http://scubadivingimages.com/if-a-scuba-diver-fills-his-lungs-to-full-capacity-of-5-3-l-when-30-m-below-the-surface-to-what-volume-would-h.html Scuba diving images, pics, photos, videos and more... Mon, 12 Sep 2011 17:45:10 +0000 hourly 1 http://wordpress.org/?v=3.2.1 http://scubadivingimages.com/if-a-scuba-diver-fills-his-lungs-to-full-capacity-of-5-3-l-when-30-m-below-the-surface-to-what-volume-would-h.html/comment-page-1/#comment-347 husoski Thu, 11 Feb 2010 15:17:09 +0000 http://scubadivingimages.com/if-a-scuba-diver-fills-his-lungs-to-full-capacity-of-5-3-l-when-30-m-below-the-surface-to-what-volume-would-h.html#comment-347 The pressure increases linearly as the diver descends, with the difference given by: ΔP = ρgy, where ρ ~= 10^3 kg/m^3 is the density of the water, g ~= 9.8 m/s^2 is the acceleration of gravity and y is the *depth* (positive axis pointing down) in meters, to give the pressure difference in Pa. If V0 is the volume of air at the surface (in m^3 for SI units), P0 = 1 atm is the surface air pressure (you convert to Pa), and V = 5.3 L = 5.3 * 10^-3 m^3 is the volume at a depth y = 30 m, then you have all you need to solve for V0 P0*V0 = P*V = (P0 + ΔP)V V0 = V * (1 + ΔP/P0) V0 = V * (1 + ρgy/P0) Plug numbers and compute. You should probably convert m^3 back to L for your answer. For a sanity check, I know from scuba lessons that 33 feet of fresh water is about 1 atmosphere. That's about 10m per atm, so at 30m the pressure should be 3 atm greater than the 1atm at the surface, so your computed result should be close to 4*5.3 L ~= 21 L The pressure increases linearly as the diver descends, with the difference given by:
ΔP = ρgy, where ρ ~= 10^3 kg/m^3 is the density of the water, g ~= 9.8 m/s^2 is the acceleration of gravity and y is the *depth* (positive axis pointing down) in meters, to give the pressure difference in Pa. If V0 is the volume of air at the surface (in m^3 for SI units), P0 = 1 atm is the surface air pressure (you convert to Pa), and V = 5.3 L = 5.3 * 10^-3 m^3 is the volume at a depth y = 30 m, then you have all you need to solve for V0
P0*V0 = P*V = (P0 + ΔP)V
V0 = V * (1 + ΔP/P0)
V0 = V * (1 + ρgy/P0)
Plug numbers and compute. You should probably convert m^3 back to L for your answer.
For a sanity check, I know from scuba lessons that 33 feet of fresh water is about 1 atmosphere. That’s about 10m per atm, so at 30m the pressure should be 3 atm greater than the 1atm at the surface, so your computed result should be close to 4*5.3 L ~= 21 L

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