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Scuba Diving Calculations on Demand January 17, 2009

Posted by Chris Sullivan in Technical Diving.
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Some searches I’ve seen lately on this blog are:

  • How will salt water change the buoyancy?
  • Meters of seawater conversion 1 bar
  • Pressure of water at a depth of 1 meter
  • Convert water pressure to water depth
  • Ocean water density psi
  • Density of sea water in kpa
  • Sea water atmosphere psi
  • What is the pressure 1 bar underwater

Searches like this find my blog a lot. My most detailed explanation has more hits than any other page and continues to rack them up, but I though I’d tackle some of these directly and hopefully more completely.

So, the first thing to remember about the pressure of water is that it increases with depth, but the density of water remains constant. Apparently sea water compresses a little under very great pressures, but the effect is so minor that divers need not concern themselves with it. It is a fundamental property of pure liquids that they can’t be compressed, unlike solids and gases.

The next thing to bear in mind is the difference between absolute and gauge pressure. Absolute pressure is the force per unit area on an object while gauge pressure (for scuba diving submersible pressure gauges) is 0 at sea level, where the absolute pressure of the atmosphere is about 14.7 pounds per square inch, or 1 bar. That is, it’s relative to the pressure of the atmosphere.Many scuba diving calculations manipulate absolute pressure, so formulas will either be expressed in absolute pressure, or the conversion from gauge pressure to absolute pressure will be embedded.

For instance, the partial pressure of oxygen (PPO2) when breathing air at depth (in sea water) is 21% (the fraction of oxygen in air) times the depth+33 feet, all divided by 33 feet. i.e. it’s .21 x (d+33)/33. Adding 33 feet to the depth accounts for the additional pressure of the atmosphere, which is equivalent to 33 feet of sea water. Dividing by 33 feet converts the pressure in feet of sea water to the pressure in atmospheres. So we’re really just multiplying the fraction of oxygen in the air by the number of atmospheres in pressure.

Pressure can be measured in many ways. The most common ones are:

  • Pounds per square inch, or PSI, is used in North America and elsewhere for tire pressures, water sprinkler systems, scuba tanks, regulator intermediate pressures, and many other things.
  • Bar is used in Europe, Cuba, and many other places for the same things as PSI in North America. Millibars (thousandths of a Bar) were used in meteorology before Kilopascals (Kpa) came into popular use with the introduction of the metric system, even though both the Bar and the Millibar are metric units.
  • Kilopascals – are primarily used in meteorology to express atmospheric pressure, and in many scientific applications.
  • Inches of Mercury is used in aviation, at least in North America, to express altitude corrected atmospheric pressure. Altitude correction is required because pressure is used to measure altitude, and most airports are not at sea level. Altimeters are set to the current atmospheric pressure at sea level, and the altimeter should then read the altitude, or if parked, the airport elevation. If you’re wondering why you would measure pressure in inches of Mercury, think of a
  • Millimeters of Mercury – used to be used for the same purpose as Kilopascals but is now mostly obsolete, I think.
  • Metres of Fresh Water (MFW), Metres of Sea Water (MSW), Feet of Fresh Water (FFW), and Feet of Sea Water (FSW). These express pressure in terms of the depth, but the number depends on what liquid it is.
  • Atmosphere – A “standard atmosphere” of pressure.

Standard atmospheres appear in most of these scales, and are all the same except for rounding errors. So a standard atmosphere is 29.9213 inches of Mercury, which is close enough to aviation’s 29.92 standard pressure. Standard pressure is used in aviation is used for aircraft flying at high altitudes (the threshold is around 18,000 feet if I recall correctly). Once up that high, instead of setting the altimeters at the local sea level pressure they all use 29.92, which avoids two aircraft with different settings thinking they’re at different altitudes when they’re not.

A standard atmosphere is also 1.01325 Bar (or 1013.25 millibars) , and 101.325 Kilopascals. So now we know that a Bar is 100 Kilopascals. An atmosphere is also 760 millimetres of Mercury, and 33.8985 feet of fresh water (10.3323 metres).  This is also 33.0717 feet of salt water (10.0803 MSW). A standard atmosphere also exerts a pressure of 14.696 pounds per square inch.

So to answer the questions?

  • How will salt water change the buoyancy? Salt water is more dense than fresh water so objects, including divers, will be more buoyant. Look here to figure out by how much.
  • Meters of seawater conversion 1 bar Pressure of water at a depth of 1 meter? 1 Bar pressure is 10.0803 9.94845 metres of sea water. 1 meter of sea water is .0992037 .100508 bar.
  • Convert water pressure to water depth? See above – it depends on the units and whether the water is fresh or salt.
  • Ocean water density psi? Density is measured as mass divided by volume, like pounds per cubic inch or kilograms per cubic metre and not PSI. Salt water pressure in PSI is .444366 PSI per foot of depth, or around 14.7 PSI at 33 feet.
  • Density of sea water in kpa? Same problem as KPa is a measure of pressure like PSI and not density. Salt water pressure in kpa is 3.06379 KPa per foot of depth, or 10.0518 KPa per metre of depth.
  • Sea water atmosphere psi? The atmosphere is made of air rather than sea water so this one is difficult to interpret. As mentioned above, an atmosphere is 14.696 (usually rounded to 14.7) PSI. The equivalent depth of sea water to an atmosphere is about 33 feet, so 33 feet of sea water is about 14.7 PSI.
  • What is the pressure 1 bar underwater? It’s 1 bar of course. It’s also about 33 FSW, 34 FFW, 14.7 PSI, 100 KPA, 1000 millibars, 760 mm of Mercury (mmHg) and 29.92 inches of Mercury

All of these calculations were done using the magic of Calchemy, explained elsewhere in the blog on many occasions.

