Calculating Underwater Pressure

What depth of water (at sea level) would produce 2 atmospheres of air pressure?
- dee wood
atlanta, georgia - usa

Dee -

Well, let’s see if we can work this one out. First, we have to understand how pressure is measured. If we were to take a one inch column of air all the way up through the atmosphere, it would weigh 14.7 pounds. For this reason, we like to say that the standard air pressure (at sea level) is 14.7 pounds per square inch (psi). Water weighs more than this, though. Each one inch column that’s one foot deep will weigh 0.445 pounds.

So if you’re right at sea level, the pressure will be 14.7 psi. And for every foot you go underwater, you add another 0.445 psi. So at one foot deep, the pressure would be 14.7 psi + 0.445 psi = 15.145 psi. And at two feet deep it would be 14.7 psi + 2*(0.445 psi) = 15.59 psi, etc. In order to get to 2 atmospheres worth of air pressure, you would need to get to the point where there’s 29.4 psi (2 times 14.7 psi). To get to 29.4 psi, it turns out that you would need to be 33 feet deep. (Since 14.7 psi + 33*0.445 psi = 29.4 psi.)

-Tamara

(published on 10/22/2007)

The number of psi/foot depth is .433, not .445. You should state in your answer how this is derived: Water weighs 1gm/cubic cm.
- Brian Sargent (age 62)
Tyngsboro, Massachusetts

Brian- Thanks, you’re right. a square inch column of pure water one foot deep has 2.54^ 3*12 cubic cm (since there are 2.54 cm/inch) so the mass is 196 gm, giving a weight of 0.433 lb. I bet that the answer above was concerned with actual sea water, however, and that’s a little denser due to the dissolved salt.

Mike W.

(published on 11/03/2007)

She was correct in the beginning since salt water is denser than fresh, .445 psi per foot to be exact :P
- Anonymous

I think we’re all in agreement here. That density is the typical density of seawater. In general, the density of saltwater depends on how salty it is.

Mike W.

(published on 01/14/2008)

I understand how it works in our units, but what about in SI units?
- Scott Norton (age 18)
Trumbull, CT, 06611

In SI units, atmospheric pressure is very close to 10⁵ Pascal. Water has a mass of 10³ kg/m³. The gravitational acceleration near the Earth's surface is about 9.8 m/s². So that means the pressure goes up about 9800 Pa for each meter down, a little more for salt water.

Mike W.

(published on 09/17/2009)

I have two questions.... How do I know the pressure under one meter of water if there was no air? If I was at the bottom of a giant ice cream cone full of water would there be more pressure than if I was at the bottom of a giant test tube thats just as high? Does it matter if theres more water on top or is it just about how deep it is? Im just wondering about water not air.
- Jackie (age 16)

Pressure is how much force you feel per unit area. Every force that acts on a surface corresponds to a pressure. For example, when you press a button, you are putting pressure on it. In water (or air), the weight of the water (or air) above you exerts a force on you, so you feel water pressure (or atmospheric pressure). The presence of water pressure does not require air, so we can measure pressure directly under water. There are many ways to measure pressure. For example, we can measure how much force is exerted by water and divide it by the area of the detector.

You mentioned an important point that water pressure is the same at the same depth, regardless of the shape of the container. This may be a little counter-intuitive because there is more water in a giant ice cream cone than a giant test tube. But remember that the cone is also supporting some weight of the water! The surface of the cone is facing upward; while the wall of the test tube is vertical and cannot support any water. As a result, you would feel the same water pressure if you were in these containers of the same height.

- Tsung

(published on 01/20/2011)

References to 1 foot of change in sea water in PSI was initially stated correct as.445 psi per foot of change (Correct as per U.S. Navy dive tables) It was countered by .443 (perhaps fresh water?) Also when calculating pressure at depth the sea level pressure value e.g. 14.7 is not used in the pressure vs. depth calculations and starts at 0. We (Navy divers) have always used 44.5 psi per 100 ft.
- Bob La Bonte (age 73)
Victoria, TX USA

Hi Mr. La Bonte,

I unfortunately could not locate the exact information on the website that you are referring to. But as I understand, the issue is about the pressure at sea level. So as you dive deeper down the sea, the total measured pressure will be sum of the atmospheric pressure exerted on the water surface + liquid pressure due to a water column between you and the surface. So 14.7 corresponds to the former value, whereas your 0.445 psi/ft correspond the latter contribution. So it all depends on what one refers to when talking about the "pressure".

Yes, the discrepancy between 0.443-0.445 depends on the salt level, since pressure under some height of a liquid is density dependent, which in turn depends on the salt concentration. So such numbers may slightly vary between the Pacific Ocean and the Mediterrenean Sea. Freshwater would differ by more, since it's 2 or 3 % les dense than seawater.

Tunc+mw

(published on 12/12/2015)