Two phase flow in T-junction

Question

I have some hydrostatic/dynamic problem, maybe not that hard, but I am not able to prove it analytically.

Here is the setup: Lets assume that there is full water reservoir (details on the picture below) with valve/seal at the end of the pipe (point (2)). There is possibility that the valve/seal can break resulting in flow of water from the reservoir. The countermeasure is that there is much smaller pipe attached to the to the bigger drain pipe (point (1)) and following situation should happen: water surface is dropping down under the pipe inlet (point(3)) and letting air. That sould stop water flow in bigger pipe.

Question is: is it possible to stop steady flow of water just by letting air in this specific T-junction and can you prove it? Would it be different with bigger pipe diameter (smaller diameter ratio)?

If needed: Assume stainless steel pipe and body of reservoir. But I thing that preasure losses are insignificant here in this case.

Just by looking at Bernouli equation...I think that the water has so much kinetic and potential energy that any pipe diameter with air cannot stop this.

Thanks

Answer 1

TLDR: It should work

Water flow should stop after the surface drops bellow the pipe at point (1). In this situation, kinetic energy of the water at (4) is just as high to fully transform into potential energy at (4). So to get this water column moving, you would need something else, which could be suction from (2)-(1), but that is severed by air. If there still was be any water column in (2)-(1), it would suck air through (1)-(3) as it falls down.

Minimum diameter of the air tube

Let's say we will be testing these setups, always starting with a full tank of water by opening the outlet valve at (2). Depending on the diameter of the air tube, the outflow should stop at various levels. When there is a steady outflow with water level below (1), the pressure at (1) will be smaller than atmospheric pressure, and this pressure difference will in time suck in more and more air through the air tube. Then depending on the speed of the water flow, this added air could be either mixed into the water and taken away or it may build up at (1) and in segment (1)-(2), eventually severing the water flow.

Two phase flow in (1)-(2) should diminish the suction power compared to the situation when it is full of water. So the solution could be to find how much air you need to add into (1)-(2) for it to have the same hydrostatic pressure as water column between tank water level and (1). This required air flowrate should lead you to the minimum air pipe diameter.