Volume's effect on buoyancy: Does pressure increase?

[basem12]

Homework Statement

Writing a hypothesis to a research question on buoyancy and volume.

Relevant Equations

F = pvg (buoyancy formula)

Hey!
Im currently writing a lab on how an increase in the volume of an object will result in an increase of buoyancy force acting on an object. We fully immerse different amounts of clay playing blocks into water (using a string) on top of a scale, and calculate the buoyancy force. The reasoning I used to explain the existence of buoyant force is by saying that the pressure acting downwards at the top of the object is less than the pressure acting upwards at the bottom of the object, as the bottom of the objects is deeper into the water than the top of the object. For me, it seems logical that the pressure at the bottom of the object increases as the volume increases, as the surface area increases which means more water particles will exert a force on the object. Is this scientifically correct? And if it isn't correct, how would buoyant force increase as volume increases?

Thank you!

 

[Orodruin]

While it is true that pressure on the bottom is larger and that’s the general idea, you should not use the sole argument that pressure at the bottom increases as volume does. You can increase volume without changing the height of the object (eg, by changing its horizontal extension).

You would be better off arguing (using the pressure differential) for why buoyancy is proportional to volume and then use the argument of volume rather than an argument of increases in pressure differences.

 

[Chestermiller]

Homework Statement: Writing a hypothesis to a research question on buoyancy and volume.
Relevant Equations: F = pvg (buoyancy formula)

Hey!
Im currently writing a lab on how an increase in the volume of an object will result in an increase of buoyancy force acting on an object. We fully immerse different amounts of clay playing blocks into water (using a string) on top of a scale, and calculate the buoyancy force. The reasoning I used to explain the existence of buoyant force is by saying that the pressure acting downwards at the top of the object is less than the pressure acting upwards at the bottom of the object, as the bottom of the objects is deeper into the water than the top of the object. For me, it seems logical that the pressure at the bottom of the object increases as the volume increases, as the surface area increases which means more water particles will exert a force on the object. Is this scientifically correct? And if it isn't correct, how would buoyant force increase as volume increases?

Thank you!

Pressure increases with depth below the surface. In addition, the pressure on a submerged object does not just act up and down; the pressure force acts perpendicular to the surface of the object, but only the vertical component of the pressure force contributes to the buoyant force. This added up to the density of water times the submerged portion of the object's volume.

 

[basem12]

While it is true that pressure on the bottom is larger and that’s the general idea, you should not use the sole argument that pressure at the bottom increases as volume does. You can increase volume without changing the height of the object (eg, by changing its horizontal extension).

You would be better off arguing (using the pressure differential) for why buoyancy is proportional to volume and then use the argument of volume rather than an argument of increases in pressure differences.

Thanks for the answer! The thing is, I don't understand why buoyancy is proportional to volume. Why is it that buoyancy increases when the volume increases? I can explain this using archimedes principle, but then I'd have to explain archimedes principle and why it works. From my understanding, buoyant force exists because of the difference in pressure, so the force acting on the object (from pressure) increases as volume does, or else how would the buoyant force increase? If this is true, is it because more water particles are in contact with the object due to a larger surface area?
Thank you so much!!!

 

[hmmm27]

Buoyancy is the weight of displaced water minus the weight of the object.

If you double the volume (while retaining the orignal mass) of the object, then the weight of displaced water doubles as well.

 

[kuruman]

Buoyancy is the weight of displaced water minus the weight of the object.

The buoyant force is always the weight of the displaced water according to Archimedes' principle. If the weight of the displaced water is less than the weight of the object, the object sinks. Two sinking objects of different weights but of same external volume, have the same buoyant force acting on them.

 

[Chestermiller]

Thanks for the answer! The thing is, I don't understand why buoyancy is proportional to volume. Why is it that buoyancy increases when the volume increases? I can explain this using archimedes principle, but then I'd have to explain archimedes principle and why it works. From my understanding, buoyant force exists because of the difference in pressure, so the force acting on the object (from pressure) increases as volume does, or else how would the buoyant force increase? If this is true, is it because more water particles are in contact with the object due to a larger surface area?
Thank you so much!!!

Did you not notice that I said that the pressure acts normal too the surface of the object, but it is only the vertical component of the pressure force that matters.

 

[basem12]

Did you not notice that I said that the pressure acts normal too the surface of the object, but it is only the vertical component of the pressure force that matters.

Alright, then shouldn't the vertical component of pressure increase when the volume increases so that the buoyant force increases as well?

 

[kuruman]

Look at the drawing below that shows three boxes of different volumes. The box in (B) has the same top and bottom area as (A) but greater height. The box in (C) has greater top and bottom area as (A) but the same height.

The pressure at the top of each box is the same. The force due to the fluid is down and is equal to pressure times area. It follows that the down force at the top of (B) is equal to the down force at the top of (A) and that the down force at the top of (C) is greater than the down force at the top of (A).

What about the upward fluid force that is exerted at the bottom of each box? In all cases, the pressure at the bottom is greater than the top so that the net fluid force, a.k.a. the buoyant force, is up regardless of whether the box sinks or floats. An expression for the buoyant force is $$BF=\rho_{\text{fluid}}~g~\Delta h~A$$ where $\Delta h$ is the height of the box and $A$ the area of the top (or bottom). Note that $\Delta h~A$ is the volume of the box.

The buoyant force in (B) is greater than (A) because although the forces are equal at the top, the force at the bottom of (B) is greater, $\Delta h_B>\Delta h_A.$ The buoyant force in (C) is greater than (A) because although $\Delta h_C=\Delta h_A$, the area of (C) is greater than the area of (A). See how "increasing the volume" works? (The forces in the drawing are drawn qualitatively and not to scale.)

 

[Chestermiller]

Alright, then shouldn't the vertical component of pressure increase when the volume increases so that the buoyant force increases as well?

If you spread it out more horizontally to increase the area that way, the pressure on the bottom isn’t as high.

 

[haruspex]

I don't understand why buoyancy is proportional to volume. Why is it that buoyancy increases when the volume increases? I can explain this using archimedes principle, but then I'd have to explain archimedes principle and why it works.

Consider removing the object, and filling the hole that would leave (up to the surface of the surrounding fluid) with more fluid. Clearly this would be stable, therefore the weight of that added fluid equals the net force exerted on it by the surrounding fluid. But the surrounding fluid does not care what it is surrounding, so this must be the same net force as it exerted on the object.
I strongly suspect this reasoning is what Archimedes used.

 

[kuruman]

But the surrounding fluid does not care what it is surrounding, so this must be the same net force as it exerted on the object.

In other words, water just barely floats in water (of the same temperature.)