CHAPTER 2 — Underwater Physics 2-1
CHAPTER 2
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2-1
INTRODUCTION
2-1.1
Purpose.
This chapter describes the laws of physics as they affect humans in the
water.
2-1.2
Scope.
A thorough understanding of the principles outlined in this chapter is
essential to safe and effective diving performance.
2-2
PHYSICS
Humans readily function within the narrow atmospheric envelope present at the
earth’s surface and are seldom concerned with survival requirements. Outside the
boundaries of the envelope, the environment is hostile and our existence depends
on our ability to counteract threatening forces. To function safely, divers must
understand the characteristics of the subsea environment and the techniques that
can be used to modify its effects. To accomplish this, a diver must have a basic
knowledge of physics—the science of matter and energy. Of particular importance
to a diver are the behavior of gases, the principles of buoyancy, and the properties
of heat, light, and sound.
2-3
MATTER
Matter is anything that occupies space and has mass, and is the building block of
the physical world. Energy is required to cause matter to change course or speed.
The diver, the divers air supply, everything that supports him or her, and the
surrounding environment is composed of matter.
2-3.1
Elements.
An element is the simplest form of matter that exhibits distinct physical
and chemical properties. An element cannot be broken down by chemical means
into other, more basic forms. Scientists have identified more than 100 elements in
the physical universe. Elements combine to form the more than four million
substances known to man.
2-3.2
Atoms.
The atom is the smallest particle of matter that carries the specific proper-
ties of an element. Atoms are made up of electrically charged particles known as
protons, neutrons, and electrons. Protons have a positive charge, neutrons have a
neutral charge, and electrons have a negative charge.
2-3.3
Molecules.
Molecules are formed when atoms group together (Figure 2-1). Mole-
cules usually exhibit properties different from any of the contributing atoms. For
example, when two hydrogen atoms combine with one oxygen atom, a new
substance—water—is formed. Some molecules are active and try to combine with
many of the other molecules that surround them. Other molecules are inert and do
not naturally combine with other substances. The presence of inert elements in
2-2 U.S. Navy Diving Manual—Volume 1
breathing mixtures is important when calculating a divers decompression
obligations.
2-3.4
The Three States of Matter.
Matter can exist in one of three natural states: solid,
liquid, or gas (Figure 2-2). A solid has a definite size and shape. A liquid has a
definite volume, but takes the shape of the container. Gas has neither definite
shape nor volume, but will expand to fill a container. Gases and liquids are collec-
tively referred to as fluids.
The physical state of a substance depends primarily upon temperature and
partially upon pressure. A solid is the coolest of the three states, with its molecules
rigidly aligned in fixed patterns. The molecules move, but their motion is like a
constant vibration. As heat is added the molecules increase their motion, slip apart
from each other and move around; the solid becomes a liquid. A few of the mole-
cules will spontaneously leave the surface of the liquid and become a gas. When
the substance reaches its boiling point, the molecules are moving very rapidly in
all directions and the liquid is quickly transformed into a gas. Lowering the
temperature reverses the sequence. As the gas molecules cool, their motion is
reduced and the gas condenses into a liquid. As the temperature continues to fall,
the liquid reaches the freezing point and transforms to a solid state.
2-4
MEASUREMENT
Physics relies heavily upon standards of comparison of one state of matter or
energy to another. To apply the principles of physics, divers must be able to
employ a variety of units of measurement.
2-4.1
Measurement Systems.
Two systems of measurement are widely used
throughout the world. Although the English System is commonly used in the
United States, the most common system of measurement in the world is the Inter-
national System of Units. The International System of Units, or SI system, is a
modernized metric system designated in 1960 by the General Conference on
Weights and Measures. The SI system is decimal based with all its units related, so
that it is not necessary to use calculations to change from one unit to another. The
Figure 2-1.
Molecules. Two similar atoms
combine to form an oxygen molecule while the
atoms of two different elements, hydrogen and
oxygen, combine to form a water molecule.
Figure 2-2.
The Three States of Matter.
CHAPTER 2 — Underwater Physics 2-3
SI system changes one of its units of measurement to another by moving the
decimal point, rather than by the lengthy calculations necessary in the English
System. Because measurements are often reported in units of the English system,
it is important to be able to convert them to SI units. Measurements can be
converted from one system to another by using the conversion factors in Tables
2-10 through 2-18.
2-4.2
Temperature Measurements.
While the English System of weights and measures
uses the Fahrenheit (°F) temperature scale, the Celsius (°C) scale is the one most
commonly used in scientific work. Both scales are based upon the freezing and
boiling points of water. The freezing point of water is 32°F or 0°C; the boiling
point of water is 212°F or 100°C. Temperature conversion formulas and charts are
found in Table 2-18.
Absolute temperature values are used
when employing the ideal gas laws.
The absolute temperature scales are
based upon absolute zero. Absolute
zero is the lowest temperature that
could possibly be reached at which all
molecular motion would cease (Figure
2-3).
2-4.2.1
Kelvin Scale.
One example of an abso-
lute temperature scale is the Kelvin
scale, which has the same size degrees
as the Celsius scale. The freezing point
of water is 273°K and boiling point of
water is 373°K. Use this formula to
convert from Celsius to absolute
temperature (Kelvin):
Kelvin (K) = °C + 273
2-4.2.2
Rankine Scale.
The Rankine scale is another absolute temperature scale, which
has the same size degrees as the Fahrenheit scale. The freezing point of water is
492°R and the boiling point of water is 672°R. Use this formula to convert from
Fahrenheit to absolute temperature (degrees Rankine, °R):
°R = °F + 460
2-4.3
Gas Measurements.
When measuring gas, actual cubic feet (acf) of a gas refers to
the quantity of a gas at ambient conditions. The most common unit of measure-
ment for gas in the United States is standard cubic feet (scf). Standard cubic feet
relates the quantity measurement of a gas under pressure to a specific condition.
The specific condition is a common basis for comparison. For air, the standard
cubic foot is measured at 60°F and 14.696 psia.
Figure 2-3.
Tempera
ture Scales.
Fahrenheit, Celsius, Kelvin,
and Rankine temperature scales
showing the freezing and boiling points of
2-4 U.S. Navy Diving Manual—Volume 1
2-5
ENERGY
Energy is the capacity to do work. The six basic types of energy are mechanical,
heat, light, chemical, electromagnetic, and nuclear, and may appear in a variety of
forms (Figure 2-4). Energy is a vast and complex aspect of physics beyond the
scope of this manual. Consequently, this chapter only covers a few aspects of light,
heat, and mechanical energy because of their unusual effects underwater and their
impact on diving.
Figure 2-4.
The Six Form of Energy.
CHAPTER 2 — Underwater Physics 2-5
2-5.1
Conservation of Energy.
The Law of the Conservation of Energy, formulated in
the 1840s, states that energy in the universe can neither be created nor destroyed.
Energy can be changed, however, from one form to another.
2-5.2
Classifications of Energy.
The two general classifications of energy are potential
energy and kinetic energy. Potential energy is due to position. An automobile
parked on a hill with its brakes set possesses potential energy. Kinetic energy is
energy of motion. An automobile rolling on a flat road possesses kinetic energy
while it is moving.
2-6
LIGHT ENERGY IN DIVING
Refraction, turbidity of the water, salinity, and pollution all contribute to the
distance, size, shape, and color perception of underwater objects. Divers must
understand the factors affecting underwater visual perception, and must realize
that distance perception is very likely to be inaccurate.
2-6.1
Refraction.
Light passing from an object
bends as it passes through the diver’s
faceplate and the air in his mask (Figure
2-5). This phenomenon is called refrac-
tion, and occurs because light travels
faster in air than in water. Although the
refraction that occurs between the water
and the air in the divers face mask
produces undesirable perceptual inaccu-
racies, air is essential for vision. When a
diver loses his face mask, his eyes are
immersed in water, which has about the
same refractive index as the eye. Conse-
quently, the light is not focused normally
and the diver’s vision is reduced to a level
that would be classified as legally blind
on the surface.
Refraction can make objects appear closer than they really are. A distant object
will appear to be approximately three-quarters of its actual distance. At greater
distances, the effects of refraction may be reversed, making objects appear farther
away than they actually are. Reduced brightness and contrast combine with refrac-
tion to affect visual distance relationships.
Refraction can also affect perception of size and shape. Generally, underwater
objects appear to be about 30 percent larger than they actually are. Refraction
effects are greater for objects off to the side in the field of view. This distortion
interferes with hand-eye coordination, and explains why grasping objects under-
water is sometimes difficult for a diver. Experience and training can help a diver
learn to compensate for the misinterpretation of size, distance, and shape caused
by refraction.
Figure 2-5.
Objects Underwater
Appear Closer.
2-6 U.S. Navy Diving Manual—Volume 1
2-6.2
Turbidity of Water.
Water turbidity can also profoundly influence underwater
vision and distance perception. The more turbid the water, the shorter the distance
at which the reversal from underestimation to overestimation occurs. For example,
in highly turbid water, the distance of objects at 3 or 4 feet may be overestimated;
in moderately turbid water, the change might occur at 20 to 25 feet and in very
clear water, objects as far away as 50 to 70 feet might appear closer than they actu-
ally are. Generally speaking, the closer the object, the more it will appear to be too
close, and the more turbid the water, the greater the tendency to see it as too far
away.
