Density versus Pressure -- Balancing the bouyancy of a floating capsule

• mrapple
In summary: I would say hydrostatic pressure is only important for a closed system such as a pipe where a denser fluid rises on the other side when pushing a less dense fluid. I would say regular water pressure would be the force required to plug a hole because it is from the side and not dependent upon gravity? But, what if I am inserting the object at an angle?In that case, the pressure on the side of the object would be higher than the pressure in the water, and the object would slide into the container.
mrapple
[Mentors’ note: no template as this thread had initially been misplaced in the technical forums and was moved here]

Summary:: Enclosed Cubic foot capsule passing between two bodies of different densities but questioned pressure.

You have a tub of fresh water 32 feet high sharing a wall with a pressurized container of air. The container of pressurized air is the same size as tub of water; the difference being, it's sealed. There is a hole a foot squared 30-31 feet below the surface of the water. There is an enclosed cubic foot shaped capsule of unpressurized air. The capsule is filling the foot squared hole. Half of the capsule is in the water and half is in the container of pressurized air. Disregarding friction, what should the container of air be pressurized to in order for the capsule to not move? How much should the air container be pressurized in order for the capsule to move?

Last edited by a moderator:
What do you think and why?

Could you explain the relevance of the capsule being full of unpressurised air. Is the capsule simply being a stopper between your pressurised air container and your water container? If so, is it rigid?

Lnewqban
Is this homework? Or a take home quiz problem? If so, we can move it to a homework forum.

Ibix said:
What do you think and why?

Could you explain the relevance of the capsule being full of unpressurised air. Is the capsule simply being a stopper between your pressurised air container and your water container? If so, is it rigid?
Yes, everything is rigid. There is no relevance of the capsule being filled with unpressurized air. Yes it is a stopper.

Given equal pressure even though the densities are different the capsule won't move.

jrmichler said:
Is this homework? Or a take home quiz problem? If so, we can move it to a homework forum.
Yes but I'd like to make the question simpler. If an Enclosed Cubic foot capsule passing between two bodies of different densities but equal pressure there will be no resistance right?

mrapple said:
Given equal pressure even though the densities are different the capsule won't move.
Yes. This is just Newton's second law - if there are equal pressures on equal areas then the forces are equal and opposite and the net force is zero. So the acceleration is zero.

Note that the water pressure will vary by about 0.03 bar over the height of your stopper, while the pressurised air pressure won't vary much. So you'll be setting the air pressure to match the average water pressure.

Lnewqban
mrapple said:
Yes, everything is rigid. There is no relevance of the capsule being filled with unpressurized air. Yes it is a stopper.

Ibix said:
Yes. This is just Newton's second law - if there are equal pressures on equal areas then the forces are equal and opposite and the net force is zero. So the acceleration is zero.

Note that the water pressure will vary by about 0.03 bar over the height of your stopper, while the pressurised air pressure won't vary much. So you'll be setting the air pressure to match the average water pressure.
Thank you!

mrapple said:
Yes but I'd like to make the question simpler. If an Enclosed Cubic foot capsule passing between two bodies of different densities but equal pressure there will be no resistance right?
Any resistance should come from the buoyancy force acting on the liquid side, increasing friction and inducing an asymmetric moment respect to the square hole (making more difficulty the free sliding of the cube).
Sliding the cube into the container of pressurized air should be easier than in the opposite direction.

Thanks. To follow up, I have a container of water 35 feet deep. If I push a cubic foot container of air into the side of the tank of water 30 feet below the surface I use hydrostatic pressure not water pressure to figure out resistance correct?

mrapple said:
hydrostatic pressure not water pressure
What distinction do you make between those two terms?

I would say hydrostatic pressure is only important for a closed system such as a pipe where a denser fluid rises on the other side when pushing a less dense fluid. I would say regular water pressure would be the force required to plug a hole because it is from the side and not dependent upon gravity? But, what if I am inserting the object at an angle?

mrapple said:
I would say hydrostatic pressure is only important for a closed system such as a pipe where a denser fluid rises on the other side when pushing a less dense fluid. I would say regular water pressure would be the force required to plug a hole because it is from the side and not dependent upon gravity? But, what if I am inserting the object at an angle?
I would say that the terms are synonymous for the situation at hand.

"hydrostatic" just means that we are considering a situation in which velocity is not contributing substantially to pressure. So we do not have to worry about Bernoulli, for instance.

