How to calculate total air consumption along ascent?

[boulderjohn]

Please help solve this problem in University Calculus/Physics way

 

[loosenit2]

SAC (Surface Air Consumption) vs RMV (Respiratory Minute Volume) is the same thing: volume of gas consumed at 1bar/ata

Both are volumes of gas in litres/cubits?

not generally. Sac is generally defined as psi/min whereas rmv is generally vol/min. Rmv is more useful because it allows you to compare or transition between dissimilar tank sizes. My sac is different when using an al 80 then when using double Hp 100s but my rmv remains the same

 

[Wibble]

Psi/min is meaningless, you breathe a volume of gas and metabolise a volume of oxygen. A 3 litre rebreather cylinder compared with a 12 litre twinset which has 8 times the volume

Is RMV the existing medical term?

 

[Centrals]

Assume my RMV is 15L/min on the surface, 30L/min at 10m.
If I ascent from 10m depth to surface, ascend rate is steady 10m/min,
how much air will I consume??

If my SAC is not constant, and my ascent rate is not constant,
how could I calculate my air consumption.

Please help solve this problem in University Calculus/Physics way,
my calculus skills are rusted but if you give me a hint, I might recall the memory....
thank you.

If the SAC and ascent rate is NOT constant then there is absolutely no chance for an definitive answer.
How about time you spend on various depth?
How many unknowns you have there?

The easiest, quickest and simplest way is to use the RMV/SAC at 10m(15L/min x2) as a start.
Multiply the 30L/min by the total time, including safety stop, required to surface.

 

[Angelo Farina]

Assume my RMV is 15L/min on the surface, 30L/min at 10m.
If I ascent from 10m depth to surface, ascend rate is steady 10m/min,
how much air will I consume??

If my SAC is not constant, and my ascent rate is not constant,
how could I calculate my air consumption.

Please help solve this problem in University Calculus/Physics way,
my calculus skills are rusted but if you give me a hint, I might recall the memory....
thank you.

Your instantaneous gas consumption rate, Vdot, in normal-liter/minute, is given by the following function of depth d (in meters):
Vdot = 15*(d/10+1).
Depth is ranging form 10 meters to 0, in one minute. So the instantaneous depth d will be a function of time t (in minutes):
d = 10 * (1-t).
We replace d in the previous formula, getting:
Vdot =15*[10*(1-t)/10+1]
Vdot =15*(2-t)
Now you integrate the instantaneous gas consumption rate Vdot over time:
V = integral from 0 to 1 minute of Vdot*dt
Doing the indefinite integral you get:
V = 15*(2*t - t^2/2)
as t ranges from 0 to 1 minute, you get:
V = 15*(2-1/2) = 15*1.5 = 22.5 liters

 

[Centrals]

To have any real meaning to apply RAV/SAC in this calculation you need to know the breathing cycle of that diver per min.
So if the diver needs 15 cycles then one breath = 1L

From 10m to the top in 15 breath at 1L per breath with pressure adjustment will give you the answer.

 

[dmaziuk]

...
Doing the indefinite integral you get:
V = 15*(2*t - t^2/2)
as t ranges from 0 to 1 minute, you get:
V = 15*(2-1/2) = 15*1.5 = 22.5 liters

Or you could short-circuit it as (30 + 15)/2 = 45/2 = 22.5
Figuring out why that works out is left as an exercise to the reader.

 

[Centrals]

If the diver requires to breath 10 times over 1m ascent increment from 10m to the top.
1.5L per breath on the surface.
10m = 3L
9m = 1.9 x 1.5 = 2.85L
8m = 2.7L
7m = 2.55L
6m = 2.4L
5m = 2.25L
4m = 2.1L
3m = 1.95L
2m = 1.8L
1m = 1.65L
Total sum = 23.25L

 

[Wibble]

We need the answer to 16 decimal places for complete irrelevance.

 

[Centrals]

If the diver took one breath at 10m and another one 30sec later at 5m before reaching the surface after exactly 1 min.