4.2.3. Divergence of Velocity

Try these first

1. 1.

   Define a control volume in your own words.

   Hint

   Think about the boundaries we set while studying fluid flow.

2. 2.

   What does it mean for a flow to be incompressible?

   Hint

   Consider the relationship of density and volume in your answer.

3. 3.

   What does the divergence of velocity indicate in a flow?

   • It measures the speed of the fluid.
   • It indicates the source or sink of mass.
   • It shows the direction of the flow.

   Hint

   Consider what divergence literally measures in relation to the flow.

4. 4.

   True or False: In compressible flows, the divergence is always zero.

   • True
   • False

   Hint

   Remember the definition distinguishing compressible from incompressible flow.

5. 5.

   A fluid flows through a pipe with varying cross-sections. Analyze how mass conservation applies in calculating the velocity at different pipe segments.

   Hint

   Consider how varying flow areas influence velocities to maintain mass balance.

6. 6.

   Given a velocity vector field in a compressible flow, calculate its divergence and interpret the physical implications.

   Hint

   Think of divergence as measuring where mass accumulates or disperses in flow.