Buoyancy of a submerged barrel

[hodderman]

Hi!

I'm interested on how a 45-gallon drum (filled with air) behaves when submerged in water. I did some calculations and from what I calculated a 45-gallon drum displaces 170kg of water, therefore the upward (buoyant) force on the drum when submerged would be 170kg minus the weight of the drum..Does this buoyant force increase with depth? I know the pressure exerted by the depth of the water will increase greatly with depth, so is there a point where the pressure of water pushing down on the drum balances out the buoyant force?

i'd appreciate some help, my physics is rusty to say the least!

 

[Civilized]

I'm interested on how a 45-gallon drum (filled with air) behaves when submerged in water. I did some calculations and from what I calculated a 45-gallon drum displaces 170kg of water, therefore the [total or net] upward (buoyant - weight) force on the drum when submerged would be 170kg minus the weight of the drum.

correct!

Does this buoyant force increase with depth?

Nope! Archimedes principle, that the buoyant force is equal to the weight of the water displaced, is always correct, and clearly it does not depend on depth.

I know the pressure exerted by the depth of the water will increase greatly with depth

That's right, each additional meter of depth will add 1.4psi of pressure (the shape of the container does not matter at all). For comparison the standard pressure outside water just due to the atmosphere is 15 psi, so you would need to go about ~35 feet deep to feel double the standard atmospheric pressure.

, so is there a point where the pressure of water pushing down on the drum balances out the buoyant force?

Nope, the buoyant force does not change with depth. The reason is that the buoyant force is in fact due to the difference in pressure above and below an object. The bottom of the object i.e. the part which is at a greater depth, will also feel a greater pressue, and so the difference in pressure causes an upward force on the object called the buoyant force. But this difference in pressure never changes, because the size of the object does not change, and each meter of depth adds the same 1.4 psi.

 

[hodderman]

Thanks for the speedy reply...I found that when i was trying to work out the forces involved, the force that was on the top of the drum underneath the water grew extremely large with depth...for example, a drum in 35 feet of water feels a pressure of roughly 30psi...if the buoyant force doesn't change then that means it will still have the 170kg (- weight) force upwards, but the downward force due to the weight of the water will be much larger, will this not inhibit the drum from rising?

 

[Civilized]

The simple way to understand it is that pressure does not act only "on the top of the drum", it acts on all sides of the drum. Therefore pressure also acts on the bottom of the drum, to cancel the majority of the pressure on top of the drum. What's left over is the buoyant force, which does not depend on depth at all. The only effect that depth will have on your drum is that the increasing pressure will try to crush the drum from all sides, but of course that does not happen until extreme depths.

Just to repeat, the buoyant force does not depend on depth, and the increasing pressure as the drum goes deeper acts on all sides so the only effect of increasing depth is to 'crush' the drum from all sides.

 

[LURCH]

To verify this for yourself, you can repeat the calculation you used here:

...for example, a drum in 35 feet of water feels a pressure of roughly 30psi...

and calculate for the top of the drum, only. Then, assume some height for the barrell (I'd proabbly say 5 repeat the calculation for the bottom of the drum.

Subtract the first value from the second, and you should get 170kg. If the top of the drum is 35ft under, then the bottom is 40ft, if it's 100ft under, the bottom is 105ft, etc.

Of course, you could make a shorter barrell, but if it is to remain 50gal, it would have to be wider. In that case, you get less of a pressure differential actying over more surface area. Net result; 170kg.

 

[Naty1]

The reason buoyancy doesn't vary (much) by depth is that water like many liquids is almost incompressible. If it were compressed much, then the density would increase and buoyancy would increase...

Another reason buoyancy might vary slightly by depth is temperature: colder water is usually more dense. Also, saltwater is more dense than fresh water but salt content is I think essentially pretty constant at varying depths.

 

[Bob S]

As pointed out above, the buoyancy does not change, unless either the density of water increases, or the drum volume changes. The center of gravity of the barrel is the center of mass for the barrel. The center of buoyancy is the center of gravity for the displaced water. For rotational stability, the center of gravity should be below the center of buoyancy. See http://www.engineeringtoolbox.com/centre-gravity-buoyancy-d_1286.html The center of buoyancy depends on construction of the barrel. This is why ballast in ships works. But the water pressure increases as the depth increases, and this can change the volume of the barrel. One example of the latter is the USS Thresher nuclear submarine, which was crushed by the water pressure and sank off the coast of Massachusetts. See
http://www.history.navy.mil/photos/sh-usn/usnsh-t/ssn593.htm

 

[hodderman]

hey! Thanks for all the knowledge, I'm starting to get a grasp on the whole thing. I have one more query though...Supposing you 'ejected' a 50 gallon drum from a watertight container 35 feet below the surface of the water. If you were able to place the drum (vertically) in a watertight container with a lid 35 feet below the surface of the water and then opened the lid, would it zoom upwards? At first I thought that it obviously would, but then, seeing as it isn't displacing any water AND given the pressure being exerted on it from the water above, would it not stay in the watertight container? For this question I'm assuming that the watertight container is fixed 35 feet below the surface and is sealed so that when the lid is opened water does not rush in underneath the barrel.

I'm aware that the above situation would bring about a vacuum...imagine an air hose is attached to the base of the watertight container and the open end of the air hose is above the surface of the water to alleviate any vacuum.

 

[Bob S]

...Supposing you 'ejected' a 50 gallon drum from a watertight container 35 feet below the surface of the water. If you were able to place the drum (vertically) in a watertight container with a lid 35 feet below the surface of the water and then opened the lid, would it zoom upwards? At first I thought that it obviously would, but then, seeing as it isn't displacing any water AND given the pressure being exerted on it from the water above, would it not stay in the watertight container? For this question I'm assuming that the watertight container is fixed 35 feet below the surface and is sealed so that when the lid is opened water does not rush in underneath the barrel.

I'm aware that the above situation would bring about a vacuum...imagine an air hose is attached to the base of the watertight container and the open end of the air hose is above the surface of the water to alleviate any vacuum.

If you put about 20 psig in the air hose, the barrel would begin to rise up.

 

[hodderman]

Thanks to everyone for helping me out, I appreciate it greatly!