2-6.3
Diffusion.
Light scattering is intensified underwater. Light rays are diffused and
scattered by the water molecules and particulate matter. At times diffusion is
helpful because it scatters light into areas that otherwise would be in shadow or
have no illumination. Normally, however, diffusion interferes with vision and
underwater photography because the backscatter reduces the contrast between an
object and its background. The loss of contrast is the major reason why vision
underwater is so much more restricted than it is in air. Similar degrees of scat-
tering occur in air only in unusual conditions such as heavy fog or smoke.
2-6.4
Color Visibility.
Object size and distance are not the only characteristics distorted
underwater. A variety of factors may combine to alter a divers color perception.
Painting objects different colors is an obvious means of changing their visibility
by enhancing their contrast with the surroundings, or by camouflaging them to
merge with the background. Determining the most and least visible colors is much
more complicated underwater than in air.
Colors are filtered out of light as it enters the water and travels to depth. Red light
is filtered out at relatively shallow depths. Orange is filtered out next, followed by
yellow, green, and then blue. Water depth is not the only factor effecting the
filtering of colors. Salinity, turbidity, size of the particles suspended in the water,
and pollution all effect the color-filtering properties of water. Color changes vary
from one body of water to another, and become more pronounced as the amount of
water between the observer and the object increases.
The components of any underwater scene, such as weeds, rocks, and encrusting
animals, generally appear to be the same color as the depth or viewing range
increases. Objects become distinguishable only by differences in brightness and
not color. Contrast becomes the most important factor in visibility; even very large
objects may be undetectable if their brightness is similar to that of the background.
2-7
MECHANICAL ENERGY IN DIVING
Mechanical energy mostly affects divers in the form of sound. Sound is a periodic
motion or pressure change transmitted through a gas, a liquid, or a solid. Because
liquid is denser than gas, more energy is required to disturb its equilibrium. Once
this disturbance takes place, sound travels farther and faster in the denser medium.
Several aspects of sound underwater are of interest to the working diver.
CHAPTER 2 — Underwater Physics 2-7
2-7.1
Water Temperature and Sound.
In any body of water, there may be two or more
distinct contiguous layers of water at different temperatures; these layers are
known as thermoclines. The colder a layer of water, the greater its density. As the
difference in density between layers increases, the sound energy transmitted
between them decreases. This means that a sound heard 50 meters from its source
within one layer may be inaudible a few meters from its source if the diver is in
another layer.
2-7.2
Water Depth and Sound.
In shallow water or in enclosed spaces, reflections and
reverberations from the air/water and object/water interfaces produce anomalies in
the sound field, such as echoes, dead spots, and sound nodes. When swimming in
shallow water, among coral heads, or in enclosed spaces, a diver can expect peri-
odic losses in acoustic communication signals and disruption of acoustic
navigation beacons. The problem becomes more pronounced as the frequency of
the signal increases.
Because sound travels so quickly underwater (4,921 feet per second), human ears
cannot detect the difference in time of arrival of a sound between each ear. Conse-
quently, a diver cannot always locate the direction of a sound source. This
disadvantage can have serious consequences for a diver or swimmer trying to
locate an object or a source of danger, such as a powerboat.
2-7.2.1
Diver Work and Noise.
Open-circuit scuba affects sound reception by producing
high noise levels at the diver’s head and by creating a screen of bubbles that
reduces the effective sound pressure level (SPL). When several divers are working
in the same area, the noise and bubbles affect communication signals more for
some divers than for others, depending on the position of the divers in relation to
the communicator and to each other.
A neoprene wet suit is an effective barrier to sound above 1,000 Hz and it becomes
more of a barrier as frequency increases. This problem can be overcome by
exposing a small area of the head either by cutting holes at the ears of the suit or
by folding a small flap away from the surface.
2-7.2.2
Pressure Waves.
Sound is transmitted through water as a series of pressure
waves. High-intensity sound is transmitted by correspondingly high-intensity
pressure waves. A high-pressure wave transmitted from the water surrounding a
diver to the open spaces within the body (ears, sinuses, lungs) may increase the
pressure within these open spaces, causing injury. Underwater explosions and
sonar can create high-intensity sound or pressure waves. Low intensity sonar, such
as depth finders and fish finders, do not produce pressure waves intense enough to
endanger divers. However, anti-submarine sonar-equipped ships do pulse
dangerous, high-intensity pressure waves.
It is prudent to suspend diving operations if a high-powered sonar transponder is
being operated in the area. When using a diver-held pinger system, divers are
advised to wear the standard ¼-inch neoprene hood for ear protection. Experi-
ments have shown that such a hood offers adequate protection when the ultrasonic
pulses are of 4-millisecond duration, repeated once per second for acoustic source
2-8 U.S. Navy Diving Manual—Volume 1
levels up to 100 watts, at head-to-source distances as short as 0.5 feet (Pence and
Sparks, 1978).
2-7.3
Underwater Explosions.
An underwater explosion creates a series of waves that
are transmitted as hydraulic shock waves in the water, and as seismic waves in the
seabed. The hydraulic shock wave of an underwater explosion consists of an initial
wave followed by further pressure waves of diminishing intensity. The initial
high-intensity shock wave is the result of the violent creation and liberation of a
large volume of gas, in the form of a gas pocket, at high pressure and temperature.
Subsequent pressure waves are caused by rapid gas expansion in a non-compress-
ible environment, causing a sequence of contractions and expansions as the gas
pocket rises to the surface.
The initial high-intensity shock wave is the most dangerous; as it travels outward
from the source of the explosion, it loses its intensity. Less severe pressure waves
closely follow the initial shock wave. Considerable turbulence and movement of
the water in the area of the explosion are evident for an extended time after the
detonation.
2-7.3.1
Type of Explosive and Size of the Charge.
Some explosives have characteris-
tics of high brisance (shattering power in the immediate vicinity of the explosion)
with less power at long range, while the brisance of others is reduced to increase
their power over a greater area. Those with high brisance generally are used for
cutting or shattering purposes, while high-power, low-brisance explosives are
used in depth charges and sea mines where the target may not be in immediate
contact and the ability to inflict damage over a greater area is an advantage. The
high-brisance explosives create a high-level shock and pressure waves of short
duration over a limited area. Low brisance explosives create a less intense shock
and pressure waves of long duration over a greater area.
2-7.3.2
Characteristics of the Seabed.
Aside from the fact that rock or other bottom
debris may be propelled through the water or into the air with shallow-placed
charges, bottom conditions can affect an explosion’s pressure waves. A soft
bottom tends to dampen reflected shock and pressure waves, while a hard, rock
bottom may amplify the effect. Rock strata, ridges and other topographical
features of the seabed may affect the direction of the shock and pressure waves,
and may also produce secondary reflecting waves.
2-7.3.3
Location of the Explosive Charge.
Research has indicated that the magnitude of
shock and pressure waves generated from charges freely suspended in water is
considerably greater than that from charges placed in drill holes in rock or coral.
2-7.3.4
Water Depth.
At great depth, the shock and pressure waves are drawn out by the
greater water volume and are thus reduced in intensity. An explosion near the
surface is not weakened to the same degree.
2-7.3.5
Distance from the Explosion.
In general, the farther away from the explosion,
the greater the attenuation of the shock and pressure waves and the less the inten-
sity. This factor must be considered in the context of bottom conditions, depth of
CHAPTER 2 — Underwater Physics 2-9
water, and reflection of shock and pressure waves from underwater structures and
topographical features.
2-7.3.6
Degree of Submersion of the Diver.
A fully submerged diver receives the total
effect of the shock and pressure waves passing over the body. A partially
submerged diver whose head and upper body are out of the water, may experience
a reduced effect of the shock and pressure waves on the lungs, ears, and sinuses.
However, air will transmit some portion of the explosive shock and pressure
waves. The head, lungs, and intestines are the parts of the body most vulnerable to
the pressure effects of an explosion. A pressure wave of 500 pounds per square
inch is sufficient to cause serious injury to the lungs and intestinal tract, and one
greater than 2,000 pounds per square inch will cause certain death. Even a pres-
sure wave of 500 pounds per square inch could cause fatal injury under certain
circumstances.
2-7.3.7
Estimating Explosion Pressure on a Diver.
There are various formulas for esti-
mating the pressure wave resulting from an explosion of TNT. The equations vary
in format and the results illustrate that the technique for estimation is only an
approximation. Moreover, these formulas relate to TNT and are not applicable to
other types of explosives.
The formula below (Greenbaum and Hoff, 1966) is one method of estimating the
pressure on a diver resulting from an explosion of tetryl or TNT.
Where:
P = pressure on the diver in pounds per square inch
W = weight of the explosive (TNT) in pounds
r = range of the diver from the explosion in feet
Sample Problem.
Determine the pressure exerted by a 45-pound charge at a
distance of 80 feet.
1.
Substitute the known values.
P
13 000 W
3
,
r
-----------------------------
=
P
13 000 45
3
,
80
-----------------------------
=
2-10 U.S. Navy Diving Manual—Volume 1
2.
Solve for the pressure exerted.
Round up to 579 psi.
A 45-pound charge exerts a pressure of 579 pounds per square inch at a distance of
80 feet.
2-7.3.8
Minimizing the Effects of an Explosion.
