# Calculate pressure of air trapped underwater

Seal top end of straw, partially submerge straw in water, how do I calculate the air pressure inside the straw?

Bonus points for compensating for any secondary factors like temp, humidity or flex of the straw. Application: measuring water level in 5 gallon aquarium to accuracy of about 5mm.

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My research told me this question did not exist on StackExchange :) I figure pressure is related to weight of displaced water but volume of water displaced is related to hw much the air compresses which then leads me into a loop. – Brian Low Nov 8 '12 at 5:25

The pressure in the straw is (almost) the same throughout the straw. I say almost because air does have some weight so the pressure would be slightly higher at the bottom of the straw than the top, but this is going to be a very small effect.

The pressure at the air/water interface has to be the same as the pressure of the water, otherwise the water would flow into or out of the straw until the pressures equalised. So if you can calculate the pressure of the water you can calculate the pressure of the air in the straw.

The flex of the walls of the straw doesn't affect this concusion. However it does affect the volume of the straw so if you're using the distance the water enters the straw you will have to correct for a volume increase. If the straw is stretchy the water will be able to enter the straw further for the same pressure.

Temperature will change the density of the water and therefore the pressure. You need a table of water density:temp, or some suitable approximate equation to estimate it. I don't think humidity will have much effect, though I'm not sure I'd swear to this in court.

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Before you made me think of it, I had assumed that the water pressure outside would compress the straw and reduce the volume available for the air, but you are absolutely right: higher pressure inside, so it actually stretches! – Jaime Nov 8 '12 at 0:49
Thanks. How do you calculate the pressure of the water? The weight of the displaced water? – Brian Low Nov 8 '12 at 5:21
I'm reluctant to say too much because this is obviously a homework question or project. A few moments Googling will tell you how water pressure varies with depth and you're more likely to remember it! (I sound like my teacher now :-) If you're really stuck ask a new question about it here. – John Rennie Nov 8 '12 at 6:53
@JohnRennie Thanks, I appreciate the time you spent. I am also a bit discouraged - this is obviously a homework question because no adult could be ignorant enough to ask this? – Brian Low Nov 9 '12 at 4:05
@BrianLow: we get lots of students posting their coursework questions and it's important we don't just answer them otherwise we undermine the educational process and the students earn nothing! Some of these questions are very hard, so it's not that the questions are easy! Anyhow, my apologies if you were asking a genuine question and not asking for help with your coursework. If you still want to know how to calculate the pressure underwater comment here and I'll edit my answer to include it. – John Rennie Nov 9 '12 at 7:07