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If you think diving physics is hard… March 5, 2009

Posted by Chris Sullivan in Training.
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When studying the math behind the partial pressure of gases, we use Dalton’s law which states that the total pressure of a mixed gas is equal to the sum of the partial pressures of the component gases. While this works pretty well for mixing diving gases, the “law” is not the whole truth. As the pressure goes up, the law breaks down due to interaction between the gas molecules, and a more accurate description of what’s going on is described by Van Der Waal’s equations. These equations are sometimes used when mixing helium as even at 3000 PSI or so, the prediction using Dalton’s law is significantly different from the truth. In practice, Van Der Waal’s may or may not be used, as other factors, like the increase in cylinder temperature during filling are equally confusing, and gas mixers develop rules of thumb to determine how much of each gas to add to arrive at a particular mix once everything cools down.

Similarly, we learn that the pressure of sea water increases by 1 atmosphere every 33 feet, or 10 metres. Many of us know that these numbers are rounded, and even the definition of an atmosphere varies between applications (aviation, weather forecasting, etc.). Compounding this, the density of sea water (and thus its pressure) vary based on salinity, temperature, depth and even latitude. Divers ignore all of these factors except for the salinity difference between fresh and salt water. Sonar engineers, though, care about such matters as the accuracy of sonar is very dependent on understanding these subtle differences.

Likewise the speed of sound, which we learn is around 1,500 metres per second in water (1410 in fresh, 1550 in sea water), can vary even further in various combinations of salinity, temperature and pressure. This is extremely important when sonar tries to “see” through haloclines, thermoclines and other underwater phenomena.

We also treat water as incompressible. This is not quite true, but close enough for almost all practical purposes. Water is very slightly compressible. However even at 400 bar the volume only decreases by 1.8%. So for diving we can go on assuming that it’s incompressible for practical purposes, but if your diving instructor contends that water isn’t compressible, you can confidently but respectfully disagree.

As we try to look at increasingly subtle properties of the liquid medium in which we dive, the more we complicated the mathematics gets. Fortunately for us divers, knowing how to apply a few basic laws suffices for almost anything we need to do.

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