The behavior of all gases
is affected by three factors: the temperature of the gas, the pressure
of the gas, and the volume of the gas. The relationships among these three
factors have been defined in what are called the Gas Laws. Five of these,
Dalton's Law, Boyle's Law, Charles' Law, Henry's Law, and the General Gas
Law, are of special importance to the diver.
Let P, V, and
T
respectively denote absolute pressure, volume, and absolute temperature
of the gas. Subscript indexes ( 1, 2, etc. )
are used to distinguish values at different moments such as initial, final,
etc. Other special symbols are defined further.
Dalton's Law
The
total pressure exerted by a mixture of gases is equal to the sum of the
pressures that would be exerted by each of the gases if it alone were present
and occupied the total volume.
PTotal=
Ppl+ Pp2+
... + Ppn
Pp denotes the partial pressure
of the particular gas component
In a gas mixture, the portion
of the total pressure contributed by a single gas is called the partial
pressure of that gas.
Boyle's Law
At
constant temperature, the volume of a gas varies inversely with absolute
pressure, while the density of a gas varies directly with absolute pressure.
P1V1
=
P2V2
= constant
at constant T
Boyle's Law is important to
divers because it relates changes in the volume of a gas to changes in
pressure (depth) and defines the relationship between pressure and volume
in breathing gas supplies.
Charles' Law
At
a constant pressure, the volume of a gas varies directly with absolute
temperature. For any gas at a constant volume, the pressure of a gas varies
directly with absolute temperature.
| P1 |
= |
T1 |
|
V1 |
= |
T1 |
¯¯¯¯
P2 |
¯¯¯¯
T2 |
|
¯¯¯¯
V2 |
¯¯¯¯
T2 |
| at constant
volume |
|
at constant
pressure |
Temperature significantly affects
the pressure and volume of a gas; it is therefore essential to have a method
of including this effect in calculations of pressure and volume. To a diver,
knowing the effect of temperature is essential, because the temperature
of the water deep in the oceans or in lakes is often significantly different
from the temperature of the air at the surface.
Henry's Law
The
amount of any given gas that will dissolve in a liquid at a given temperature
is a function of the partial pressure of the gas that is in contact with
the liquid and the solubility coefficient of the gas in the particular
liquid.
_Vg_
= 
P1
VL
.
Vg volume
of the gas dissolved at STP (standard T and P)
VL
volume of the liquid
Bunson solubility coefficient at specified temperatures
P1
partial pressure in atmospheres of the gas above the liquid
This law simply states that,
because a large percentage of the human body is water, more gas will dissolve
into the blood and body tissues as depth increases, until the point of
saturation is reached. Depending on the gas, saturation takes from 8 to
24 hours or longer. As long as the pressure is maintained, and regardless
of the quantity of gas that has dissolved into the diver's tissues, the
gas will remain in solution.
A simple example of the way
in which Henry's Law works can be seen when a bottle of carbonated soda
is opened. Opening the container releases the pressure suddenly, causing
the gases in solution to come out of solution and to form bubbles. This
is similar to what happens in a diver's tissues if the prescribed ascent
rate is exceeded. The significance of this phenomenon
for divers is developed fully in the discussion of decompression.
The General Gas Law
Boyle's and Charles' laws
can be conveniently combined into what is known as the General Gas Law,
expressed mathematically as follows:
| P1V1 |
= |
P2V2 |
¯¯¯¯
T1 |
¯¯¯¯
T2 |
Gas Flow
There are occasions when
it is desirable to determine the rate at which gas flows through orifices,
hoses, and other limiting enclosures. This can be approximated for a given
gas by employing Poiseuille's equation for gases, which is expressed mathematically
as:
V
gas flow, in cm3× sec-1
![[Delta Character]](media/34delta.gif)
P
pressure gradient between 2 ends of tube, in dynes × cm-1
r
radius of tube, in cm
L
length of tube, in cm
viscosity, in poise
This equation can be used only
in relatively simple systems that involve laminar flow and do not include
a number of valves or restrictions. For practical applications, the diver
should note that, as resistance increases, flow decreases in direct proportion.
Therefore, if the length of a line is increased, the pressure must be increased
to maintain the same flow. Nomograms for flow resistance through diving
hoses can be found in Volume 2 of the US Navy Diving Manual (1987).
