Is pressure linear?

[Russjstewart]

My apologies if this has been done to death, but a quick search did not bring anything up. I have always worked on the theory that pressure is linear and constant. Given 10 metres (33ft) is 2 ATA and 20 metres is (66ft )is 3ATA etc the assumption that 3 metres would be 1.3 ATA seems reasonable to me. Over possibly a more than a few red wines a friend argued against this based o n older bourdon tube depth gauges where the distance between 0-10 feet is greater than 10-20 feet and 20-30 is greater than 10-20 feet.. Have I been wrong. I had to dig out a really old Tekna vague to check the distance

 

[Steelyeyes]

Pressure is linear, the movement of a bourdon tube gauge is not.

Theory | Bourdon tube pressure gauge [with animation]

 

[RTC'83]

Agree with previous post, so you can disregard what follows.

Gauge pressure is not absolute preasure. You need to add 14.7 psi.(1 atm)
So at the surface your gauge preasure will be 0, your absolute preasure at the surface is
0+14.7 (1atm)= 1 AP

Salt Water = .445 psi/ft
Fresh Water = .432 psi/ft

PxV=K
(.0445x33)+14.7= 29.385
29.385/14.7 (1atm)=1.9989 round to 2 AP

Pressure increases predictably every 33 ft, but remember to add the 1 atmosphere from the air. So at 66 ft is 2 atm + 1 = 3 absolute pressure at 66 ft

Then you can find any pressure (p) or volume ( v) with Boyle’s Law (assumes that temperature remains constant)
P1xV1= P2xV2

 

[Russjstewart]

Thanks Steelyeys and RTC'83, I am not losing the plot, may have to cut down on the red wine, the link to the explanation of bourdon tube was great as was the re hash of boules law

Cheers

 

[RainPilot]

It’s the same with any spring type gauge, the bottom and top ends are inconsistent due to the spring force.

We have a lot of those in aircraft.

 

[Russjstewart]

Thanks

 

[broncobowsher]

Pressure is linear
Going from the surface (1ATA) to 10M doubles the pressure.
If you have $1 in your pocket and someone gives you $1 more you just got 100% more money.
If you have $10 in your pocket and someone gives you $1 more you just got 10% more money, but you still got $1 more.
The pressure has gone up the same amount.

The non-linear depth gauges are the same thing. The first bit you are doubling the pressure (adding the first $1) but at depth they don't move as much when you add to the $10.

 

[drbill]

Although I'm nitpicking a bit, pressure is not linear (although within recreational depths it may be). Water density can change with temperature and salinity although these changes are minimal.

 

[broncobowsher]

I thought about muddying up the waters with variable density and water does compress ever so slightly. But those are mostly for the theoretical world and not applicable to what was asked. So I went the other way and tried to simplify it.

Air pressure (above the water, altitude) gets into that non-linear thing a lot faster. Since the air is compressed by the air above it. For lower altitudes a quick value is loose ½PSI per 1,000' of elevation. That works fine for about the first 15,000 feet or so, pretty much any place a person will normally find them selves on the ground at. But that doesn't work at higher altitudes otherwise space would start at about 30,000' of elevation. But 30,000' altitude is still about 300mBar. OK, you got me, I went off into a slightly related tangent that really doesn't involve the original question.

 

[boulderjohn]

OK, you got me, I went off into a slightly related tangent that really doesn't involve the original question.

Maybe, but it is good that you at least mention the impact altitude has on pressure during a dive. A lot of people never think about it.

When I worked with DM candidates here in Colorado, I used to give them a story problem to work out related to buoyancy in local diving. I never had a student figure out on his or her own that buoyancy changes when changing depths at altitude are more dramatic than at sea level. I also never had one realize that the MODs for nitrox at our altitude are different from the sea level MODs you see in standard charts. (I have even made MOD charts for the diving we do that depends upon them.)