When expecting an underwater blast, the
diver shall get out of the water and out of range of the blast whenever possible. If
the diver must be in the water, it is prudent to limit the pressure he experiences
from the explosion to less than 50 pounds per square inch. To minimize the
effects, the diver can position himself with feet pointing toward and head directly
away from the explosion. The head and upper section of the body should be out of
the water or the diver should float on his back with his head out of the water.
2-8
HEAT ENERGY IN DIVING
Heat is crucial to man’s environmental balance. The human body functions within
only a very narrow range of internal temperature and contains delicate mecha-
nisms to control that temperature.
Heat is a form of energy associated with and proportional to the molecular motion
of a substance. It is closely related to temperature, but must be distinguished from
temperature because different substances do not necessarily contain the same heat
energy even though their temperatures are the same.
Heat is generated in many ways. Burning fuels, chemical reactions, friction, and
electricity all generate heat. Heat is transmitted from one place to another by
conduction, convection, and radiation.
2-8.1
Conduction, Convection, and Radiation.
Conduction is the transmission of heat
by direct contact. Because water is an excellent heat conductor, an unprotected
diver can lose a great deal of body heat to the surrounding water by direct
conduction.
Convection is the transfer of heat by the movement of heated fluids. Most home
heating systems operate on the principle of convection, setting up a flow of air
currents based on the natural tendency of warm air to rise and cool air to fall. A
diver seated on the bottom of a tank of water in a cold room can lose heat not only
by direct conduction to the water, but also by convection currents in the water. The
warmed water next to his body will rise and be replaced by colder water passing
along the walls of the tank. Upon reaching the surface, the warmed water will lose
P
13 000 45
3
,
80
-----------------------------
=
13 000
,
3.56
×
80
----------------------------------
=
578.5=
CHAPTER 2 — Underwater Physics 2-11
heat to the cooler surroundings. Once cooled, the water will sink only to be
warmed again as part of a continuing cycle.
Radiation is heat transmission by electromagnetic waves of energy. Every warm
object gives off waves of electromagnetic energy, which is absorbed by cool
objects. Heat from the sun, electric heaters, and fireplaces is primarily radiant
heat.
2-8.2
Heat Transfer Rate.
To divers, conduction is the most significant means of trans-
mitting heat. The rate at which heat is transferred by conduction depends on two
basic factors:
The difference in temperature between the warmer and cooler material
The thermal conductivity of the materials
Not all substances conduct heat at the same rate. Iron, helium, and water are excel-
lent heat conductors while air is a very poor conductor. Placing a poor heat
conductor between a source of heat and another substance insulates the substance
and slows the transfer of heat. Materials such as wool and foam rubber insulate the
human body and are effective because they contain thousands of pockets of
trapped air. The air pockets are too small to be subject to convective currents, but
block conductive transfer of heat.
2-8.3
Diver Body Temperature.
A diver will start to become chilled when the water
temperature falls below a seemingly comfortable 70°F (21°C). Below 70°F, a
diver wearing only a swimming suit loses heat to the water faster than his body
can replace it. Unless he is provided some protection or insulation, he may quickly
experience difficulties. A chilled diver cannot work efficiently or think clearly,
and is more susceptible to decompression sickness.
Suit compression, increased gas density, thermal conductivity of breathing gases,
and respiratory heat loss are contributory factors in maintaining a divers body
temperature. Cellular neoprene wet suits lose a major portion of their insulating
properties as depth increases and the material compresses. As a consequence, it is
often necessary to employ a thicker suit, a dry suit, or a hot water suit for extended
exposures to cold water.
The heat transmission characteristics of an individual gas are directly proportional
to its density. Therefore, the heat lost through gas insulating barriers and respira-
tory heat lost to the surrounding areas increase with depth. The heat loss is further
aggravated when high thermal conductivity gases, such as helium-oxygen, are
used for breathing. The respiratory heat loss alone increases from 10 percent of the
body’s heat generating capacity at one ata, to 28 percent at 7 ata, to 50 percent at
21 ata when breathing helium-oxygen. Under these circumstances, standard insu-
lating materials are insufficient to maintain body temperatures and supplementary
heat must be supplied to the body surface and respiratory gas.
2-12 U.S. Navy Diving Manual—Volume 1
2-9
PRESSURE IN DIVING
Pressure is defined as a force acting upon a particular area of matter. It is typically
measured in pounds per square inch (psi) in the English system and Newton per
square centimeter (N/cm
2
) in the System International (SI). Underwater pressure
is a result of the weight of the water above the diver and the weight of the atmo-
sphere over the water. There is one concept that must be remembered at all
times—any diver, at any depth, must be in pressure balance with the forces at that
depth. The body can only function normally when the pressure difference between
the forces acting inside of the divers body and forces acting outside is very small.
Pressure, whether of the atmosphere, seawater, or the divers breathing gases,
must always be thought of in terms of maintaining pressure balance.
2-9.1
Atmospheric Pressure.
Given that one atmosphere is equal to 33 feet of sea water
or 14.7 psi, 14.7 psi divided by 33 feet equals 0.445 psi per foot. Thus, for every
foot of sea water, the total pressure is increased by 0.445 psi. Atmospheric pres-
sure is constant at sea level; minor fluctuations caused by the weather are usually
ignored. Atmospheric pressure acts on all things in all directions.
Most pressure gauges measure differential pressure between the inside and outside
of the gauge. Thus, the atmospheric pressure does not register on the pressure
gauge of a cylinder of compressed air. The initial air in the cylinder and the gauge
are already under a base pressure of one atmosphere (14.7 psi or 10N/cm
2
). The
gauge measures the pressure difference between the atmosphere and the increased
air pressure in the tank. This reading is called gauge pressure and for most
purposes it is sufficient.
In diving, however, it is important to include atmospheric pressure in computa-
tions. This total pressure is called absolute pressure and is normally expressed in
units of atmospheres. The distinction is important and pressure must be identified
as either gauge (psig) or absolute (psia). When the type of pressure is identified
only as psi, it refers to gauge pressure. Table 2-10 contains conversion factors for
pressure measurement units.
2-9.2
Terms Used to Describe Gas Pressure.
Four terms are used to describe gas
pressure:
Atmospheric
. Standard atmosphere, usually expressed as 10N/cm
2
, 14.7 psi,
or one atmosphere absolute (1 ata).
Barometric
. Essentially the same as atmospheric but varying with the weather
and expressed in terms of the height of a column of mercury. Standard
pressure is equal to 29.92 inches of mercury, 760 millimeters of mercury, or
1013 millibars.
Gauge
. Indicates the difference between atmospheric pressure and the
pressure being measured.
CHAPTER 2 — Underwater Physics 2-13
Absolute
. The total pressure being exerted, i.e., gauge pressure plus
atmospheric pressure.
2-9.3
Hydrostatic Pressure.
The water on the surface pushes down on the water below
and so on down to the bottom where, at the greatest depths of the ocean (approxi-
mately 36,000 fsw), the pressure is more than 8 tons per square inch (1,100 ata).
The pressure due to the weight of a water column is referred to as hydrostatic
pressure.
The pressure of seawater at a depth of 33 feet equals one atmosphere. The absolute
pressure, which is a combination of atmospheric and water pressure for that depth,
is two atmospheres. For every additional 33 feet of depth, another atmosphere of
pressure (14.7 psi) is encountered. Thus, at 99 feet, the absolute pressure is equal
to four atmospheres. Table 2-1 shows how pressure increases with depth.
The change in pressure with depth is so pronounced that the feet of a 6-foot tall
person standing underwater is exposed to pressure that is almost 3 pounds per
square inch greater than that exerted at his head.
2-9.4
Buoyancy.
Buoyancy is the force that makes objects float. It was first defined by
the Greek mathematician Archimedes, who established that “Any object wholly or
partly immersed in a fluid is buoyed up by a force equal to the weight of the fluid
displaced by the object.” This is known as Archimedes’ Principle and applies to all
objects and all fluids.
2-9.4.1
Archimedes’ Principle.
According to Archimedes’ Principle, the buoyancy of a
submerged body can be established by subtracting the weight of the submerged
body from the weight of the displaced liquid. If the total displacement (the weight
of the displaced liquid) is greater than the weight of the submerged body, the
buoyancy is positive and the body will float or be buoyed upward. If the weight of
the body is equal to that of the displaced liquid, the buoyancy is neutral and the
body will remain suspended in the liquid. If the weight of the submerged body is
greater than that of the displaced liquid, the buoyancy is negative and the body
will sink.
The buoyant force on an object is dependent upon the density of the substance it is
immersed in (weight per unit volume). Fresh water has a density of 62.4 pounds
Table 2-1. Pressure Chart.
Depth Gauge Pressure Atmospheric Pressure Absolute Pressure
0 One Atmosphere 1 ata (14.7 psia)
33 fsw + One Atmosphere 2 ata (29.4 psia)
66 fsw + One Atmosphere 3 ata (44.1 psia)
99 fsw + One Atmosphere 4 ata (58.8 psia)
2-14 U.S. Navy Diving Manual—Volume 1
per cubic foot. Sea water is heavier, having a density of 64.0 pounds per cubic
foot. Thus an object is buoyed up by a greater force in seawater than in fresh
water, making it easier to float in the ocean than in a fresh water lake.
2-9.4.2
Diver Buoyancy.
