# Commercial diving/Diving physics

Relevance: Scuba diving, Surface supplied diving, Surface oriented wet bell diving.

Required outcomes:

1. Demonstrate the ability to apply basic math skills in simple equations / fractions found in diving physics calculations involving gases, liquids, and solids, in units of metric measurements including conversion tables.
The diver will work with units of measurement and the industry standard multiples and conversions of linear dimensions, area, volume, mass, force, pressure, density, time and temperature, including buoyancy and weight.
2. Describe the relationship between pressure, volume and density in a gas (Boyles’ Law) including using the formula in calculations, and the effects of changes in volume due to pressure variations on diving equipment, gas consumption and the human body, including the mechanism of barotraumas of descent and ascent.
3. Discuss Gay-Lussac’s Law and the relationship between pressure and temperature including using the formula to calculate change of pressure for a given change of temperature
4. Discuss Henry’s Law and how the solubility of gases within a divers tissues affects the diver's health and safety
5. Discuss the composition of the atmosphere and gases and the relationship of partial pressure of the gases in a mixture (Dalton’s Law) including formula and calculations and effects on descent and ascent.
The diver will be familiar with the constituents and their proportions in atmospheric air and other breathing gases for diving, and the common contaminants. Calculate partial pressures for a given breathing gas for changes in pressure.
6. Describe the effects of temperature of the environment on diving including the effects on the divers equipment and the principles and importance of thermal balance of the diver
7. Describe the effects of the underwater environment on illumination and visibility and sound and hearing including the impact on the safety of diver
8. Discuss Archimedes’ Principle and buoyancy as applied to diving operations including use of formula in calculations of lifting gas quantities and apparent weight of immersed objects

## Units of measurement used in diving

The units of measurement commonly used in diving involve length, area and volume, mass, force, pressure, time, temperature, and density.

Please note that the letter case (capitalisation) of unit symbols is very important. Wrong case => wrong unit. Get them right. If in doubt, write them out in full.[1]

The multiples and decimal fractions of units of measurement in the metric system include:

prefix abbreviation
(symbol)
scale factor / multiplier example symbol meaning
micro- μ 1/1000 000 0.000001 10-6 micrometer μm 1/1000 000 metre
milli- m 1/1000 0.001 10-3 millimetre mm 1/1000 metre
centi- c 1/100 0.01 10-2 centimetre cm 1/100 metre
deci- d 1/10 0.1 10-1 decimetre dm 1/10 metre
deca- da 10 10 decametre dam 10 metres
hecto- h 100 102 hectometre hm 100 metres
kilo- k 1000 103 kilometre km 1000 metres
Mega- M 1000 000 106 Megametre Mm 1000 000 metres
Length is the distance between two points. the standard unit is the metre (m), and the fractional and multiple units most commonly used are the millimetre (mm) and kilometre (km). the centimetre and decimetre are occasionally also used.
Area is a measure of size of a surface, and the standard units are the square metre (m2), square millimetre (mm2) and square kilometre (km2)
Volume is a measure of the size of a space, and the standard units include the cubic metre (m3), cubic millimetre (mm3) and cubic kilometre (km3), but also the litre, which is a cubic decimetre (dm3), or 1/1000 cubic metre (10-3m3)
Mass is a measure of the resistance to acceleration when a force is applied,[2] and the standard units are the gram (g), kilogram (kg) and tonne (1000kg)
Density
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Force
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Pressure
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Time is the measure of duration. The base unit is the second (s). Other standardised units are the minute (60 seconds) and hour (60 minutes, or 3600 seconds).
Temperature The standard unit is the Kelvin (K). The degree Celsius (°C) has the same magnitude, but a different zero point.

Section footnotes

1. This is not just being pedantic, getting the units wrong can have expensive or fatal consequences.
2. It is more complicated than this, but the details are not of practical importance

## Ambient pressure

Most commercial diving is done at ambient pressure. This means the pressure of the surrounding environment, and is the combination of the atmospheric pressure at the surface and the hydrostatic pressure of the liquid in which the dive is done. This concept can be extended to the pressurised interior of a diving chamber, a caisson, or any other pressurised environment. Whenever the diver is exposed to the pressure of the environment, that pressure is the ambient pressure for the diver at that time.

