Calculating Filling Time for a Diving Tank with Changing Hydrostatic Pressure

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To calculate the filling time for a diving tank at 100m underwater, the filling speed can be determined using the formula sqrt(2*g*h), where h is the depth. As the tank fills with water, the pressure inside will not remain at atmospheric pressure, complicating the calculation. The ideal gas law can be applied, but it's noted that air escapes as bubbles rather than being compressed. It is suggested that the filling time could approach infinity due to decreasing pressure differences, leading to an exponential filling rate with a horizontal asymptote. Understanding these dynamics is crucial for accurate calculations in underwater scenarios.
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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