Hint

   Visualize the changes across circular cross-sections.