The exception to this is diving in single atmosphere suits, which maintain normal atmospheric pressure on the inside by using a rigid shell with pressure-resistant joints to isolate the external pressure. This is not within the scope of the SA Diving Regulations as the diver is not directly exposed to a raised pressure.

A pressure may be measured relative to the ambient pressure of the gauge casing, known as gauge pressure, or relative to a vacuum, known as absolute pressure. The subscript or suffix "gauge" or "g" may be used to indicate gauge pressure when the context does not make it clear, and the subscript or suffix "absolute", "abs", or "a" to indicate absolute pressure.

The usual symbol for pressure is P or p, and a pressure difference between two points may be indicated as delta P (ΔP, δP, etc), as delta is a general purpose symbol for a difference. A horizontal pressure difference in a fluid will cause it to flow.

## Gas laws

### Relationship between pressure and volume

For a fixed amount ${\displaystyle n}$ of an ideal gas at a constant temperature ${\displaystyle T}$, the absolute pressure ${\displaystyle P}$ is inversely proportional to the volume ${\displaystyle V}$. This is commonly known as Boyle's law.

${\displaystyle P\propto {\frac {1}{V}}}$

In other words the product of the absolute pressure and volume is constant.

This can be expressed as ${\displaystyle PV=k}$ where ${\displaystyle k}$ is a constant

or ${\displaystyle P_{1}V_{1}=P_{2}V_{2}}$, provided that ${\displaystyle T_{1}=T_{2}}$

This relationship is important for the understanding of barotrauma, and is useful for gas planning calculations.

### Relationship between pressure and temperature

The pressure of a fixed mass of an ideal gas at a constant volume is directly proportional to the gas's absolute temperature. This law is called Gay-Lussac's law of pressure and temperature but can also be referred to as Amontons's law of pressure and temperature.

${\displaystyle {P}\propto {T}}$

or

${\displaystyle {\frac {P}{T}}=k}$

where ${\displaystyle P}$ is the pressure of the gas, ${\displaystyle T}$ is the absolute temperature of the gas, and ${\displaystyle k}$ is a constant.

The law can be also written as:

${\displaystyle {\frac {P_{1}}{T_{1}}}={\frac {P_{2}}{T_{2}}}}$   or   ${\displaystyle {P_{1}}{T_{2}}={P_{2}}{T_{1}}}$

This describes the loss of pressure in a diving cylinder as the gas cools, and the rise in pressure if it is heated.

### Relationship between pressure and solubility of gases in liquids

The amount of a gas that can be dissolved at equilibrium (solubility) in a liquid is proportional to its partial pressure in the adjacent gas phase. If there is less dissolved gas, it will diffuse into solution, and if there is more, it will tend to diffuse out of solution into any adjacent gas phase. This is known as Henry's law. There are other factors influencing solubility of a gas in a liquid that are not influenced by the pressure, including the temperature and the specific gas and liquid involved. In diving, the proportionality of solubility to pressure is most important for understanding the principles of decompression.

### Composition of gas mixtures and the pressures of the components

Partial pressures and Dalton's law.

The symbol for pressure is usually P or p which may use a subscript to identify the pressure, and specific gases are also referred to by subscript. When combined these subscripts are applied recursively. This means that subscripts may have subscripts as far down as needed. Two levels is common, three not particularly unusual, four is uncommon, but there is no theoretical limit.

Examples:

${\displaystyle {P_{1}}}$ or ${\displaystyle {p_{1}}}$ = pressure at time 1 (one level of subscript)
${\displaystyle {P_{H_{2}}}}$ or ${\displaystyle {p_{H_{2}}}}$ = partial pressure of hydrogen (two levels)
${\displaystyle {P_{v_{O_{2}}}}}$ or ${\displaystyle {p_{v_{O_{2}}}}}$ = venous partial pressure of oxygen (three levels)

The alternative convention pp is often used for partial pressure as it is easier to type. The chemical symbol should still take the numbers of atoms as subscripts. Examples:

ppCO2 - partial pressure of carbon dioxide

When discussing partial pressures, all the pressures are absolute pressures. The total pressure of a mixture is what is measured by a pressure gauge. Gases can be mixed in any proportion, and once mixed, will stay mixed. It may take some time for complete mixing to occur, but once that has happened, the components will not separate again in ordinary circumstances. Breathing gases for diving are considered nonreactive at the temperatures and pressures at which they should be used.

