2007/12/13

Diving 107: Scuba Diving Underwater Physics

The original page can be found here: http://quashnick.net/scuba/university/diving107.html

33.03 feet sea water = 1 Atmosphere pressure = 14.7 psi
34.03 feet fresh water = 1 Atmosphere pressure = 14.7 psi

$\blue \Huge PV=nRT$
$\blue \Huge P=\frac{T}{V}$ or $\blue \Huge V=\frac{T}{P}$ or $\blue \Huge T=PV$
$P$ = pressure in psi
$V$ = volume in ft3
$n$ = moles of gas (1 mole = 6.022 x 1023 atoms)
$R$ = gas constant 10.7316 psi ft3 / lbmol °R
$T$ = temperature in Rankine (°R) = °F + 459.6

$\blue \Huge P_{guage} = \frac{(14.7_{psi})(depth_{sea\ water})}{33.03_{feet\ sea\ water}}$

$\blue \Huge P_{absolute} = 14.7 + \frac{(14.7_{psi})(depth_{sea\ water})}{33.03_{feet\ sea\ water}}$

Sea water weighs 64.58 lbs/ft3 or 8.6213 lbs/gallon Specific gravity = 1.035
Fresh water weighs 62.4 lbs/ft3 or 8.3303 lbs/gallon Specific gravity = 1.000

Bouyant Force (Archemedes Principle):
$\blue \Huge F_{buoyant} = W_{in\ air} - W_{in\ water} = dgv$
$F_{buoyant}$ is the buoyant force
$W_{in\ air}$ also known as dry weight
$W_{in\ water}$ is weight in water [remember that negative numbers are positively buoyant]
$d$ is the density of the liquid [salt water is 64.58 lbs/ft3 and fresh water is 62.4 lbs/ft3]
$g$ is the gravitational acceleration 32.37 ft/sec2 (normally written as 1 in the equation i.e. 1 gravity)
$v$ is the volume of the object in cubic feet (ft3)

For calculating the tissue depth for Haldanean decompression M-values, an easy to remember formula is:
$\blue \Huge D_{final}=[1-2^{-(t/h)}] \cdot D_{actual}$
$D_{final}$ = the final tissue depth
$D_{actual}$ = actual dive depth
$t$ = time underwater
$h$ = halftime compartment

I have written a function for the R language which calculates the EAD, PO2 and working depth for any FO2 breathing gas blend.
You can find my simple function here: http://quashnick.net/scuba/university/Nitrox_for_R.txt
A better option is to use the R-Project (http://r-project.org) Package called scuba. You can find it here: http://cran.r-project.org/src/contrib/Descriptions/scuba.html