Lung capacity has a significant effect on buoyancy of a diver. A
diver with full lungs displaces a greater volume of water and, therefore, is more
buoyant than with deflated lungs. Individual differences that may affect the buoy-
ancy of a diver include bone structure, bone weight, and body fat. These
differences explain why some individuals float easily while others do not.
A diver can vary his buoyancy in several ways. By adding weight to his gear, he
can cause himself to sink. When wearing a variable volume dry suit, he can
increase or decrease the amount of air in his suit, thus changing his displacement
and thereby his buoyancy. Divers usually seek a condition of neutral to slightly
negative buoyancy. Negative buoyancy gives a diver in a helmet and dress a better
foothold on the bottom. Neutral buoyancy enhances a scuba divers ability to
swim easily, change depth, and hover.
2-10
GASES IN DIVING
Knowledge of the properties and behavior of gases, especially those used for
breathing, is vitally important to divers.
2-10.1
Atmospheric Air.
The most common gas used in diving is atmospheric air, the
composition of which is shown in Table 2-2. Any gases found in concentrations
different than those in Table 2-2 or that are not listed in Table 2-2 are considered
contaminants. Depending on weather and location, many industrial pollutants may
be found in air. Carbon monoxide is the most commonly encountered and is often
present around air compressor engine exhaust. Care must be taken to exclude the
pollutants from the divers’ compressed air by appropriate filtering, inlet location,
and compressor maintenance. Water vapor in varying quantities is present in
compressed air and its concentration is important in certain instances.
For most purposes and computations, diving air may be assumed to be composed
of 79 percent nitrogen and 21 percent oxygen. Besides air, varying mixtures of
oxygen, nitrogen, and helium are commonly used in diving. While these gases are
discussed separately, the gases themselves are almost always used in some
mixture. Air is a naturally occurring mixture of most of them. In certain types of
diving applications, special mixtures may be blended using one or more of the
gases with oxygen.
2-10.2
Oxygen.
Oxygen (O
2
) is the most important of all gases and is one of the most
abundant elements on earth. Fire cannot burn without oxygen and people cannot
survive without oxygen. Atmospheric air contains approximately 21 percent
oxygen, which exists freely in a diatomic state (two atoms paired off to make one
molecule). This colorless, odorless, tasteless, and active gas readily combines with
other elements. From the air we breathe, only oxygen is actually used by the body.
The other 79 percent of the air serves to dilute the oxygen. Pure 100 percent
oxygen is often used for breathing in hospitals, aircraft, and hyperbaric medical
CHAPTER 2 — Underwater Physics 2-15
treatment facilities. Sometimes 100 percent oxygen is used in shallow diving oper-
ations and certain phases of mixed-gas diving operations. However, breathing
pure oxygen under pressure may induce the serious problems of oxygen toxicity.
2-10.3
Nitrogen.
Like oxygen, nitrogen (N
2
) is diatomic, colorless, odorless, and taste-
less, and is a component of all living organisms. Unlike oxygen, it will not support
life or aid combustion and it does not combine easily with other elements.
Nitrogen in the air is inert in the free state. For diving, nitrogen may be used to
dilute oxygen. Nitrogen is not the only gas that can be used for this purpose and
under some conditions it has severe disadvantages as compared to other gases.
Nitrogen narcosis, a disorder resulting from the anesthetic properties of nitrogen
breathed under pressure, can result in a loss of orientation and judgment by the
diver. For this reason, compressed air, with its high nitrogen content, is not used
below a specified depth in diving operations.
2-10.4
Helium.
Helium (He) is a colorless, odorless, and tasteless gas, but it is mona-
tomic (exists as a single atom in its free state). It is totally inert. Helium is a rare
element, found in air only as a trace element of about 5 parts per million (ppm).
Helium coexists with natural gas in certain wells in the southwestern United
States, Canada, and Russia. These wells provide the world’s supply. When used in
diving to dilute oxygen in the breathing mixture, helium does not cause the same
problems associated with nitrogen narcosis, but it does have unique disadvantages.
Among these is the distortion of speech which takes place in a helium atmosphere.
The “Donald Duck” effect is caused by the acoustic properties of helium and it
impairs voice communications in deep diving. Another negative characteristic of
helium is its high thermal conductivity which can cause rapid loss of body and
respiratory heat.
Table 2-2. Components of Dry Atmospheric Air.
Component
Concentration
Percent by Volume Parts per Million (ppm)
Nitro
g
en 78.084
Oxy
g
en 20.946
Carbon Dioxide 0.033
Ar
g
on 0.0934
Neon 18.18
Helium 5.24
Krypton 1.14
Xenon 0.08
Hydro
g
en 0.5
Methane 2.0
Nitrous Oxide 0.5
2-16 U.S. Navy Diving Manual—Volume 1
2-10.5
Hydrogen.
Hydrogen (H
2
) is diatomic, colorless, odorless, and tasteless, and is so
active that it is rarely found in a free state on earth. It is, however, the most abun-
dant element in the visible universe. The sun and stars are almost pure hydrogen.
Pure hydrogen is violently explosive when mixed with air in proportions that
include a presence of more than 5.3 percent oxygen. Hydrogen has been used in
diving (replacing nitrogen for the same reasons as helium) but the hazards have
limited this to little more than experimentation.
2-10.6
Neon.
Neon (Ne) is inert, monatomic, colorless, odorless, and tasteless, and is
found in minute quantities in the atmosphere. It is a heavy gas and does not exhibit
the narcotic properties of nitrogen when used as a breathing medium. Because it
does not cause the speech distortion problem associated with helium and has supe-
rior thermal insulating properties, it has been the subject of some experimental
diving research.
2-10.7
Carbon Dioxide.
Carbon dioxide (CO
2
) is colorless, odorless, and tasteless when
found in small percentages in the air. In greater concentrations it has an acid taste
and odor. Carbon dioxide is a natural by-product of animal and human respiration,
and is formed by the oxidation of carbon in food to produce energy. For divers, the
two major concerns with carbon dioxide are control of the quantity in the
breathing supply and removal of the exhaust after breathing. While some carbon
dioxide is essential, unconsciousness can result when it is breathed at increased
partial pressure. In high concentrations the gas can be extremely toxic. In the case
of closed and semiclosed breathing apparatus, the removal of excess carbon
dioxide generated by breathing is essential to safety.
2-10.8
Carbon Monoxide.
Carbon monoxide (CO) is a colorless, odorless, tasteless, and
poisonous gas whose presence is difficult to detect. Carbon monoxide is formed as
a product of incomplete fuel combustion, and is most commonly found in the
exhaust of internal combustion engines. A divers air supply can be contaminated
by carbon monoxide when the compressor intake is placed too close to the
compressors engine exhaust. The exhaust gases are sucked in with the air and sent
on to the diver, with potentially disastrous results. Carbon monoxide seriously
interferes with the blood’s ability to carry the oxygen required for the body to
function normally. The affinity of carbon monoxide for hemoglobin is approxi-
mately 210 times that of oxygen. Carbon monoxide dissociates from hemoglobin
at a much slower rate than oxygen.
2-10.9
Kinetic Theory of Gases.
On the surface of the earth the constancy of the atmo-
sphere’s pressure and composition tend to be accepted without concern. To the
diver, however, the nature of the high pressure or hyperbaric, gaseous environ-
ment assumes great importance. The basic explanation of the behavior of gases
under all variations of temperature and pressure is known as the kinetic theory of
gases.
The kinetic theory of gases states: “The kinetic energy of any gas at a given tem-
perature is the same as the kinetic energy of any other gas at the same tempera-
ture.” Consequently, the measurable pressures of all gases resulting from kinetic
activity are affected by the same factors.
CHAPTER 2 — Underwater Physics 2-17
The kinetic energy of a gas is related to the speed at which the molecules are mov-
ing and the mass of the gas. Speed is a function of temperature and mass is a
function of gas type. At a given temperature, molecules of heavier gases move at a
slower speed than those of lighter gases, but their combination of mass and speed
results in the same kinetic energy level and impact force. The measured impact
force, or pressure, is representative of the kinetic energy of the gas. This is illus-
trated in Figure 2-6.
2-11
GAS LAWS
Gases are subject to three closely interrelated factors—temperature, pressure, and
volume. As the kinetic theory of gases points out, a change in one of these factors
must result in some measurable change in the other factors. Further, the theory
indicates that the kinetic behavior of any one gas is the same for all gases or
mixtures of gases. Consequently, basic laws have been established to help predict
the changes that will be reflected in one factor as the conditions of one or both of
the other factors change. A diver needs to know how changing pressure will effect
the air in his suit and lungs as he moves up and down in the water. He must be able
to determine whether an air compressor can deliver an adequate supply of air to a
proposed operating depth. He also needs to be able to interpret the reading on the
pressure gauge of his tanks under varying conditions of temperature and pressure.
The answers to such questions are calculated using a set of rules called the gas
laws. This section explains the gas laws of direct concern to divers.
2-11.1
Boyle’s Law.
Boyle’s law states that at constant temperature, the absolute pres-
sure and the volume of gas are inversely proportional. As pressure increases the
gas volume is reduced; as the pressure is reduced the gas volume increases.
Boyle’s law is important to divers because it relates to change in the volume of a
Figure 2-6.
