Fluid Dynamics: Air Rising from Water Questions

[Another God]

I'm curious about some fluid dynamics stuff, and my first series of questions I have are to do with how air rises out of water...

Having done some scuba diving, I know that divers use bladders to achieve neutral bouyancy and positive bouyancy so as to hover or rise through the water.

Now for the questions: What sort of upward force is exerted by air under water?

Take a cubic meter of air for the sake of ease. Is it the inverted equivalent of 1 cubic meter of water being tipped out of a bucket? ie: mass = 1kg, acceleration = 9.8m/s/s? (of course, the 'air resistance' would be very different to the 'water resistance') Or is it different because of the fact that the bubble is going 'up'?

I do realize that the 'upward force' being exerted by the air in the divers bladder is a consequence of the water displacement, but can someone more accurately explain how that works? How does the displaced water 'push the air up?' instead of ...well...pushing down more.

 

[Doc Al]

Originally posted by Another God
Now for the questions: What sort of upward force is exerted by air under water?

Consider an imaginary 1 meter long cube in the water. Water pressure is squashing it on all sides. The force on the bottom of the cube pushing it upwards is greater than the force on the top pushing down (since water pressure is greater at the bottom). Archimedes principle says that the combined effect of the fluid pushing on our imaginary cube equals the weight of the fluid that the cube displaces. That's the buoyant force, acting upwards.

Now if the cube is filled with water, the buoyant force is balanced by the weight of the water. No surprize there... nothing happens. But if the cube is filled with... nothing... or air (something lightweight), then you have a net force acting upwards. That's how bubbles and bladders get pushed up.

The upward force is exerted by the water, not the air!

 

[russ_watters]

Originally posted by Another God
Take a cubic meter of air for the sake of ease. Is it the inverted equivalent of 1 cubic meter of water being tipped out of a bucket?

Yes, that's a good analogy. Air is so much lighter than water, its mass can be pretty much ignored. So a 1m^3 air pocket is a hole where 1m^3 of water should be. The buoyant force is equal to the weight of that missing water.

I do realize that the 'upward force' being exerted by the air in the divers bladder is a consequence of the water displacement, but can someone more accurately explain how that works? How does the displaced water 'push the air up?' instead of ...well...pushing down more.

Another way to think of pressure is that it is equal to the weight of the column of water. If for example your hypothetical 1m^3 bucket is 10m down, it has 10m^3 of water on top of it, with a total weight of 98n and therefore a pressure acting on the top of the bucket at 98n/m^2.

But wait - the bottom of the bucket is 11m down. The pressure 11m down is 11*9.8=107.8n/m^2. And that 107.8n force is pushing up on the bubble. Since there is some missing water there, you only have 98n pushing down but have 107.8n pushing up. The difference between the two pressures (forces) is 9.8n and is equal to the net force pushing up on the bucket.

 

[Cliff_J]

Interesting thought - wouldn't the compressibility of the air (assuming the containment vessel is not solid) need to be factored in as well?

Cliff

 

[chroot]

Cliff,

Yes, bubbles expand as they rise. Larger bubbles rise faster than smaller ones. Usually, large bubbles fragment into many smaller ones on the way up.

- Warren

 

[Another God]

so bubbles are compressable...but water isn't is it?

 

[LURCH]

Originally posted by Another God
so bubbles are compressable...but water isn't is it?

That's essentially correct. The most frequently-used comparison is that water is about as compressable as iron.