12.2.4. Pressure Fields in Rotating Fluids

Try these first

1. 1.

   Define the term 'Center of Buoyancy'.

   Hint

   Think about where the upward force is concentrated.

2. 2.

   What does 'Metacentric Height' indicate?

   Hint

   Remember the relationship between center of gravity and metacenter.

3. 3.

   What happens to an iceberg's center of buoyancy as it melts from below?

   • It remains unchanged
   • It shifts upwards
   • It shifts downwards

   Hint

   Consider how the submerged part decreases.

4. 4.

   True or False: A metacentric height above the center of gravity leads to stable floating.

   • True
   • False

   Hint

   Think about stability in balance.

5. 5.

   A cylindrical container filled with liquid is rotating at a uniform rate. If the radius of the container is 2m and the height is 4m, determine the shape of the free surface and the pressure distribution at different heights.

   Hint

   Use the equations for fluid dynamics to derive the relationships.

6. 6.

   Analyze a ship with a metacentric height of 1m. If the center of gravity is 0.9m, determine its stability and implications under heavy loading.

   Hint

   Consider how stability changes with load variations.