Kinetic Energy. The kinetic energy of the molecules inside the container (a) produces a constant
pressure on the internal surfaces. As the container volume is decreased (b), the molecules per unit volume
(density) increase and so does the pressure. As the energy level of the molecules increases from the addition of
thermal energy (heat), so does the pressure (c).
2-18 U.S. Navy Diving Manual—Volume 1
gas caused by the change in pressure, due to depth, which defines the relationship
of pressure and volume in breathing gas supplies.
The formula for Boyles law is:
Where:
C = a constant
P = absolute pressure
V = volume
Boyle’s law can also be expressed as:
Where:
P
1
= initial pressure
V
1
= initial volume
P
2
= final pressure
V
2
= final volume
When working with Boyle’s law, pressure may be measured in atmospheres abso-
lute. To calculate pressure using atmospheres absolute:
or
Sample Problem 1.
An open diving bell with a volume of 24 cubic feet is to be
lowered into the sea from a support craft. No air is supplied to or lost from the bell.
Calculate the volume of the air in the bell at 99 fsw.
1.
Rearrange the formula for Boyle’s law to find the final volume (V
2
):
2.
Calculate the final pressure (P
2
) at 99 fsw:
3.
Substitute known values to find the final volume:
The volume of air in the open bell has been compressed to 6 ft.
3
at 99 fsw.
CPV
×
=
P
1
V
1
P
2
V
2
=
P
ata
Depth fsw 33 fsw+
33 fsw
---------------------------------------------------
=
P
ata
psig 14.7psi +
14.7psi
-------------------------------------
=
V
2
P
1
V
1
P
2
------------
=
P
2
99 fsw 33 fsw+
33 fsw
-----------------------------------------
=
4ata=
V
2
1ata 24ft
3
×
4ata
------------------------------
=
6ft
3
=
CHAPTER 2 — Underwater Physics 2-19
2-11.2
Charles’/Gay-Lussacs Law.
When working with Boyle’s law, the temperature of
the gas is a constant value. However, temperature significantly affects the pressure
and volume of a gas. Charles’/Gay-Lussac’s law describes the physical relation-
ships of temperature upon volume and pressure. Charles’/Gay-Lussac’s law states
that at a constant pressure, the volume of a gas is directly proportional to the
change in the absolute temperature. If the pressure is kept constant and the abso-
lute temperature is doubled, the volume will double. If the temperature decreases,
volume decreases. If volume instead of pressure is kept constant (i.e., heating in a
rigid container), then the absolute pressure will change in proportion to the abso-
lute temperature.
The formulas for expressing Charles’/Gay-Lussac’s law are as follows.
For the relationship between volume and temperature:
Where: Pressure is constant
T
1
= initial temperature (absolute)
T
2
= final temperature (absolute)
V
1
= initial volume
V
2
= final volume
And, for the relationship between pressure and temperature:
Where: Volume is constant
P
1
= initial pressure (absolute)
P
2
= final pressure (absolute)
T
1
= initial temperature (absolute)
T
2
= final temperature (absolute)
Sample Problem 1.
An open diving bell of 24 cubic feet capacity is lowered into
the ocean to a depth of 99 fsw. The surface temperature is 80°F, and the
temperature at depth is 45°F. From the sample problem illustrating Boyle’s law,
we know that the volume of the gas was compressed to 6 cubic feet when the bell
was lowered to 99 fsw. Apply Charles’/Gay-Lussac’s law to determine the volume
when it is effected by temperature.
V
1
T
1
------
V
2
T
2
------=
P
1
T
1
------
P
2
T
2
------
=
2-20 U.S. Navy Diving Manual—Volume 1
1.
Convert Fahrenheit temperatures to absolute temperatures (Rankine):
2.
Transpose the formula for Charles’/Gay-Lussac’s law to solve for the final
volume (V
2
):
3.
Substitute known values to solve for the final volume (V
2
):
The volume of the gas at 99 fsw is 5.61 ft
3
.
Sample Problem 2.
A 6-cubic foot flask is charged to 3000 psig and the
temperature in the flask room is 72 °F. A fire in an adjoining space causes the
temperature in the flask room to reach 170 °F. What will happen to the pressure in
the flask?
1.
Convert gauge pressure unit to atmospheric pressure unit:
P
1
= 3000 psig + 14.7 psi
= 3014.7 psia
2.
Convert Fahrenheit temperatures to absolute temperatures (Rankine):
°R = °F + 460
T
1
= 72°F + 460
= 532°R
T
2
= 170°F + 460
= 630°R
3.
Transpose the formula for Gay-Lussac’s law to solve for the final pressure
(P
2
):
°
R
°
F 460+=
T
1
80
°
F 460+=
540
°
R=
T
2
45
°
F 460+=
505
°
R=
V
2
V
1
T
2
T
1
-------------
=
V
2
6 ft.
3
505
×
540
---------------------------
=
5.61 ft.
3
=
P
2
P
1
T
2
T
1
------------
=
CHAPTER 2 — Underwater Physics 2-21
4.
Substitute known values and solve for the final pressure (P
2
):
The pressure in the flask increased from 3000 psig to 3555.33 psig. Note that the
pressure increased even though the flask’s volume and the volume of the gas
remained the same.
This example also shows what would happen to a scuba cylinder that was filled to
capacity and left unattended in the trunk of an automobile or lying in direct
sunlight on a hot day.
2-11.3
The General Gas Law.
Boyle, Charles, and Gay-Lussac demonstrated that
temperature, volume, and pressure affect a gas in such a way that a change in one
factor must be balanced by corresponding change in one or both of the others.
Boyle’s law describes the relationship between pressure and volume, Charles’/
Gay-Lussac’s law describes the relationship between temperature and volume and
the relationship between temperature and pressure. The general gas law combines
the laws to predict the behavior of a given quantity of gas when any of the factors
change.
The formula for expressing the general gas law is:
Where:
P
1
= initial pressure (absolute)
V
1
= initial volume
T
1
= initial temperature (absolute)
P
2
= final pressure (absolute)
V
2
= final volume
T
2
= final temperature (absolute)
Two simple rules must be kept in mind when working with the general gas law:
There can be only one unknown value.
The equation can be simplified if it is known that a value remains unchanged
(such as the volume of an air cylinder) or that the change in one of the
variables is of little consequence. In either case, cancel the value out of both
sides of the equation to simplify the computations.
Sample Problem 1.
Your ship has been assigned to salvage a sunken LCM
landing craft located in 130 fsw. An exploratory dive, using scuba, is planned to
P
2
3014.7 630
×
532
-------------------------------
=
1 899 261
,,
532
---------------------------
=
3570.03 psia 14.7=
3555.33
si
=
P
1
V
1
T
1
------------
P
2
V
2
T
2
------------
=
2-22 U.S. Navy Diving Manual—Volume 1
survey the wreckage. The scuba cylinders are charged to 2,250 psig, which raises
the temperature in the tanks to 140 °F. From experience in these waters, you know
that the temperature at the operating depth will be about 40°F. Apply the general
gas law to find what the gauge reading will be when you first reach the bottom.
(Assume no loss of air due to breathing.)
1.
Simplify the equation by eliminating the variables that will not change. The
volume of the tank will not change, so V
1
and V
2
can be eliminated from the
formula in this problem:
2.
Calculate the initial pressure by converting the gauge pressure unit to the
atmospheric pressure unit:
P
1
= 2,250 psig + 14.7
= 2,264.7 psia
3.
Convert Fahrenheit temperatures to Rankine (absolute) temperatures:
Conversion formula: °R = °F + 460
T
1
= 140 °F + 460
= 600 °R
T
2
= 40 °F + 460
= 500°R
4.
Rearrange the formula to solve for the final pressure (P
2
):
5.
Fill in known values:
6.
Convert final pressure (P
2
) to gauge pressure:
P
2
= 1,887.25 psia - 14.7
= 1,872.55 psig
The gauge reading when you reach bottom will be 1,872.55 psig.
Sample Problem 2.
During the survey dive for the operation outlined in Sample
Problem 1, the divers determined that the damage will require a simple patch. The
P
1
T
1
------
P
2
T
2
------
=
P
2
P
1
T
2
T
1
------------
=
P
2
2 264.7 psia
,
500
°
R
×
600
°
R
-----------------------------------------------------=
1887.25 psia=
CHAPTER 2 — Underwater Physics 2-23
Diving Supervisor elects to use surface-supplied MK 21 equipment. The
compressor discharge capacity is 60 cubic feet per minute, and the air temperature
on the deck of the ship is 80°F.
Apply the general gas law to determine whether the compressor can deliver the
proper volume of air to both the working diver and the standby diver at the oper-
ating depth and temperature.
1.
Calculate the absolute pressure at depth (P
2
):
2.
Convert Fahrenheit temperatures to Rankine (absolute) temperatures:
Conversion formula:
°R = °F + 460
T
1
= 80°F + 460
= 540°R
T
2
= 40°F + 460
= 500°R
3.
Rearrange the general gas law formula to solve for the volume of air at depth
(V
2
):
4.
Substitute known values and solve:
Based upon an actual volume (displacement) flow requirement of 1.4 acfm for a
deep-sea diver, the compressor capacity is sufficient to support the working and
standby divers at 130 fsw.
