Surface consumption rate = Depth consumption rate / absolute pressure at depth, or SCR = DCR PD(ata) This is actually a special case of a more general formula that looks more like an ordinary gas law formula. We are, after all, dealing with a pressure vs. density problem, and you will recall that the pressure-density relationship was a corollary to Boyle’s law. The more general formula is: CR1 = CR2 P1 P2 where CR is the gas consumption rate and P is the absolute pressure at each of two ambient pressures. In calculating a surface consumption rate, the surface ambient pressure happens to be “1 ata.” Your initial answers will probably be in bars per minute or psi per minute because your submersible pressure gauge tells you gas pressure, not gas volume. Pressure units per minute are perfectly valid and can be manipulated and used to determine how long your air supply will last at depth, but only as long as you continue to use a like scuba cylinder. Surface consumption rates expressed in pressure units per minute are not transferable across unlike cylinders because variant cylinder types deliver different volumes of gas per pressure unit. In cylinders marked to usual international standards, for example, a 10 liter/200 bar cylinder contains 10 L per bar, while a 12 liter/232 bar cylinder has 12 L per bar. More notably, in cylinders marked to U.S. Department of Transportation standards, a 95 ft3/2,640 psi steel cylinder holds 3.9 ft3 per 100 psi, while an 80 ft3/3,000 psi aluminum cylinder has only 2.67 ft3 per 100 psi, and a 50 ft3/3,000 psi aluminum cylinder has 1.67 ft3 per 100 psi. Converting your SCR in pressure units per minute to an SCR in volume per minute (a surface RMV) gives you a number that you can easily use with any cylinder to determine the duration of your air at depth. Your surface RMV can always be converted to an SCR in pressure units per minute for any other cylinder. Sample problems: SI/metric A diver breathes 40 bars from a 12.2 L/232 bar cylinder in 10 minutes at a constant depth of 15 msw. What is the diver’s surface RMV in liters per minute? What would be the duration of this cylinder on a dive to 30 msw, assuming the diver plans to begin the ascent with 50 bars as a reserve pressure? First establish the diver’s air consumption rate at depth (DCR) and the absolute pressure at depth: DCR = 40 bars / 10 minutes = 4 bars per minute Pdepth = (15 msw x 0.1 atm/msw) + 1 atm = 2.5 ata Then determine the surface air consumption rate: SCR = DCR = 4 bars / minute = 1.6 bars/minute PD(ata) 2.5 ata The cylinder’s charged volume to charged pressure ratio is used to determine the diver’s SCR in liters per minute (Lpm). In a cylinder marked with international specifications, this ratio of liters per bar happens to be numerically the same as the water capacity of the cylinder. SCRLpm = 1.6 bars/min x 12.2 L/bar = 19.5 Lpm The diver should note an SCR of 19.5 or 20 Lpm in his or her logbook for future reference. How long will the diver be able to dive at a depth of 30 msw? Since we are using the same cylinder with which we made the original measurement, we can solve the problem using the diver’s SCR in bars per minute. First determine the ambient pressure at 30 msw: PD = (30 msw x 1 atm/10 msw) + 1 atm = 4 ata The diver’s DCR can be found using: CR1 = CR2 , or P1 P2 1.6 bars/minute = DCR 1 ata 4 ata DCR = 1.6 bars/min x 4 ata = 6.4 bars/min 1 ata Chapter 3- Diving Physics Diving Physics 93
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