the density is directly proportional to the pressure. Expressed mathematically: P1 = P2 D1 D2 where P and D are the absolute pressure and density for the two sets of conditions. Boyle’s law can be illustrated using cylinder capacities: SI/metric A scuba cylinder with an internal volume (water capacity) of 12.2 liters has a service pressure of 232 bars. What is the air capacity of the fully charged cylinder? The volume of air is a simple application of Boyle’s law. The fully charged cylinder pressure is a “gauge pressure.” Since we should use absolute pressure, the absolute pressure of the fully charged cylinder is 233 bars (232 + 1). At that pressure, the air is compressed into a volume of 12.2 liters. To determine what the volume of this air will be if it is allowed to expand to a normal atmospheric pressure of 1 bar, we start with the formula for Boyle’s law: P1V1 = P2V2 Substituting the known quantities: 233 bars x 12.2 L = 1 bar x V2 and V2 = 2,830.4 L Note: In practice, bars and atmospheres of pressure are often used interchangeably, as was done here, although there is a difference of about one percent. If you wish to solve the problem using true atmospheres of pressure, apply the conversion: one atmosphere = 1.103 bars. Of course, if you intend to be that exact, remember also that there will still be one atmosphere (12.2 liters) of air remaining in the cylinder when it is “empty.” U.S./Imperial What is the actual internal volume (water capacity) of an aluminum 80 cubic foot cylinder with a service pressure of 3,000 psig? This is similar to the SI/metric problem above, except that we are finding a volume. The fully charged pressure is 3,014.7 psia, at which pressure 80 cubic feet of air have been compressed into whatever is the internal volume of the cylinder. Applying Boyle’s law: Chapter 3- Diving Physics P1V1 = P2V2 3,014.7 psi x V1 = 14.7 psi x 80 ft3 V1 = 0.39 ft3 (or 674 in3) When a scuba air compressor is used to fill your cylinder or it is used to fill a cascade of storage cylinders, it is a direct application of Boyle’s law. Boyle’s law is presented in every entry-level scuba course, although it may not be called by name. It could have been called pressure / volume relationships, and you were presented with a diagram of an inverted bucket or an air-filled balloon being taken down and up in the water column. Squeezes, equalization of air spaces, reverse blocks, and lung rupture injuries are all examples of Boyle’s law in action. Air consumption problems (or gas management problems) and deliverable volume of air from a cylinder at depth also use Boyle’s law. You now have tools that make it possible to solve many problems involving Boyle’s law. Using what you have learned in the discussion of pressure, you are able to determine the absolute pressure (in any of several measurement units) at any depth in the ocean or in low altitude lakes. Using this pressure information and Boyle’s law you can relate air volumes in a flexible container to any water depth. You can discover the volume of deliverable air in a scuba cylinder at various depths. You can compare air consumption at depths or determine personal air consumption rates using data you have established on your dives. Using the high altitude atmospheric pressure tables found elsewhere in this book, you can even make similar determinations for altitude diving. Sample problems: SI/metric 1. You have determined that it will require 60 liters of air to raise an object from a depth of 23 meters in a (sea level) lake. How many liters of air will be required from your cylinder to supply this 60 liters at depth? First determine the absolute pressure at a depth of 23 mfw: Pa = (23 mfw x 0.097 atm/mfw) + 1 atm = 3.23 ata Diving Physics 87
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