P
2
130 fsw 33 fsw+
33 fsw
----------------------------------------------=
4.93 ata=
V
2
P
1
V
1
T
2
P
2
T
1
-------------------
=
V
2
1 ata 60 cfm
×
500
°
R
×
4.93 ata 540
°
R
×
---------------------------------------------------------
=
11.26 acfm at bottom conditions=
2-24 U.S. Navy Diving Manual—Volume 1
Sample Problem 3.
Find the actual cubic feet of air contained in a 700-cubic inch
internal volume cylinder pressurized to 3,000 psi.
1.
Simplify the equation by eliminating the variables that will not change. The
temperature of the tank will not change so T
1
and T
2
can be eliminated from
the formula in this problem:
P
1
V
1
= P
2
V
2
2.
Rearrange the formula to solve for the initial volume:
Where:
P
1
= 14.7 psi
P
2
= 3,000 psi + 14.7 psi
V
2
= 700 in
3
3.
Fill in the known values and solve for V
1
:
4.
Convert V
1
to cubic feet:
2-12
GAS MIXTURES
If a diver used only one gas for all underwater work, at all depths, then the general
gas law would suffice for most of his necessary calculations. However, to accom-
modate use of a single gas, oxygen would have to be chosen because it is the only
one that provides life support. But 100 percent oxygen can be dangerous to a diver
as depth and breathing time increase. Divers usually breathe gases in a mixture,
either air (21 percent oxygen, 78 percent nitrogen, 1 percent other gases) or
oxygen with one of the inert gases serving as a diluent for the oxygen. The human
body has a wide range of reactions to various gases under different conditions of
pressure and for this reason another gas law is required to help compute the differ-
ences between breathing at the surface and breathing under pressure.
V
1
P
2
V
2
P
1
------------
=
V
1
3014.7 psia 700 in
3
×
14.7 psi
----------------------------------------------------
=
143 557.14 in
,
3
=
V
1
143 557.14in
,
3
1728
3
------------------------------------
=
83.07 scf=
(1728 in
3
= 1 ft
3
)
CHAPTER 2 — Underwater Physics 2-25
2-12.1
Dalton’s Law.
Dalton’s law states: “The total pressure exerted by a mixture of
gases is equal to the sum of the pressures of each of the different gases making up
the mixture, with each gas acting as if it alone was 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 (pp) of that gas. An easily understood example is that of
a container at atmospheric pressure (14.7 psi). If the container were filled with
oxygen alone, the partial pressure of the oxygen would be one atmosphere. If the
same container at 1 atm were filled with dry air, the partial pressures of all the
constituent gases would contribute to the total partial pressure, as shown in Table
2-3.
If the same container was filled with air to 2,000 psi (137 ata), the partial pressures
of the various components would reflect the increased pressure in the same
proportion as their percentage of the gas, as illustrated in Table 2-4.
The formula for expressing Daltons law is:
Where: A, B, and C are gases and
Table 2-3. Partial Pressure at 1 ata.
Gas Percent of Component
Atmospheres Partial
Pressure
N
2
78.08 0.7808
O
2
20.95 0.2095
CO
2
.03 0.0003
Other .94 0.0094
Tot al 100.00 1.0000
Table 2-4. Partial Pressure at 137 ata.
Gas Percent of Component
Atmospheres Partial
Pressure
N
2
78.08 106.97
O
2
20.95 28.70
CO
2
.03 0.04
Other .94 1.29
Total 100.00 137.00
P
Total
pp
A
pp
B
pp
C
+++=
pp
A
P
Total
%Vol
A
×
1.00
--------------------------------------
=
2-26 U.S. Navy Diving Manual—Volume 1
Another method of arriving at the same conclusion is to use the T formula. When
using the T formula, there can be only one unknown value. Then it is merely a
case of multiplying across, or dividing up to solve for the unknown value.The T
formula is illustrated as:
Sample Problem 1.
Use the T formula to calculate oxygen partial pressure given
10 ata and 16 percent oxygen.
1.
Fill in the known values:
2.
Multiply the pressure by the volume to solve for the oxygen partial pressure
(pp):
The oxygen partial pressure is 1.6.
Sample Problem 2.
What happens to the breathing mixture at the operating depth
of 130 fsw (4.93 ata)? The air compressor on the ship is taking in air at the surface,
at normal pressure and normal mixture, and sending it to the diver at pressure
sufficient to provide the necessary balance. The composition of air is not changed,
but the quantity being delivered to the diver is five times what he was breathing on
the surface. More molecules of oxygen, nitrogen, and carbon dioxide are all
compressed into the same volume at the higher pressure. Use Dalton’s law to
determine the partial pressures at depth.
1.
Calculate the oxygen partial pressure at depth.
ppO
2
= .21 (surface)
×
4.93 ata
= 1.03 ata
2.
Calculate the nitrogen partial pressure at depth.
ppN
2
= .79 (surface)
×
4.93 ata
= 3.89 ata
3.
Calculate the carbon dioxide partial pressure at depth.
ppCO
2
= .0003 (surface)
×
4.93 ata
= .0014 ata
partial pressure
atmosphere(s) absolute % volume (in decimal form)
pp
10 .16
------------------
1.6 ppO
2
10 .16
-----------------------
CHAPTER 2 — Underwater Physics 2-27
2-12.1.1
Expressing Small Quantities of Pressure.
Expressing partial pressures of gases
in atmospheres absolute (ata) is the most common method employed in large
quantities of pressure. Partial pressures of less than 0.1 atmosphere are usually
expressed in millimeters of mercury (mmHg). At the surface, atmospheric pres-
sure is equal to 1 ata or 14.7 psia or 760 mmHg. The formula used to calculate the
ppCO
2
at 130 fsw in millimeters of mercury is:
2-12.1.2
Calculating Surface Equivalent Value.
From the previous calculations, it is
apparent that the diver is breathing more molecules of oxygen breathing air at 130
fsw than he would be if using 100 percent oxygen at the surface. He is also
inspiring five times as many carbon dioxide molecules as he would breathing
normal air on the surface. If the surface air were contaminated with 2 percent (0.02
ata) carbon dioxide, a level that could be readily accommodated by a normal
person at one ata, the partial pressure at depth would be dangerously high—0.0986
ata (0.02 x 4.93 ata). This partial pressure is commonly referred to as a surface
equivalent value (sev) of 10 percent carbon dioxide. The formula for calculating
the surface equivalent value is:
2-12.2
Gas Diffusion.
Another physical effect of partial pressures and kinetic activity is
that of gas diffusion. Gas diffusion is the process of intermingling or mixing of gas
molecules. If two gases are placed together in a container, they will eventually mix
completely even though one gas may be heavier. The mixing occurs as a result of
constant molecular motion.
An individual gas will move through a permeable membrane (a solid that permits
molecular transmission) depending upon the partial pressure of the gas on each
side of the membrane. If the partial pressure is higher on one side, the gas mole-
cules will diffuse through the membrane from the higher to the lower partial
pressure side until the partial pressure on sides of the membrane are equal. Mole-
cules are actually passing through the membrane at all times in both directions due
to kinetic activity, but more will move from the side of higher concentration to the
side of lower concentration.
Body tissues are permeable membranes. The rate of gas diffusion, which is related
to the difference in partial pressures, is an important consideration in determining
the uptake and elimination of gases in calculating decompression tables.
ppCO
2
0.03
100
----------
4.93 ata
760mmHg
1ata
---------------------------
××
=
1.12mmHg=
sev
pp at depth (in ata) 100%
×
1 ata
------------------------------------------------------------------
=
0.0986 ata
1 ata
-------------------------
100%
×
=
9.86% CO
2
=
2-28 U.S. Navy Diving Manual—Volume 1
2-12.3
Humidity.
Humidity is the amount of water vapor in gaseous atmospheres. Like
other gases, water vapor behaves in accordance with the gas laws. However,
unlike other gases encountered in diving, water vapor condenses to its liquid state
at temperatures normally encountered by man.
Humidity is related to the vapor pressure of water, and the maximum partial pres-
sure of water vapor in the gas is governed entirely by the temperature of the gas.
As the gas temperature increases, more molecules of water can be maintained in
the gas until a new equilibrium condition and higher maximum partial pressure are
established. As a gas cools, water vapor in the gas condenses until a lower partial
pressure condition exists regardless of the total pressure of the gas. The tempera-
ture at which a gas is saturated with water vapor is called the dewpoint.
In proper concentrations, water vapor in a divers breathing gas can be beneficial
to the diver. Water vapor moistens body tissues, thus keeping the diver comfort-
able. As a condensing liquid, however, water vapor can freeze and block air
passageways in hoses and equipment, fog a divers faceplate, and corrode his
equipment.
2-12.4
Gases in Liquids.
When a gas comes in contact with a liquid, a portion of the gas
molecules enters into solution with the liquid. The gas is said to be dissolved in the
liquid. Solubility is vitally important because significant amounts of gases are
dissolved in body tissues at the pressures encountered in diving.
2-12.5
Solubility.
Some gases are more soluble (capable of being dissolved) than others,
and some liquids and substances are better solvents (capable of dissolving another
substance) than others. For example, nitrogen is five times more soluble in fat than
it is in water.
Apart from the individual characteristics of the various gases and liquids, tempera-
ture and pressure greatly affect the quantity of gas that will be absorbed. Because a
diver is always operating under unusual conditions of pressure, understanding this
factor is particularly important.
2-12.6
Henry’s Law.
