Bouyant Force on submerged hollow object with air trapped inside

[rcummings89]

Hello,

I'm reading about buoyant forces, but my book does not mention anything about an object with air (or any gas/fluid whose density is less than that of the fluid the whole object is immersed in). So for simplicity's sake, if you have a sealed, hollow cylinder completely submerged in water with air trapped inside, how do you calculate the buoyant force(s)? I was thinking maybe it was

F_B,air = ρ_airgV_air
F_B,water = ρ_watergV_water

then add them together but that doesn't seem right...

 

[Doc Al]

To calculate the buoyant force on an object, all that matters is the weight of the displaced fluid. The object's density or whether it is hollow is irrelevant. (Those things will affect the weight of the object, but not the buoyant force acting on it.)

 

[rcummings89]

Doc Al,

This question is also related to a conversation I had with a student doing research involving a mechanical fish in a flow tank. The fish he has (at this point essentially a metal skeleton) is quite heavy for the air-bearings he is using, and he told me he wants to attach a rubber "skin" to so that he can fill the hollow inside with air and increase the buoyant force. From what you say it sounds like he is mistaken to what force he is actually increasing, but intuitively it sounds correct, if he fills the fish with air, it will be "lighter" in reference to its supports.

Now I read that if the density of the object (in this case the air) is less than that of the fluid, it will float, but in this instance what force would that be, and how is it calculated?

 

[SteamKing]

When the air bladders are inflated, they are in effect displacing an amount of water equal to the volume of the bladder. The weight of the water displaced is the buoyant force.

 

[Doc Al]

From what you say it sounds like he is mistaken to what force he is actually increasing, but intuitively it sounds correct, if he fills the fish with air, it will be "lighter" in reference to its supports.

Sounds to me like adding a rubber skin will increase the volume of water displaced and thus increase the buoyant force.

Now I read that if the density of the object (in this case the air) is less than that of the fluid, it will float, but in this instance what force would that be, and how is it calculated?

You have to compare the buoyant force (due to the displaced water) with the weight of everything contained within the "skin". (But yes, if the average density of the object is less than that of water, it will float.)

 

[rcummings89]

Ok, I think I was mixing up my concepts. Thanks a lot guys!

 

[russ_watters]

Consider a mirror-image example of a ship: Floating on the surface, it is highly buoyant and floats easily. The exact same ship, filled with water, will sink. Difference? When on the surface, the interior of the ship is "filled" with air.

I suppose you might say that when you punch a hole in the side of a ship and it sinks, you aren't just letting the water in, you are forcing the air out.