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- Homework Statement
- Hello,

Here is my problem: "We have a closed tank of large size which contains a liquid topped by air at a pressure equal to the atmospheric pressure. If the tank is closed, as the water flows out, the volume of air above the free surface increases, so the pressure decreases (law of perfect gases). We seek to find the pressure variation (𝛥P) at the surface of the water in the tank as a function of the z axis (whose origin is at B) and to give the expression of v (the flow velocity) as a function of z."

- Relevant Equations
- I know that:

-according to the perfect gas equation P=nRT/V so that pressure is proportional to volume, so that P(t=0)*V(t=0)=P(t=1)*V(t=1)

-That the initial pressure at the surface of the water is P =Patm

-by applying bernoulli between A and B, we have classical V0=sqrt(2gh)

I can imagine the experiment: the pressure at the surface will drop while the tank is emptying (if no air bubbles enter through the evacuation of course, otherwise it restores the pressure atm at the surface). The flow speed decreases as a function of time until the external pressure maintains a liquid level above the drain (thus stopping the flow). I can't put this resonance in mathematical form (𝛥P as a function of z and v as a function of z)

thank you in advance for those who will help me,

Sincerely

thank you in advance for those who will help me,

Sincerely