Water/air trap pressure formula

I have been set the problem of finding a method that does not use electronics to test a pressure switch. The switch itself is set to trigger at a pressure of 4.4 inches water (+-0.4). The method needs to be simple without any complex setup needed at the time of testing.

The image above is the solution I came up with. This has been accepted by my tutor and cannot be changed. Water will be poured into a tube connected to a sealed container until the increased air pressure triggers the pressure switch. A 2.5mm ruler will be marked/attached to one side of the container to check the level at which the switch triggers.

The issue I’m having is one of correct formulas to demonstrate the model. I am computer science based, not physics, which is making it a little difficult to understand the correct formula to use.

My questions are as follows:
1. When the water reaches the equivalent of 4.4" on the ruler will the subsequent increase in air pressure within the container be equivalnet and therefore trigger the switch at the correct time?

2. If not can somebody possibly briefly explain the correlation between the two pressures and/or point me in the direction of the correct formula?

This is not a graded piece of work. It is simple a problem my tutor has set me to help boost my knowledge in a subject I am lacking experience in.

Thank you.

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