How Do You Calculate the Depth of Oil in a Sinking Barge?

[chimmy48]

Homework Statement

A rectangular barge floats in water, ρw. When it is empty it is immersed at depth D below the surface. Oil with density, ρo, is poured into the barge until it is about to sink. Find a relationship for the depth of the oil at this point in terms of the initial depth, D, the total height of the barge H and the barge width W.

Homework Equations

P = ρgh

The Attempt at a Solution

Well, we basically have three situations here. One when its floating, the other when its immersed (the container is empty) and the last one, when oil is poured into the container until it sinks. So we have the depth of the oil that is poured into the container to figure out in terms of H, D and W.

At first, i started to think, maybe we could establish a volume relationship, but then i ran into problems, whilst doing that. So, i guess its recommended to include pressure into it, since we have density of the oil and the water. But this is all i have thought about. I really don't know how to approach it. I really really need help please. Thanks!

 

[TVP45]

Can you show some of your work? Perhaps you could start with a free body diagram identifying all the forces acting on the barge in each situation.