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Do you know if my work is correct for this kind of situation?

if air intake is a function of depth you would need an integral to do it right

Well, intake is a function of pressure which is a function of depth

because the first way I did was to calculate with a fixed quantity of gas

Ah, we integrate wrt to time?

Oh, ok ok I see :P

or you could make pressure a function of depth
A(P(h))dt

something like\[dP=\rho gdh\]\[dA(P)=f(\rho gh)\rho gdh\]A is some function of pressure f(P)

Air intake.. that would be his breathing speed?

then you could have\[dA\propto dP=k\rho gdh\]

Alright, I'll try it out, thanks!

Good luck. Thinking about it makes me remember why I didn't like fluid mechanics all that much.

In case of failure, I'll call you :P

the above if pressure is directly proportional to depth

I mean air intake propto depth