Calculating Filling Time for a Diving Tank with Changing Hydrostatic Pressure

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SUMMARY

This discussion focuses on calculating the filling time for a diving tank subjected to changing hydrostatic pressure. The filling speed is determined using the formula sqrt(2*g*h), where h is the depth (100m). As the tank is submerged, the pressure inside the tank is no longer atmospheric, and the filling speed decreases due to the pressure differential. The conclusion indicates that the filling time approaches infinity as the pressure difference diminishes, resulting in an exponential filling volume with a horizontal asymptote.

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Engineers, physicists, and students involved in fluid dynamics, diving operations, or any field requiring an understanding of pressure effects on gas behavior in submerged environments.

jean
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Hey,

Let's imagine I have a tank, filled with air at atmospheric pressure. This tank have a closing/opening valve.
I dive this tank at 100m under water and opened ce valve, my filling speed will be sqrt( 2*g*h) with h=100m.
Now, if i want to dive the tank (with a volume X) continuously at a velocity Vd. How can i calculate, how much time it will take to fill it ? Asa water enter the tank, the pressure won't be Patm anymore..
Thanks !
 
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jean said:
Hey,

Let's imagine I have a tank, filled with air at atmospheric pressure. This tank have a closing/opening valve.
I dive this tank at 100m under water and opened ce valve, my filling speed will be sqrt( 2*g*h) with h=100m.
Now, if i want to dive the tank (with a volume X) continuously at a velocity Vd. How can i calculate, how much time it will take to fill it ? Asa water enter the tank, the pressure won't be Patm anymore..
Thanks !
Use the ideal gas law for the air pressure in the tank.

By the way, is this a homework problem?
 
Yes i can use P1 V1 = P2 V2 (but i guess the air goes away in bubble and not compressed right ?) and no it's not a homework. The answer may be: it will take an infinite time to fill the tank because while we go in depth, the difference of pressure btw the outside and the inside will decrease and so the filling speed... The volume filled will be like an exponential with an horizontal asymptote.. What do you think? Thanks
 

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