Henry’s law states: “The amount of any given gas that will dissolve
in a liquid at a given temperature is directly proportional to the partial pressure of
that gas.Because a large percentage of the human body is water, the law simply
states that as one dives deeper and deeper, more gas will dissolve in the body
tissues and that upon ascent, the dissolved gas must be released.
2-12.6.1
Gas Tension.
When a gas-free liquid is first exposed to a gas, quantities of gas
molecules rush to enter the solution, pushed along by the partial pressure of the
gas. As the molecules enter the liquid, they add to a state of gas tension. Gas
tension is a way of identifying the partial pressure of that gas in the liquid.
The difference between the gas tension and the partial pressure of the gas outside
the liquid is called the pressure gradient. The pressure gradient indicates the rate
at which the gas enters or leaves the solution.
CHAPTER 2 — Underwater Physics 2-29
2-12.6.2
Gas Absorption.
At sea level, the body tissues are equilibrated with dissolved
nitrogen at a partial pressure equal to the partial pressure of nitrogen in the lungs.
Upon exposure to altitude or increased pressure in diving, the partial pressure of
nitrogen in the lungs changes and tissues either lose or gain nitrogen to reach a
new equilibrium with the nitrogen pressure in the lungs. Taking up nitrogen in
tissues is called absorption or uptake. Giving up nitrogen from tissues is termed
elimination or offgassing. In air diving, nitrogen absorption occurs when a diver is
exposed to an increased nitrogen partial pressure. As pressure decreases, the
nitrogen is eliminated. This is true for any inert gas breathed.
Absorption consists of several phases, including transfer of inert gas from the
lungs to the blood and then from the blood to the various tissues as it flows
through the body. The gradient for gas transfer is the partial pressure difference of
the gas between the lungs and blood and between the blood and the tissues.
The volume of blood flowing through tissues is small compared to the mass of the
tissue, but over a period of time the gas delivered to the tissue causes it to become
equilibrated with the gas carried in the blood. As the number of gas molecules in
the liquid increases, the tension increases until it reaches a value equal to the
partial pressure. When the tension equals the partial pressure, the liquid is satu-
rated with the gas and the pressure gradient is zero. Unless the temperature or
pressure changes, the only molecules of gas to enter or leave the liquid are those
which may, in random fashion, change places without altering the balance.
The rate of equilibration with the blood gas depends upon the volume of blood
flow and the respective capacities of blood and tissues to absorb dissolved gas. For
example, fatty tissues hold significantly more gas than watery tissues and will thus
take longer to absorb or eliminate excess inert gas.
2-12.6.3
Gas Solubility.
The solubility of gases is affected by temperature—the lower the
temperature, the higher the solubility. As the temperature of a solution increases,
some of the dissolved gas leaves the solution. The bubbles rising in a pan of water
being heated (long before it boils) are bubbles of dissolved gas coming out of
solution.
The gases in a divers breathing mixture are dissolved into his body in proportion
to the partial pressure of each gas in the mixture. Because of the varied solubility
of different gases, the quantity of a particular gas that becomes dissolved is also
governed by the length of time the diver is breathing the gas at the increased pres-
sure. If the diver breathes the gas long enough, his body will become saturated.
The dissolved gas in a divers body, regardless of quantity, depth, or pressure,
remains in solution as long as the pressure is maintained. However, as the diver
ascends, more and more of the dissolved gas comes out of solution. If his ascent
rate is controlled (i.e., through the use of the decompression tables), the dissolved
gas is carried to the lungs and exhaled before it accumulates to form significant
bubbles in the tissues. If, on the other hand, he ascends suddenly and the pressure
is reduced at a rate higher than the body can accommodate, bubbles may form,
disrupt body tissues and systems, and produce decompression sickness.
2-30 U.S. Navy Diving Manual—Volume 1
Table 2-5. Symbols and Values.
Symbol Value
°F De
g
rees Fahrenheit
°C De
g
rees Celsius
°R De
g
rees Rankine
A Area
C Circumference
D Depth of Water
H Hei
g
ht
L Len
g
th
P Pressure
r Radius
T Temperature
t Time
V Volume
W Width
Dia Diameter
Dia
2
Diameter Squared
Dia
3
Diameter Cubed
Π 3.1416
ata Atmospheres Absolute
pp Partial Pressure
psi Pounds per Square Inch
psi
g
Pounds per Square Inch Gau
g
e
psia Pounds per Square Inch Absolute
fsw Feet of Sea Water
fpm Feet per Minute
scf Standard Cubic Feet
BTU British Thermal Unit
cm
3
Cubic Centimeter
kw hr Kilowatt Hour
mb Millibars
CHAPTER 2 — Underwater Physics 2-31
Table 2-6. Buoyancy (In Pounds).
Fresh Water (
V cu ft
x 62.4) -
Weight of Unit
Salt Water (
V cu ft
x 64) -
Weight of Unit
Table 2-7. Formulas for Area.
Square or Rectangle A = L x W
Circle A = 0.7854 x Dia
2
or
Table 2-8. Formulas for Volumes.
Compartment
V
=
L
x
W
x
H
Sphere = π x 4/3 x
r
3
= 0.5236 x
Dia
3
Cylinder V = π x
r
2
x
L
= π x 1/4 x
Dia
2
x
L
= 0.7854 x
Dia
2
x
L
Table 2-9. Formulas for Partial Pressure/Equivalent Air Depth.
Partial Pressure Measured in psi
Partial Pressure Measured in ata
Partial Pressure Measured in fsw
T formula for Measuring Partial Pressure
Equivalent Air Depth for N
2
O
2
Diving Measured
in fsw
Equivalent Air Depth for N
2
O
2
Diving Measured
in meters
A =
π
r
2
pp D 33 fsw+()0.445 psi
%V
100%
---------------


××=
pp
D + 33 fsw
33 fsw
----------------------------
%V
100 %
-----------------
×
=
pp D 33fsw
+
()
%V
100%
---------------
×=
pp
ata %
----------------
EAD
1.0 O
2
%()D33+()
.79
-------------------------------------------------------
33=
EAD
1.0 O
2
%()M10+()
.79
--------------------------------------------------------
10=
2-32 U.S. Navy Diving Manual—Volume 1
Table 2-10. Pressure Equivalents.
Columns of Mercury
at 0°C
Columns of Water*
at 15° C
Atmos-
pheres
Bars
10 Newton
Per Square
Centimeter
Pounds
Per Square
Inch
Meters Inches Meters Inches
Feet
(FW)
Feet
(FSW)
1 1.01325 1.03323 14.696 0.76 29.9212 10.337 406.966 33.9139 33.066
0.986923 1 1.01972 14.5038 0.750062 29.5299 10.2018 401.645 33.4704 32.6336
0.967841 0.980665 1 14.2234 0.735559 28.959 10.0045 393.879 32.8232 32.0026
0.068046 0.068947 0.070307 1 0.0517147 2.03601 0.703386 27.6923 2.30769 2.25
1.31579 1.33322 1.35951 19.33369 1 39.37 13.6013 535.482 44.6235 43.5079
0.0334211 0.0338639 0.0345316 0.491157 0.0254 1 0.345473 13.6013 1.13344 1.1051
0.09674 0.09798 0.099955 1.42169 0.073523 2.89458 1 39.37 3.28083 3.19881
0.002456 0.002489 0.002538 0.03609 0.001867 0.073523 0.02540 1 0.08333 0.08125
0.029487 0.029877 0.030466 0.43333 0.02241 0.882271 0.304801 12 1 0.975
0.030242 0.030643 0.031247 0.44444 0.022984 0.904884 0.312616 12.3077 1.02564 1
1. Fresh Water (FW) = 62.4 lbs/ft
3
; Salt Water (fsw) = 64.0 lbs/ft
3
.
2. The SI unit for pressure is Kilopascal (KPA)—1KG/CM
2
= 98.0665 KPA and by definition 1 BAR = 100.00 KPA @ 4ºC.
3. In the metric system, 1 MSW is defined as 1 BAR. Note that pressure conversion from MSW to FSW is different than len
g
th
conversion; i.e., 10 MSW = 32.6336 FSW and 10 M = 32.8083 feet.
Table 2-11. Volume and Capacity Equivalents.
Cubic
Centi-
meters
Cubic
Inches
Cubic
Feet
Cubic
Yards
Milliliters Liters Pint Quart Gallon
1 .061023 3.531 x 10
-5
1.3097 x 10
-6
.999972 9.9997 x 10
-4
2.113 x 10
-3
1.0567 x 10
-3
2.6417x 10
-4
16.3872 1 5.787 x 10
-4
2.1434 x 10
-5
16.3867 0.0163867 0.034632 0.017316 4.329 x 10
-3
28317 1728 1 0.037037 28316.2 28.3162 59.8442 29.9221 7.48052
764559 46656 27 1 764538 764.538 1615.79 807.896 201.974
1.00003 0.0610251 3.5315 x 10
-5
1.308 x 10
-6
1 0.001 2.1134 x 10
-3
1.0567 x 10
-3
2.6418 x 10
-4
1000.03 61.0251 0.0353154 1.308 x 10
-3
1000 1 2.11342 1.05671 0.264178
473.179 28.875 0.0167101 6.1889 x 10
-4
473.166 0.473166 1 0.5 0.125
946.359 57.75 0.0334201 1.2378 x 10
-3
946.332 0.946332 2 1 0.25
3785.43 231 0.133681 49511 x 10
-3
3785.33 3.78533 8 4 1
CHAPTER 2 — Underwater Physics 2-33
Table 2-12. Length Equivalents.
