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

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SUMMARY

The discussion focuses on calculating the depth of oil in a rectangular barge just before it sinks, considering the barge's initial immersion depth (D), total height (H), and width (W). The key equation used is P = ρgh, where P represents pressure, ρ is density, g is gravitational acceleration, and h is the depth. The problem involves analyzing three states: the barge floating empty, immersed, and filled with oil until it sinks. A volume relationship and pressure considerations are essential for deriving the depth of the oil.

PREREQUISITES
  • Understanding of fluid mechanics principles, particularly buoyancy.
  • Familiarity with pressure calculations in fluids using P = ρgh.
  • Knowledge of density concepts for different materials (water and oil).
  • Ability to create and interpret free body diagrams.
NEXT STEPS
  • Explore buoyancy principles in fluid mechanics.
  • Study the relationship between density and pressure in fluids.
  • Learn how to derive equations for submerged objects in fluids.
  • Investigate free body diagram techniques for analyzing forces in static systems.
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Students in physics or engineering disciplines, particularly those studying fluid mechanics, as well as professionals involved in marine engineering or naval architecture.

chimmy48
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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!
 
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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.
 

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