Is the Upthrust Equation for Fully Submerged Objects Incorrect?

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Discussion Overview

The discussion revolves around the validity of an equation for calculating the pressure at the bottom of a fully submerged object, specifically a cube. Participants explore the implications of pressure distribution, buoyancy, and the influence of object density in a static versus dynamic context.

Discussion Character

  • Debate/contested
  • Technical explanation
  • Conceptual clarification

Main Points Raised

  • One participant questions the correctness of the equation, which includes both the fluid density and the density of the cube in its formulation.
  • Another participant challenges the assumption that the equation is wrong, asking for justification based on textbook definitions.
  • Concerns are raised about the pressure distribution near the edges of the object and whether the situation is static or dynamic.
  • Some participants suggest that the hydrostatic pressure is primarily determined by the fluid column above the object, rather than the object's density.
  • There is a discussion about the buoyancy of the object and whether it is moving or stationary, which may affect the applicability of the equation.
  • One participant emphasizes the need to consider "other factors" that could influence the pressure calculation, hinting at complexities not addressed in the original equation.

Areas of Agreement / Disagreement

Participants do not reach a consensus on the correctness of the equation. Multiple competing views are presented regarding the factors that influence pressure in submerged objects.

Contextual Notes

Participants express uncertainty about the assumptions underlying the equation and the definitions of terms used, particularly in relation to buoyancy and pressure distribution.

Olivia197
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Please may somebody explain why this equation for the pressure at the bottom of a fully submerged object is wrong (assuming it is a cube). Thank you!

Pressure = ( density of the fluid x h[1] x g ) + ( density of the cube x (h[2] - h[1] ) x g)
 
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What makes you think it's wrong?
 
Why do you expect it to be right?
How do you imagine the pressure distribution close to the edge of the object? Jumping?

Is this a static situation? If you include dynamics, things get more complicated.
 
Mister T said:
What makes you think it's wrong?
Well, in my textbook it says that the pressure is the density of the liquid x h [2] x g.
 
mfb said:
Why do you expect it to be right?
How do you imagine the pressure distribution close to the edge of the object? Jumping?

Is this a static situation? If you include dynamics, things get more complicated.
Sorry I am not quite sure what you mean!
 
Olivia197 said:
Well, in my textbook it says that the pressure is the density of the liquid x h [2] x g.

Then anything different from that would be wrong. It seems to me that you've answered your own question.

Olivia197 said:
Please may somebody explain why this equation for the pressure at the bottom of a fully submerged object is wrong

.
 
Olivia197 said:
Sorry I am not quite sure what you mean!
Well, reduce it to the first question: why do you expect your expression to be right?
 
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mfb said:
Well, reduce it to the first question: why do you expect your expression to be right?
Could (s)he express, in words, what that equation is describing? That may help with the understanding.
 
That equation might work -- is the object neutrally, positively or negatively buoyant? Is it moving or constrained not to move?
 
  • #10
russ_watters said:
That equation might work -- is the object neutrally, positively or negatively buoyant? Is it moving or constrained not to move?
I see where you are going with this but the hydrostatic pressure is not really affected by the density of the object (or the object at all). The pressure at the bottom face is due to the column of fluid, rather than the object (unless there is some extra factor involved that we haven't been told about).
 
  • #11
sophiecentaur said:
I see where you are going with this but the hydrostatic pressure is not really affected by the density of the object (or the object at all). The pressure at the bottom face is due to the column of fluid, rather than the object (unless there is some extra factor involved that we haven't been told about).
The answer to my question is "other factors" and will actually push the solution toward the normal hydrostatic pressure equation when the OP realizes the impact of the constraints the answer adds.
 

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