Centi-
meters
Inches Feet Yards Meters Fathom
Kilo-
meters
Miles
Int. Nau-
tical Miles
1 0.3937 0.032808 0.010936 0.01 5.468 x 10
-3
0.00001 6.2137 x 10
-5
5.3659 x 10
-6
2.54001 1 0.08333 0.027778 0.025400 0.013889 2.540 x 10
-5
1.5783 x 10
-5
1.3706 x 10
-5
30.4801 12 1 0.33333 0.304801 0.166665 3.0480 x 10
-4
1.8939 x 10
-4
1.6447 x 10
-4
91.4403 36 3 1 0.914403 0.5 9.144 x 10
-4
5.6818 x 10
-4
4.9341 x 10
-4
100 39.37 3.28083 1.09361 1 0.5468 0.001 6.2137 x 10
-4
5.3959 x 10
-4
182.882 72 6 2 1.82882 1 1.8288 x 10-
3
1.1364 x 10
-3
9.8682 x 10
-4
100000 39370 3280.83 1093.61 1000 546.8 1 0.62137 0.539593
160935 63360 5280 1760 1609.35 80 1.60935 1 0.868393
185325 72962.4 6080.4 2026.73 1853.25 1013.36 1.85325 1.15155 1
Table 2-13. Area Equivalents.
Square
Miles
Square
Centimeters
Square
Inches
Square
Feet
Square
Yards
Acres
Square
Miles
1 10000 1550 10.7639 1.19599 2.471 x 10
-4
3.861 x 10
-7
0.0001 1 0.155 1.0764 x 10
-3
1.196 x 10
-4
2.471 x 10
-8
3.861 x 10
-11
6.4516 x 10
-4
6.45163 1 6.944 x 10
-3
7.716 x 10
-4
1.594 x 10
-7
2.491 x 10
-10
0.092903 929.034 144 1 0.11111 2.2957 x 10
-5
3.578 x 10
-8
0.836131 8361.31 1296 9 1 2.0661 x 10
-4
3.2283 x 10
-7
4046.87 4.0469 x 10
7
6.2726 x 10
6
43560 4840 1 1.5625 x 10
-3
2.59 x 10
6
2.59 x 10
10
4.0145 x 10
9
2.7878 x 10
7
3.0976 x 10
6
640 1
Table 2-14. Velocity Equivalents.
Centimeters
Per Second
Meters
Per Second
Meters Per
Minute
Kilometers
Per Hour
Feet
Per Second
Feet Per
Minute
Miles
Per Hour
Knots
1 0.01 0.6 0.036 0.0328083 1.9685 0.0223639 0.0194673
100 1 60 3.6 3.28083 196.85 2.23693 1.9473
1.66667 0.016667 1 0.06 0.0546806 3.28083 0.0372822 0.0324455
27.778 0.27778 16.667 1 0.911343 54.6806 0.62137 0.540758
30.4801 0.304801 18.288 1.09728 1 60 0.681818 0.593365
0.5080 5.080 x 10
-3
0.304801 0.018288 0.016667 1 0.0113636 9.8894 x 10
-3
44.7041 0.447041 26.8225 1.60935 1.4667 88 1 0.870268
51.3682 0.513682 30.8209 1.84926 1.6853 101.118 1.14907 1
2-34 U.S. Navy Diving Manual—Volume 1
Table 2-15. Mass Equivalents.
Kilograms Grams Grains Ounces Pounds Tons (short) Tons (long) Tons (metric)
1 1000 15432.4 35.274 2.20462 1.1023 x 10
-3
9.842 x 10
-4
0.001
0.001 1 15432.4 0.035274 2.2046 x 10
-3
1.1023 x 10
-6
9.842 x 10
-7
0.000001
6.4799 x 10
-5
0.6047989 1 2.2857 x 10
-3
1.4286 x 10
-4
7.1429 x 10
-8
6.3776 x 10
-8
6.4799 x 10
-8
0.0283495 28.3495 437.5 1 0.0625 3.125 x 10
-5
2.790 x 10
-5
2.835 x 10
-5
0.453592 453.592 7000 16 1 0.0005 4.4543 x 10
-4
4.5359 x 10
-4
907.185 907185 1.4 x 10
7
32000 2000 1 0.892857 0.907185
1016.05 1.016 x 10
6
1.568 x 10
7
35840 2240 1.12 1 1.01605
1000 10
6
1.5432 x 10
7
35274 2204.62 1.10231 984206 1
Table 2-16. Energy or Work Equivalents.
International
Joules
Ergs
Foot -
Pounds
International
Kilowatt
Hours
Horse Power
Hours
Kilo -
Calories
BTUs
1 10
7
0.737682 2.778 x 10
-7
3.7257 10
-7
2.3889 x 10
-4
9.4799 x 10
-4
10
-7
1 7.3768 x 10
-8
2.778 x 10
-14
3.726 x 10
-14
2.389 x 10
-11
9.4799 x 10
-11
1.3566 1.3556 x 10
7
1 3.766 x 10
-7
5.0505 x 10
-7
3.238 x 10
-4
1.285 x 10
-3
3.6 x 10
6
3.6 x 10
13
2.6557 x 10
6
1 1.34124 860 3412.76
2.684 x 10
6
2.684 x 10
13
1.98 x 10
6
0.745578 1 641.197 2544.48
4186.04 4.186 x 10
10
3087.97 1.163 x 10
-3
1.596 x 10
-3
1 3.96832
1054.87 1.0549 x 10
10
778.155 2.930 x 10
-4
3.93 x 10
-4
0.251996 1
Table 2-17. Power Equivalents.
Horse
Power
International
Kilowatts
International
Joules/
Second
Kg-M
Second
Foot lbs.
Per Second
IT Calories
Per Second
BTUs
Per Second
1 0.745578 745.578 76.0404 550 178.11 0.7068
1.34124 1 1000 101.989 737.683 238.889 0.947989
1.3412 x 10
-3
0.001 1 0.101988 0.737682 0.238889 9.4799 x 10
-4
0.0131509 9.805 x 10
-3
9.80503 1 7.233 2.34231 9.2951 x 10
-3
1.8182 x 10
-3
1.3556 x 10
-3
1.3556 0.138255 1 0.323837 1.2851 x 10
-3
5.6145 x 10
-3
4.1861 x 10
-3
4.18605 0.426929 3.08797 1 3.9683 x 10
-3
1.41483 1.05486 1054.86 107.584 778.155 251.995 1
CHAPTER 2 — Underwater Physics 2-35
Table 2-18. Temperature Equivalents.
Conversion Formulas:
°C °F °C °F °C °F °C °F °C °F °C °F °C °F
-100
-98
-96
-94
-92
-148.0
-144.4
-140.8
-137.2
-133.6
-60
-58
-56
-54
-52
-76.0
-72.4
-68.8
-65.2
-61.6
-20
-18
-16
-14
-12
-4.0
-0.4
3.2
6.8
10.4
20
22
24
26
28
68.0
71.6
75.2
78.8
82.4
60
62
64
66
68
140.0
143.6
147.2
150.8
154.4
100
102
104
106
108
212.0
215.6
219.2
222.8
226.4
140
142
144
146
148
284.0
287.6
291.2
294.8
298.4
-90
-88
-86
-84
-82
-130.0
-126.4
-122.8
-119.2
-115.6
-50
-48
-46
-44
-42
-58.0
-54.4
-50.8
-47.2
-43.6
-10
-8
-6
-4
-2
14.0
17.6
21.2
24.8
28.4
30
32
34
36
38
86.0
89.6
93.2
96.8
100.4
70
72
74
76
78
158.0
161.6
165.2
168.8
172.4
110
112
114
116
118
230.0
233.6
237.2
240.8
244.4
150
152
154
156
158
302.0
305.6
309.2
312.8
316.4
-80
-78
-76
-74
-72
-112.0
-108.4
-104.8
-101.2
-97.6
-40
-38
-36
-34
-32
-40.0
-36.4
-32.8
-29.2
-25.6
0
2
4
6
8
32
35.6
39.2
42.8
46.4
40
42
44
46
48
104.0
107.6
111.2
114.8
118.4
80
82
84
86
88
176.0
179.6
183.2
186.8
190.4
120
122
124
126
128
248.0
251.6
255.2
258.8
262.4
160
162
164
166
168
320.0
323.6
327.2
330.8
334.4
-70
-68
-66
-64
-62
-94.0
-90.4
-86.8
-83.2
-79.6
-30
-28
-26
-24
-22
-22.0
-18.4
-14.8
-11.2
-7.6
10
12
14
16
18
50.0
53.6
57.2
60.8
64.4
50
52
54
56
58
122.0
125.6
129.2
132.8
136.4
90
92
94
96
98
194.0
197.6
201.2
204.8
208.4
130
132
134
136
138
266.0
269.6
273.2
276.8
280.4
170
172
174
176
178
338.0
341.6
345.2
348.8
352.4
°
C
°
F32
()
5
9
---
×
=
°
F
9
5
---
°
C
×


32
+
=
2-36 U.S. Navy Diving Manual—Volume 1
Figure 2-7.
Depth, Pressure, Atmosphere Graph.