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Consider the picture below: enter image description here

The microcontroller takes care of maintaining the pressure $P_1$ constant. In addition, the flow $F$, the area of the pipe ($A_p$) and the area of the hole ($A_h$) are known.

What it the relation between $P_1$ and the leakage flow $F_L$?

Is it possible to calculate the leakage flow with precision?

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Assuming $A_h$ is small, and the pressure at the orifice is $P_2$, you have a situation of orifice flow.

The flow rate strongly depends on the shape of the orifice.

It also depends on the thickness of the pipe wall, because if it is thick, the leak will take the form of a channel dominated by viscous flow.

So it will take some experimentation. You can't calculate it with precision from simple physics.

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