Boyle’s Law is a theory on the effects of pressure upon a compressed gas, and although the name of the theory and it’s general application to SCUBA diving is very well known among divers all over the world, its’ actual parameters, I believe, has escaped many recreational divers today. There are many different formulas and theorems of physics and chemistry that diver’s understand basically, but the advanced concept behind many of these knowledge stems, seems to have been lost among divers. Understandably so, many recreational; and for that matter commercial and military divers; do not need, nor use the theorems and equations that govern many of the effects while operating about underwater. This is not laziness, the time required to teach and ensure comprehension would be silly to undertake unless you were an expert, or educator in the particular field. However, I feel that many of the theorems and equations that effect scuba diver’s underwater should be addressed and explained in a little more detail than what is normally explained. Either out of curiosity, or simply wanting to know the details behind why we as diver’s do the things we do to keep from getting DCS or expansion injuries, this should clarify things more for those who didn’t know, but wish they did…
Boyle’s Law has been discussed on this site in brief, and the basic concept is taught to open water students. Basically, Boyle’s Law theorized that any given mass of a gas was inversely proportional to the volume and pressure at any given temperature when confined. Water pressure and the volume of the body of water affect the confined compressed gas that SCUBA divers breath. The air that SCUBA divers breathe is a mix of oxygen and nitrogen, the same gas mix that is breathed by humans above water; only this air is highly compressed inside the cylinder, and breathed through high pressure hoses underwater where the effects of Boyle’s law makes the mass of the gas even smaller and more tightly packed within the cylinder. Here is an example:
I have a friend who drives a semi-truck for a living. He delivers chips and tortillas. These products are sealed into bags at near sea level. One of his deliveries is nearly 9,000 feet above sea level, when he offloads there, the bags appear to have ballooned in size. This is because at sea level the air that was trapped in the bag was at a lower altitude where atmospheric pressure is high, but as he went up in altitude to make his delivery, the atmospheric pressure is lower than at sea level, so the bags expanded, as the mass of the gas trapped inside the bags expanded.
The same happens underwater. The deeper a diver goes the smaller the given mass of a gas will get, which means that the diver breathing that gas will use it quicker at say 70 feet then he/she would at 10 feet, because the gas is more tightly compacted at 70 feet than it is at 10 feet.
There are several ways to write the equation that expresses this theory:
PiVi = PfVf
Pi = Initial Pressure Vi = Initial Volume Pf = Final Pressure Vf = Final Volume
This expression is the most common expression for use in SCUBA diving applications, and most divers have seen this in their open water certification classes. It allows the calculation for varying conditions, which most SCUBA find themselves in when diving. The original Law stated by Robert Boyle, and the ones that are commonly taught at University and secondary level education, is written thus:
PV = k
P = Pressure V = Volume k = Constant
So now we know the equation we will be using to determine the theorem’s application to recreational diving. A point of instruction: the initial and final units for the placed values must be the same; conversion can be done to determine the difference in units (i.e.: pounds to bar or cubic feet/inches to Pascals). Also let us de-sexy this equation and explain what it actually states: as pressure increases, volume decreases; and as volume increases, pressure decreases. There are calculators on the internet that will help you solve for one of the variables. Boyle’s Law equations should give you the other 3 variables, and only require the solving of one of the variables; remember that the units must be the same, convert after solving for the chosen variable. The most frustrating thing to do with this equation will be to determine which variables were taken at the same time and are therefore “paired”, and which is the variable which must be solved for. It seems complicated, and unless you’re a chemist or physicist, you’ll probably never use it. Just remember the basics, increasing pressure = decreasing volume, and increasing volume = decreasing pressure.
You now have a slightly more detailed grasp of the equation involving Boyle’s Law and how it affects you as a diver underwater. Coming Soon: Archimedes Principle…
Dive Safe, Dive Often