Does buoyancy depend on shape and volume?

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Main Question or Discussion Point

If buoyancy is due to the pressure differential as we go deeper in a liquid, then that pressure differential should depend on the vertical dimension of the immersed object. Eg. if we have a long cylinder vertically placed, the pressure differential between its top surface and its bottom surface will be bigger than the differential of a shorter cylinder. Is this true?
 

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  • #2
SammyS
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If buoyancy is due to the pressure differential as we go deeper in a liquid, then that pressure differential should depend on the vertical dimension of the immersed object. Eg. if we have a long cylinder vertically placed, the pressure differential between its top surface and its bottom surface will be bigger than the differential of a shorter cylinder. Is this true?
Asking Archimedes ... The buoyant force is equal to the weight of the displaced fluid. Buoyancy does depend on volume, not shape.

So how does this square with your analysis?
A cylinder of the same volume but of half the vertical dimension, will have twice the area on each end. Force is area × pressure. The shorter cylinder will have 1/2 the pressure difference, but the net force will be the same.
 
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No, the volume doesn't have to be the same. Afterall, buoyancy only depends on density. The density of the two cylinders can be the same.

I hope you understand what I am trying to do. I am trying to correlate the hydrostatic pressure gradient and the buoyancy.
 
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SammyS
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No, the volume doesn't have to be the same. Afterall, buoyancy only depends on density. The density of the two cylinders can be the same.

I hope you understand what I am trying to do. I am trying to correlate the hydrostatic pressure gradient and the buoyancy.
I was looking at the related concept of buoyant force.

As you say, buoyancy only depends on density. So do you actually have a question here?

Normally we assume that the liquid is not compressible . If the buoyant object is rigid, then how can the buoyancy depend upon hydrostatic pressure gradient?
 
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I was looking at the related concept of buoyant force.

As you say, buoyancy only depends on density. So do you actually have a question here?

Normally we assume that the liquid is not compressible . If the buoyant object is rigid, then how can the buoyancy depend upon hydrostatic pressure gradient?
What does hydrostatic pressure gradient exerted to a buoyant object has to do with its rigidity?
 
  • #6
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No, the volume doesn't have to be the same. Afterall, buoyancy only depends on density. The density of the two cylinders can be the same.

I hope you understand what I am trying to do. I am trying to correlate the hydrostatic pressure gradient and the buoyancy.
All you need to do is to compare boats with the same displacement but different hull designs. A fin keel sailboat goes far deeper in the water than a flat bottomed barge with the same displacement.

@SammyS gave you the correct answer.
Asking Archimedes ... The buoyant force is equal to the weight of the displaced fluid. Buoyancy does depend on volume, not shape.
 
  • #7
sophiecentaur
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If you take a hollow cylinder and chuck it in the water, it will float, laying horizontally. It will experience the same buoyant force whichever way you orientate it (say you restrain it in a vertical mesh tube) because it will displace the same volume of water. But the Potential Energy will be at its lowest with the cylinder horizontal. You need to do work on it to make it float upright, despite the fraction of water that's displaced being the same. Orientation and shape can appear to have an effect on upthrust when they don't actually.
 
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SammyS
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What does hydrostatic pressure gradient exerted to a buoyant object has to do with its rigidity?
Well, if it's not rigid it will be compressed somewhat by the hydrostatic force, thus its buoyancy will be reduced.
 
  • #9
SammyS
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No, the volume doesn't have to be the same. Afterall, buoyancy only depends on density. The density of the two cylinders can be the same.

I hope you understand what I am trying to do. I am trying to correlate the hydrostatic pressure gradient and the buoyancy.
Well I see that I was too hasty with my previous reply.

I was looking at the related concept of buoyant force.
...
After checking for a more technical definition of buoyancy, I see that it is generally referred to as the buoyant force.

Therefore, buoyancy has everything to do with the volume of a submerged object.
 
  • #10
sophiecentaur
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Well, if it's not rigid it will be compressed somewhat by the hydrostatic force, thus its buoyancy will be reduced.
Hence, rising bubbles get bigger and bigger and rise faster and faster.
 
  • #11
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It is important to remember that there are two forces acting on an object in or on a liquid. The first is the weight of the object, the second is the weight of the liquid displaced. Subtract the weight of the displaced liquid from the weight of the object and you can tell if the object can float (result < 0), if it's neutral (result = 0) or if it will sink (result > 0). In the case of an object that changes volume under pressure the depth of submersion makes a difference because it changes the volume of the object.
 

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