"water" just means that the working fluid is water rather than air or hydraulic fluid.

Last edited:
When using a lever the movement is in the shape of an arch. Do I use cos (for example) to calculate the force for both the output and the input? If not, why? Thanks

mrapple said:
When using a lever the movement is in the shape of an arch. Do I use cos (for example) to calculate the force for both the output and the input? If not, why? Thanks
So you are mating a lever moving in a circular arc with a cube-shaped lump which is moving linearly. If you have a rack and pinion arrangement, a constant torque would work nicely. Can you supply a drawing?

Lnewqban said:
Any resistance should come from the buoyancy force acting on the liquid side, increasing friction and inducing an asymmetric moment respect to the square hole (making more difficulty the free sliding of the cube).
Sliding the cube into the container of pressurized air should be easier than in the opposite direction.
The buoyant object is being pushed into a hole at the bottom a tub of water 40 feet below the surface of the water. This object is being pushed in at a 45 degree angle downward. What equation do I use to find out the force needed to push the object into the tub of water neglecting friction?

Ibix said:
Yes. This is just Newton's second law - if there are equal pressures on equal areas then the forces are equal and opposite and the net force is zero. So the acceleration is zero.

Note that the water pressure will vary by about 0.03 bar over the height of your stopper, while the pressurised air pressure won't vary much. So you'll be setting the air pressure to match the average water pressure.
Also, a float with 5 pounds of water displacement is resting on the bottom of a pool 10 feet deep. The float is tethered to the bottom of the pool via a string that is pulled tight lengthwise and so is also laying on the bottom of the pool. The string is 4 feet long. If the float is released the float must travel in an arch because of the string tether. What equation do I use to figure out the resulting upward force of the float if it is traveling in an arch?

mrapple said:
Also, a float with 5 pounds of water displacement is resting on the bottom of a pool 10 feet deep. The float is tethered to the bottom of the pool via a string that is pulled tight lengthwise and so is also laying on the bottom of the pool. The string is 4 feet long. If the float is released the float must travel in an arch because of the string tether. What equation do I use to figure out the resulting upward force of the float if it is traveling in an arch?
Please start a new thread with your new question, and be sure to show your work on the solution. That is how we handle schoolwork-type questions at PF. Thank you.

1. What is the relationship between density and pressure in a floating capsule?

The relationship between density and pressure in a floating capsule is that as the density of the capsule increases, the pressure it exerts on the surrounding fluid also increases. This is due to the fact that the weight of the capsule is directly related to its density, and the greater the weight, the greater the force it exerts on the fluid.

2. How does balancing the buoyancy of a floating capsule affect its density and pressure?

Balancing the buoyancy of a floating capsule involves adjusting its weight and volume in order to achieve equilibrium between the upward buoyant force and the downward gravitational force. This can affect the density and pressure of the capsule, as changes in weight and volume will also change the overall density and pressure it exerts on the fluid.

3. What factors influence the density and pressure of a floating capsule?

The density and pressure of a floating capsule are influenced by a variety of factors, including the mass and volume of the capsule, the density of the fluid it is floating in, and the depth at which it is floating. Changes in any of these factors can impact the overall density and pressure of the capsule.

4. How does the depth at which a capsule is floating affect its density and pressure?

The depth at which a capsule is floating can affect its density and pressure due to changes in the surrounding fluid pressure. As the depth increases, the pressure of the fluid also increases, which can compress the capsule and change its density. This, in turn, can affect the pressure it exerts on the fluid.

5. How can density and pressure be controlled in a floating capsule?

Density and pressure can be controlled in a floating capsule through various means, such as adjusting its weight and volume, changing the density of the fluid it is floating in, or changing the depth at which it is floating. By carefully balancing these factors, the density and pressure of the capsule can be controlled to achieve the desired buoyancy and stability.

• Introductory Physics Homework Help
Replies
15
Views
1K
• Engineering and Comp Sci Homework Help
Replies
56
Views
3K
• Mechanics
Replies
40
Views
3K
• Engineering and Comp Sci Homework Help
Replies
3
Views
1K
• Mechanics
Replies
10
Views
4K
• DIY Projects
Replies
39
Views
9K
• Introductory Physics Homework Help
Replies
2
Views
2K
• Mechanics
Replies
5
Views
2K
• General Engineering
Replies
8
Views
7K
• Introductory Physics Homework Help
Replies
5
Views
6K