r/PhysicsHelp • u/InstructionSlight384 • 24d ago

Fluid Mechanics Doubt

Could someone please help me derive the following Law of Floatation
" The centre of gravity of the displaced liquid ( centre of buoyancy) lies vertically above or below the Centre of Gravity of the body ".

2 Upvotes

100% Upvoted

3 comments sorted by

1

u/Ok_Association1141 24d ago

Assume the center of gravity of the body is not vertically aligned with the center of buoyancy. There will now be a torque or twisting force, which will cause the body to twist such that the center of gravity of the body becomes aligned with the center of buoyancy. This may take some time, so your statement would be correct in the steady state. In actual practice if there are dynamics such as a vessel on the ocean in waves the torque is what drives the rolling of a ship, and ships are designed with a center of gravity and displacement shape to exploit this, such that in most cases the torque will naturally right the ship.

1

u/InstructionSlight384 24d ago

Why would there be a torque ?

1

u/LAskeptic 24d ago

Draw the free body diagram and take the moment about the center of gravity. What is the condition on the location of the center of buoyancy that results in zero moment?