Bubble Hydrodynamics: Find Numerical Solution to Air Bubble at 20m Depth

[Sajmon]

Diver at a depth of 20 m below the water breaths 1 liter of air. With what acceleration the air bubble begins to move against the surface ,how his speed varies with time and what is its volume at a depth of 5 m? The water temperature is 20° C. Part of a solution will be need to find numerically.

Thanks in advance

 

[Sajmon]

please help anybody

 

[rl.bhat]

As the bubble rises, pressure on it decreases. Volume increases.
Bouncy force on the bubble depends on the displaced liquid. As bubble rises volume increases, bouncy force increases. Hence the velocity of the bubble increases.
Since temperature of the water remains constant, you can find the volume at 5 m by using P1V1 = P2V2. Here P1 and P2 are the total pressure at 20m and 5 m.

 

[Sajmon]

But, how do you get velocity of a bubble?

 

[Sajmon]

Nobody knows how you get a velocity and acceleration of a bubble?

 

[rl.bhat]

Part of a solution will be need to find numerically

So they are not expecting the values of velocity and accceleration.
If you want you can find out, net force on the bubble is the weight of the displaced water which is not constant. Weight of the bubble is negligible compared to the weight of the displaced liquid. You can find the weight of the bubble at the depth of 5 m by knowing the volume and density of the air at 20 degree C. Now see whether you can proceed.