Water/air trap pressure formula

[Calymi]

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.

 

[Chestermiller]

You need to measure the height of the water in the riser into which you are pouring the water (i.e., the height above the water surface). Measuring it in the big container won't do you much good, unless you are willing to do some calculations to determine the pressure of the air inside the container, based on the reduced air volume and the ideal gas law.

Chet

 

[Calymi]

Thanks for the reply Chet.

I'm happy to do the calculations if they aren't stupidly excessive. How would the meausred water in the riser correlate to the air pressure? I.e. Particular ratio? Overall water + added height of riser water = desired inches?

Apologies if the questions seem stupid, this isn't something that I've done before and I'd rather make sure I understand it correctly than muddle through and get the answer by chance.

Caly

 

[Chestermiller]

Thanks for the reply Chet.

I'm happy to do the calculations if they aren't stupidly excessive. How would the meausred water in the riser correlate to the air pressure? I.e. Particular ratio? Overall water + added height of riser water = desired inches?

Apologies if the questions seem stupid, this isn't something that I've done before and I'd rather make sure I understand it correctly than muddle through and get the answer by chance.

Caly

Riser water height - tank water height = desired inches

 

[HalfLostAndSearching]

I understand your concern about finding the correct formula to demonstrate your model. The relationship between water and air pressure can be described by the hydrostatic pressure formula, which states that the pressure at any point in a fluid is equal to the weight of the fluid column above that point. In this case, the weight of the water column in the tube will create an equal pressure on the air inside the sealed container.

To answer your first question, when the water reaches the equivalent of 4.4 inches on the ruler, the air pressure inside the container will indeed increase and trigger the pressure switch. This is because the weight of the water column will create a pressure that is equivalent to 4.4 inches of water.

To further explain the correlation between the two pressures, the pressure switch is designed to trigger at a specific pressure, in this case 4.4 inches of water. This means that when the air pressure inside the container reaches 4.4 inches of water, it will be equal to the trigger pressure and the switch will be activated.

I would recommend using the hydrostatic pressure formula to calculate the pressure at different points in the water column and compare it to the trigger pressure of 4.4 inches of water. This will help you understand the relationship between the two pressures and ensure that your model is accurate.

I hope this helps and good luck with your project! Remember, as a scientist, it is important to always question and seek understanding in order to find the most accurate and reliable solutions.