Diving Theory
Miscellaneous dive related physics can be found at this site Diving
Physics. It also includes u/w photography.
Archimedes' Principle explains the nature of buoyancy.
An object immersed in a liquid, either wholly
or partially, receives an up thrust equal to the weight of the
liquid displaced by the object.
Using Archimedes' Principle, the buoyancy of a submerged object can
be calculated by subtracting the weight of the submerged object from
the weight of the displaced liquid.
- If the total displacement, i.e., the weight of the displaced
liquid, is greater than the weight of the submerged object, the
buoyancy will be positive and the object will float.
- If the weight of the object is equal to that of the displaced
liquid, the buoyancy will be neutral and the object will remain
suspended in the liquid.
- If the weight of the submerged object is greater than that of
the displaced liquid, the buoyancy will be negative and the body
will sink.
The buoyant force of water is dependent on its density, that is, its
weight per unit volume. Sea water is more dense than fresh water, therefore
a diver in seawater will be more buoyant than in fresh water, hence
the need for a heavier weight belt when diving in the sea.
Lung capacity can have a significant effect on the buoyancy of a submerged
person. A diver with full lungs displaces a greater volume of
water and therefore is more buoyant than the same diver with deflated
lungs.
The behaviour of all gases is affected by three factors: the
temperature, pressure and volume of the gas. The relationships among
these three factors have been defined in what are called the Gas Laws.
The following:
are of special importance to the diver.
Boyle's Law states:
At constant temperature, the
volume of a gas varies inversely with absolute pressure, while
the density of a gas varies directly with absolute pressure.
For any gas at a constant temperature, Boyle's Law is:
-
|
PV |
|
= K |
| where |
|
P |
|
= absolute pressure |
|
V |
|
= volume |
|
K |
|
= constant. |
Boyle's Law is important to divers because it relates changes in pressure
i.e., depth, to changes in the volume of a gas and defines the relationship
between pressure and volume in breathing gas supplies.
| Suppose you had a balloon containing 4 litres of air at the surface
of the water. This balloon is under 1 Bar of pressure. If we take
the balloon underwater to a depth of 10 Metres, it is now under
2 Bar of pressure. Boyle's Law then tells us that since we have
twice the pressure, the volume of the balloon will be decreased
to one half. It follows then, that taking the balloon to 20 Metres,
the pressure would compress the balloon to one third its original
size, 30 Metres would make it 1/4, etc.
If we bring the balloon in the previous example back up to
the surface, it would increase in size due to the lessening
pressure until it reached the surface and returned to its original
size, 4 litre. This is because the air in the balloon is compressed
from the pressure when submerged, but returns to its normal
size and pressure when it returns to the surface. |
Relationship between pressure and volume
| Depth |
Volume |
Volume
(litres) |
Density |
| Surface |
1 |
4 |
1 |
| 10 Meters |
1/2 |
2 |
2 |
| 20 Meters |
1/3 |
1.3 |
3 |
| 30 Meters |
1/4 |
1 |
4 |
| 40 Meters |
1/5 |
0.8 |
5 |
|
Along with the volume of air in the balloon, the surrounding pressure
will affect the density of the air as well. Density, simply stated,
is how close the air molecules are packed together. The air in the
balloon or container at the surface is at its standard density, but
when we descend to the 10 Metres where its volume is reduced to one
half, the density has doubled. At 20 Metres, the density has tripled.
This is because the pressure has pushed the air molecules closer together.
The reverse also happens, suppose we inflate a balloon at 30 Metres We
know the air at this depth is 4 times denser than at the surface. As
the balloon ascends, the external pressure lessens and the balloon
will expand, eventually bursting.
In these examples of Boyle's Law, the temperature of the gas was considered
a constant value. However, 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 deep water is often
significantly different from the temperature of the air at the surface. The
gas law that describes the physical effects of temperature on pressure and
volume is Charles' Law.
Charles' Law states:
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.
Stated mathematically:
-
|
P1 |
= |
T1 |
(volume constant) |
|
¯¯¯¯
P2 |
¯¯¯¯
T2 |
|
V1 |
= |
T1 |
(pressure constant) |
|
¯¯¯¯
V2 |
¯¯¯¯
T2 |
| where |
|
P1 = |
initial pressure (absolute) |
|
P2 = |
final pressure (absolute) |
|
T1 = |
initial pressure (absolute) |
|
T2 = |
final pressure (absolute) |
Henry's Law states:
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.
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 water is opened. Opening the container
releases the pressure suddenly, causing the gases in solution to come
out of the solution and to form bubbles. This is similar to what happens
in a diver's tissues if the prescribed ascent rate is exceeded.
Dalton's Law states:
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.
In a gas mixture, the portion of the total pressure contributed by
a single gas is called the partial pressure of that gas. Stated mathematically:
-
|
PTotal |
= Ppl + Pp2 + Ppn |
| where |
|
PTotal |
= total pressure of that gas |
|
Pp1 |
= partial pressure of gas component 1 |
|
Pp2 |
= partial pressure of gas component 2 |
|
Ppn |
= partial pressure of other gas components. |
-
If a container (at 1 Bar) were filled with oxygen alone,
the partial pressure of the oxygen would be 1 Bar. If the same container
were filled with air, the partial pressures of each of the gases comprising
air would contribute to the total pressure, as shown in the following
table:
Percent of Component × Total Pressure (Absolute)
= Partial Pressure
| Gas |
Percent of
component |
Partial Pressure
(Bar) |
| Nitrogen |
78.0 |
0.78 |
| Oxygen |
21.00 |
.21 |
| Others |
.1 |
1 |
| Total |
100.00 |
1.0000 |
When diving at a depth of 40 metres (5 Bar) you multiply the partial
pressures by 5 and calculate the partial pressures at that depth
| Gas |
Percent of
component |
Partial Pressure
at 1 Bar |
Bar |
Partial Pressure
at 5 Bar
(40 meters) |
| Nitrogen |
78.0 |
0.78 |
x 5 |
3.9 |
| Oxygen |
21.00 |
.21 |
x 5 |
1.05 |
| Others |
.1 |
1 |
x 5 |
5 |
| Total |
100.00 |
1.0000 |
x 5 |
|
