Fluid Dynamics: Air Rising from Water Questions

In summary, the conversation discusses the concept of buoyancy and how it relates to air and water. The upward force exerted on objects in water is due to the displaced water, not the air. The analogy of a 1 cubic meter bucket filled with water and a 1 cubic meter pocket of air is used to explain this concept. The difference in pressure at different depths is also mentioned, along with the compressibility of air and water.
  • #1
Another God
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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.
 
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  • #2
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 bouyant force, acting upwards.

Now if the cube is filled with water, the bouyant 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!
 
  • #3
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.
 
  • #4
Interesting thought - wouldn't the compressibility of the air (assuming the containment vessel is not solid) need to be factored in as well?

Cliff
 
  • #5
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
 
  • #6
so bubbles are compressable...but water isn't is it?
 
  • #7
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.
 

1. How does air rise from water in fluid dynamics?

In fluid dynamics, air rises from water due to differences in density. As water is heated, it becomes less dense and rises, while cooler air sinks. This creates convection currents, with warmer air rising and cooler air sinking. As the warm air rises, it carries water vapor with it, which can then condense and form clouds.

2. What factors affect the rate at which air rises from water?

The rate at which air rises from water is affected by temperature, pressure, and the properties of the air and water. Higher temperatures and lower pressures will cause air to rise faster, while the density and viscosity of the air and water will also play a role.

3. How does the shape of the container affect air rising from water?

The shape of the container can affect the rate at which air rises from water. In a tall, narrow container, the air will have a longer distance to travel before reaching the surface, resulting in slower rising. In a wider, shallower container, the air will have a shorter distance to travel, resulting in faster rising.

4. What happens when air rises from water in a closed system?

In a closed system, the air will continue to rise until it reaches a point of equilibrium, where the temperature and density are equal throughout the system. At this point, the air will no longer rise and will instead circulate in a circular motion, with warmer air rising and cooler air sinking.

5. How is air rising from water related to weather patterns?

Air rising from water plays a significant role in weather patterns. As warm air rises, it cools and releases moisture, resulting in the formation of clouds and precipitation. This process, known as convection, is responsible for the movement of air masses and the formation of weather systems, such as thunderstorms and hurricanes.

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