# Fluid Mechanics Upthrust question

So the definition of up-thrust says it is caused because the top and bottom of a submerged object are at different depths so there is a difference in pressure which causes an overall upwards force known as up-thrust.

I am a bit confused here though. So in this case in the diagram it tells that if an object is submerged, the pressure at the bottom of the cube is greater than at the top(since more depth at the bottom) this causes a net movement upwards known as up-thrust.

Formula being:
Force acting on top of cube= ρgAh
Force acting on bottom of cube= ρgAh2

Okay so what happens if the object is sinking?
Seeing the two equations, I don't see how the top of the cube should get a higher pressure than the bottom of the cube as the height of the bottom of the cube is still at a greater depth, then shouldn't there still be a much higher pressure acting at the bottom of the cube that causes it to go upwards?

I mean all the variables in both cases(except for h) should be same so subbing in all the values to both equations will still result in a higher force for the bottom of the cube since the depth is more for that one.

I am still learning fluid mechanics so it could be a stupid question
(edited 1 year ago)
Original post by Goldenknight
So the definition of up-thrust says it is caused because the top and bottom of a submerged object are at different depths so there is a difference in pressure which causes an overall upwards force known as up-thrust.

I am a bit confused here though. So in this case in the diagram it tells that if an object is submerged, the pressure at the bottom of the cube is greater than at the top(since more depth at the bottom) this causes a net movement upwards known as up-thrust.

Formula being:
Force acting on top of cube= ρgAh
Force acting on bottom of cube= ρgAh2

Okay so what happens if the object is sinking?
Seeing the two equations, I don't see how the top of the cube should get a higher pressure than the bottom of the cube as the height of the bottom of the cube is still at a greater depth, then shouldn't there still be a much higher pressure acting at the bottom of the cube that causes it to go upwards?

I mean all the variables in both cases(except for h) should be same so subbing in all the values to both equations will still result in a higher force for the bottom of the cube since the depth is more for that one.

I am still learning fluid mechanics so it could be a stupid question

The upthrust is a force (not a movement) - it always acts upward

The weight force due to the mass of the body doesn't just vanish though.

if the upthrust is greater than the weight force then the body will rise (net force upwards)
but if the weight is greater than the upthrust the body will sink (net force downwards)

i.e. I'm disagreeing with the equation for net force given in that picture unless there's another part of the explanation I'm not seeing.
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Though the explanation in terms of pressure on the top and bottom of an object is correct it's often more useful to think about the density of an object compared to the density of the fluid it's in. then you don't have less to worry about for objects with weird and irregular shapes. if the object density is lower than the fluid density the object floats upward in the fluid and vice versa.
(edited 1 year ago)
Original post by Joinedup
The upthrust is a force (not a movement) - it always acts upward

The weight force due to the mass of the body doesn't just vanish though.

if the upthrust is greater than the weight force then the body will rise (net force upwards)
but if the weight is greater than the upthrust the body will sink (net force downwards)

i.e. I'm disagreeing with the equation for net force given in that picture unless there's another part of the explanation I'm not seeing.
-----
Though the explanation in terms of pressure on the top and bottom of an object is correct it's often more useful to think about the density of an object compared to the density of the fluid it's in. then you don't have less to worry about for objects with weird and irregular shapes. if the object density is lower than the fluid density the object floats upward in the fluid and vice versa.

Ah okayy so I should ignore the pressure definition about this and just focus on the density definition?
Also can you tell me about what is wrong with the equation in the picture?
(edited 1 year ago)
Original post by Goldenknight
Ah okayy so I should ignore the pressure definition about this and just focus on the density definition?

Well I wouldnt say ignore, but the net force on an object in liquid is the combination of weight and upthrust.
Original post by Joinedup
Well I wouldnt say ignore, but the net force on an object in liquid is the combination of weight and upthrust.

The pressure thing when an object is sinking is actually the part confusing me. I am guessing that there is some other factor that increases the pressure at the top of the cube that causes it to sink?

If there are more complicated things going on beyond the scope of A level syllabus then I think I can just stick to the density definition
(edited 1 year ago)
Original post by Goldenknight
The pressure thing when an object is sinking is actually the part confusing me. I am guessing that there is some other factor that increases the pressure at the top of the cube that causes it to sink?

@Joinedup's explanation has all the key points, but just for a bit of extra clarity:

The force pushing up on the bottom is greater than the force pushing down on the top (becasue the bottom is at a greater depth), so the resultant of these two forces is upwards. This is the upthrust.

The thing that is a little misleading in the diagram in the first post is that when they talk about the net force (the upthrust), they should make it clear that this is the net force resulting from the pressure from the fluid only. It is not the total resultant force that the body feels. You also have to take it's weight into account, which of course acts downwards.

If the weight (downwards) is larger than the upthrust (upwards), then the resultant force on the body will be downwards, and it will sink

But if the weight is smaller than the upthruse, then the resultant force on the body will be upwards, and it will float.

Original post by Pangol
@Joinedup's explanation has all the key points, but just for a bit of extra clarity:

The force pushing up on the bottom is greater than the force pushing down on the top (becasue the bottom is at a greater depth), so the resultant of these two forces is upwards. This is the upthrust.

The thing that is a little misleading in the diagram in the first post is that when they talk about the net force (the upthrust), they should make it clear that this is the net force resulting from the pressure from the fluid only. It is not the total resultant force that the body feels. You also have to take it's weight into account, which of course acts downwards.

If the weight (downwards) is larger than the upthrust (upwards), then the resultant force on the body will be downwards, and it will sink

But if the weight is smaller than the upthruse, then the resultant force on the body will be upwards, and it will float.

Ahhh I got it now!! Thank you both for the clarification. Yeah the diagram made it more confusing it seems but now looking at your explanation too I understand how it works.