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Comments»

1. Chapter 9 | Offshore Welders - January 22, 2009

[…] Scuba Diving Calculations on Demand « Chronicle of an older diver […]

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2. steve - June 6, 2009

Hi can you tell me if a depth gauge has been set for fresh water can it be used for sea water

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deepstop - June 7, 2009

Hi Steve. Thanks. I think this is my first technical question!

The short answer is that it sure can. Because salt water is more dense, a gauge calibrated for fresh water will read a little deeper than the actual depth. For any recreational diving situation, that shouldn’t present any problems at all. The error will only be about 4 feet even at the maximum recommended recreational diving depth of 130 feet, and as you’d actually be shallower, for decompression purposes the dive would be slightly more conservative than allowed by standard tables.

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3. steve - June 7, 2009

Hi deepstop thanks for the message, much appreciated.

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4. Matt - August 5, 2009

Is the pressure at all dependent on temperature as well as depth? It seems to me that the density of water may change with temperature and so the weight of water might change and therefore the pressure. The reason I ask is because I have an instrument in fresh water that measures pressure and the depth of water. When I try to use conversions to calculate the depth based on the measured pressure my number is never really correct.

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5. deepstop - August 5, 2009

Hi Matt,

Thanks for your question. The density of water changes with temperature, but not by very much. In normal diving, say from 4C to 30C, the density differs by less than 1/2 of a percent, so the effect on depth measurement is going to be tiny, less than 6 inches at recreational depths.

Chris

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6. mark - October 14, 2009

How did you get 1 bar = 10.0803 metres of sea water?

According to Calchemy and hand calculations (assuming 1 cc sea water = 1.025 gm), 1 bar = 9.94845 metres sea water.

I used, in Calchemy:
Expression: 1 bar
Result Unit: m; dens_sea_water; grav

BTW, thanks for the Calchemy link. Excellent conversion calculator.

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deepstop - October 14, 2009

I didn’t. I got 1 atmosphere is 10.0803 metres of sea water. A bar is slightly different from a standard atmosphere.
So if you use the following in Calchemy you’ll get the same result that I did. For diving purposes both are close enough to 10 metres not to matter, of course.

Expression: 1 atm
Result Unit: m; dens_sea_water; grav

Thanks, though. You had me thinking for a while, and it was a good refresher for me on Calchemy. It’s a really cool conversion program once you get used to it, but it’s not for those with feeble math skills.

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7. mark - October 14, 2009

In the last section of your discussion, “So to answer the questions”, second item, you state 1 bar = 10.0803 .
It should read 1 atm is 10.0803 m sea water and 1 meter of sea water is .0992037 atm.

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8. deepstop - October 14, 2009

You’re absolutely right. I was looking at a different section. I’ll correct the article and thanks for pointing it out.

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9. Anabella - December 7, 2009

I have a question. I am trying to find the equation used to determine the equivalent depth. I have a container of water that is measured to be x degrees C. I heat up a device 27C higher than the water temperature for 2 hours and then submerge it into the water container a depth of 1 meter. According to the information I have, the equivalent depth is 72 inches or 1.82 meters. How do I find out this equivalent depth? Thanks!

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deepstop - December 8, 2009

Anabella. I’m not clear on what you’re asking. In diving there’s equivalent air depth for Nitrox and equivalent narcotic depth for Trimix & Heliox (& more), but neither have anything to do with temperature. Does your question pertain to diving or something else? Equivalent Depth has a variety of meanings depending on the context.
Chris

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10. david williams - February 9, 2010

mm Mercury are not obsolete; they are used thousands of times daily to measure blood pressure in medicine all around the world

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deepstop - February 22, 2010

Good point David, although some fields hang on to archaic measurements while the rest of the world moves on. The more conservative they are, the longer it goes. Aviation, for instance, still uses inches of Mercury for atmospheric pressure, and feet for altitude, even though Canada has supposedly been metric for decades.

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11. L.Shaw - September 9, 2010

hi,
my daughter loves snorkeling and is off to do a scuba diving internship next year in Greece. She is a bit slow with maths and calculations, so I said it would be best if she started practicing diving formulas before she goes off next year.
Do have any suggestions on what or where to look.
Thanks a lot
Larry

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Chris Sullivan - September 13, 2010

We get many math-challenged people in the shop. We also occasionally get 10-13 year-olds. They all seem to make it through. While some of the math in diving science is university-level, most is simple algebra and arithmetic, the x=y/z kind of stuff. If she plans to go through to divemaster or instructor, the she could read an open-water diver manual, a nitrox manual, and the PADI diving encyclopedia, or the equivalent for the agency with which she plans to do her training.

Cheers,
Chris

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