1 atm = ?? Fsw

[sam1]

I know that standard practice is 1 ATM = 33 fsw. However, I was informed recently that this is an approximation and the generally accepted conversion is 1 ATM = 32.7781 fsw (assuming a density of 1.025 kg/liter). I realize this difference is of no practical significance for diving, but I would like to understand better and I am at a loss to come up with 32.7781 given what I know about density and pressure.

Any help or links?

Thanks.

Steve

 

[ScubaSteve]

Sorry what I came up with was incorrect thus I deleted it

 

[muddiver]

The weight and density of water/sea water will very depending on the temperature of the water. Sea water off the west coast is realatively cold so it is denser than sea water in the south Pacific. Thus one has to wear more ballast (lead weight) to compensate for the denser water and increased buoyancy in the colder water off the west coast (assuming the same wet suit in both locations).

33 FSW = 1 ATM is an average used to simplefy caculations. The same thing is done in basic college chemistry and physics classes where one cubic foot of fresh water is considered to be 62.4 lbs for calculation.

Also remember that diving tables are an approximation based on imperical data and due to the difference in the physiology of each diver it is not exact. So a little fudge on water depth is not going to make a difference.

 

[redacted]

Ouch - brain hurts

1 ATM = 14.696 psi
1cu ft fw = 62.4 lb
density fw = 1
density sw = 1.027

1 cu in fw = 62.4/12^3 = .0361 lb per cu inch

14.696 psi / .0361 p cu in = 407 inches = 33.9 ft (fw)

33.9 ffw / 1.027 = 33.0 fsw

 

[bleeb]

FWIW, for 1.025 kg/litre, I get 33.094 fsw:
(101325 Pa/atm) / [(1.025e-3 kg/cm3) * (9.8 m/s2) / (1e-4 cm2)] / (2.54 cm/") / (12"/')

Working in reverse, for 32.7781 fsw = 1.035 kg/litre, which is slightly high, but not unheard of. From Wikipedia (Seawater), typical surface density is 1.020 to 1.029 kg/litre. However, the Dead Sea has a nominal surface density of 1.24 kg/litre.

 

[Blackwood]

I know that standard practice is 1 ATM = 33 fsw. However, I was informed recently that this is an approximation and the generally accepted conversion is 1 ATM = 32.7781 fsw (assuming a density of 1.025 kg/liter). I realize this difference is of no practical significance for diving, but I would like to understand better and I am at a loss to come up with 32.7781 given what I know about density and pressure.
Steve

I get 33 feet using 1.025kg/L

Using 32.7781 feet, I back out a density of 1.034kg/L.

As muddiver suggested, IT ALL DEPENDS ON THE DENSITY.

Really what you are asking is: how tall must a 1in² column of water be to weigh 14.69595 pounds. Thinking of it in that terms makes writing the equations pretty simple.

In the units you've provided, the question becomes how tall must a 1m² column of water be to have a mass of 10332.27kg? (where did I get that? Well, 1ATM = 10332.27kg/1m²).

You listed density as 1.025kg/L, which is 1025kg/m³

10332.27/1025 = 10.08, 10.08m = 33.07feet

You listed 32.7781 fsw. 32.7781 feet = 9.9907m

10332.27/x = 9.9907, x = 1034.18

 

[Walter]

Actually, there's a difference between 33 fsw and 33 feet under the ocean. 33 fsw = 1 ATM by definition. Linear feet under the ocean is another story altogether. Linear feet will give the results these folk are coming up with playing with the numbers. Remember, fsw, like msw, is a measurement of pressure, not of distance.

 

[knotical]

I don’t have a clue from whence the 32.7781 fsw might have come, unless it was bad math.

The following is extracted from the Pressure Conversion Table in the back of the UHMS Journal:

1 bar = 32.646 fsw - Primary definition, assumes a density for seawater of 1.02480 at 4C
1 atm = 1.013250 bar
They combine these and get 1 atm = 33.08 fsw (rounded)

But for msw, they assume a different density of seawater
1 bar = 10.00 msw - Primary definition, assumes a density for seawater of 1.01972 at 4C

They cite the American Society for Testing and Materials.

To reinforce one of Walter’s points, the UHMS table also says: “These primary definitions for fsw and msw are arbitrary since the pressure below a column of seawater depends on the density of the water, which varies from point to point in the ocean.”

 

[uncleavi]

I thought one ATM was 0 FSW
My Bad!

 

[Blackwood]

I thought one ATM was 0 FSW
My Bad!

It is, on average.