Pressure Rise in Closed Tank with 2 Inputs

AI Thread Summary
To calculate the time for the pressure inside the closed tank to equalize with the external pressure at 200m depth, one must consider the initial conditions, including the tank's volume and the pressure differential. The pressure at 200m depth is approximately 20 bar, meaning the air bubble must rise from 1 bar to 20 bar. The volumetric flow rate of air supplied at 30 bar must be factored in, along with the orifice plate's flow rate control. The calculations would involve using the ideal gas law and principles of fluid dynamics, while ignoring frictional losses simplifies the process. This scenario presents a practical application of pressure dynamics in underwater environments.
rhino_bill
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Supposing you had a cylindrical closed tank inside the body of a submarine; the top of the tank is at 200m depth. The tank has height 2.5m and internal volume 1.8m^3.

A section of pipework is connected between the top surface of the submersible (level with the top of the tank) and to the tank (assume inlet is at the bottom of the tank); an orifice plate will control the incoming flow rate.
A separate pipe connects to the side of the tank, through which air will be supplied at a constant pressure of 30 bar; with volumetric flow rate 5.7m^3/min (if required).

Assuming the initial pressure inside the closed tank is normal atmospheric (1 bar), how would you calculate the time for the pressure of the air bubble in the top of the tank to equalise with the pressure external to the top of the tank at 200m?
Ignore frictional losses in the pipeworks.
 

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