Rank the faces in order of decreasing water pressure

[demonix]

Homework Statement

A box has six faces with three distinct areas A<B<C. Assume that A and B represent the four vertical surfaces, and the two horizontal surfaces have area C. Assume the box is not very tall. When the box is submerged, rank the faces in order of decreasing water pressure.

The pressure of the faces to be considered are P(top), P(bottom), P(B) and P(A)

Relevant Equations

I used pressure= force/area

I assumed that the same magnitude of force acts on all sides of the box. Since A had the smallest area, I ranked P(A) as having the largest pressure, followed by P(B) having the second largest and P(top) and P(bottom) having the same pressure at third largest each. However, the ranking I dervied was wrong and I am unsure how to continue on.

 

[haruspex]

I assumed that the same magnitude of force acts on all sides of the box.

Doesn't seem like a reasonable assumption. The pressure varies with depth.

But I also have a difficulty with the question asked. The pressure is not uniform on some of the faces, so how is "the pressure" to be defined on those? I suggest interpreting it as the average pressure on each face. A possible alternative is that they mean force, not pressure.

 

[demonix]

Doesn't seem like a reasonable assumption. The pressure varies with depth.

But I also have a difficulty with the question asked. The pressure is not uniform on some of the faces, so how is "the pressure" to be defined on those? I suggest interpreting it as the average pressure on each face. A possible alternative is that they mean force, not pressure.

I agree with you that it isn't a very reasonable assumption, I held it on the basis that I was unsure how to approach the question from any other angle. I believe the question refers to the average pressure, this question was posed in a worksheet from my teacher.

The second part of the question asks about the ranking of the magnitude of force on the sides of the surface.

 

[haruspex]

I agree with you that it isn't a very reasonable assumption, I held it on the basis that I was unsure how to approach the question from any other angle. I believe the question refers to the average pressure, this question was posed in a worksheet from my teacher.

The second part of the question asks about the ranking of the magnitude of force on the sides of the surface.

Ok, so what can you do instead? How does pressure vary with depth?

 

[Alex Petrosyan]

I don’t want to give away the answer straight away, but the pressure over the bottom is uniform, and so is the pressure at the top. The pressure on everything else can be determined from the condition that $p = ...$

That being said, does it matter whether they’re talking about average or “instantaneous” pressure at the sides. If you think about it, in terms of ranges of pressure, it would be obvious.