Dalton's law is an empirical law of nature, it simply describes what has been observed to happen, but is happens consistently.

Dalton's law of partial pressures states that in a mixture of ideal, non-reacting gases, the total pressure exerted is equal to the sum of the partial pressures of the individual gases. This is because in an ideal gas the molecules are usually so far apart that they do not interact with each other except when colliding. The gases used in breathing mixes for diving behave close to this ideal at pressures below about about 250bar. At higher pressures they start to get close enough to start to have other interactions.

Ptotal = P1 + P2 + P3 + etc.

In a mixture of non-reactive gases, each gas has a partial pressure which is the pressure of that gas if it alone occupied the volume of the mixture at the same temperature. The total pressure of an ideal gas mixture is the sum of the partial pressures of each individual gas in the mixture. Partial pressure proportions match volumetric ratio proportions - If a gas component is 20% by volume, the partial pressure will be 20% of the total pressure. The partial pressure of a gas is a indication of the thermodynamic activity of the gas's molecules - the higher the partial pressure, the more likely a molecule will collide with something. Gases dissolve, diffuse, and react according to their partial pressures.

Partial pressures are important in gas blending, gas toxicity and decompression physiology.

### Composition of the atmosphere and breathing gases

The atmosphere is the layer of air that surrounds the Earth and is retained by Earth's gravity.

By volume, dry air contains approximately 78% nitrogen (N2), 20.9% oxygen (O2),1% argon (Ar), 0.04% carbon dioxide (CO2), and trace amounts of other gases. For diving calculations argon and nitrogen are grouped together at 79% Nitrogen, and oxygen is rounded to 21%, except when measuring oxygen content of a breathing gas mixture, when the analyser is calibrated to 20.9% in air for best accuracy.

Air also contains a variable amount of water vapor, on average around 1% at sea level. High pressure compressed air for underwater breathing has had most of the water removed by the compressor filter and separator systems, and contains far less water, so it can be ignored for calculations.

For the diver, the most important constituent of a breathing gas is the partial pressure of oxygen. This will vary according to the ambient pressure for any given mix. The composition of a breathing gas mixture is specified by the gas fractions, which are the proportions by volume of the significant components. Impurities must be below the legal limits, and as long as this is the case, can be safely ignored for most calculations.

Breathing gases for diving are usually one of the following:

Compressed and filtered normal atmospheric air
Compressed air enriched with Oxygen (Nitrox)
A compressed mixture of Air, Oxygen and Helium (Trimix)
A compressed mixture of Helium and Oxygen (Heliox)
Pure oxygen, for decompression at shallow depths

All of these mixtures are specified by the percentage by volume of the gases in the mix, which is also the proportion of the partial pressures. Therefore, Air is 21% O2, 79% N2. The most popular Nitrox mixtures are 32% O2, 68% N2 and 36% O2, 66% N2 for working dives. Trimix and Heliox usually have low fractions of oxygen to avoid oxygen toxicity as they are used for deeper diving.

## Effects of the temperature of the environment on the heat balance and equipment of the diver

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• Heat transfer in water - convection and conduction, specific heat etc. - common risk of hypothermia, occasionally hyperthermia
• Insulation of diving suit, helmet etc, choice of type.
• Active heating - hot water suits
• Pressure loss in scuba cylinders - not very significant
• Regulator freezing - hazard - risk of gas loss

## Effects of the underwater environment on illumination and vision

(Describe the effects of the underwater environment on illumination and visibility and sound and hearing including the impact on the safety of diver)

### Focus

Light changes direction when it crosses an interface from from one medium to another; the amount is determined by the incident angle to the interface and the refractive indices of the two media. If the interface has a curved shape, and the refractive indices differ, it functions as a lens. The cornea, humours, and crystalline lens of the eye together form a composite lens that focuses images on the retina. Our eyes are adapted for viewing in air. Water, however, has approximately the same refractive index as the cornea (both about 1.33), effectively eliminating the cornea's focusing properties when immersed. When our eyes are in water, instead of focusing images on the retina, they focus them far behind the retina, resulting in an extremely blurred image.

By wearing a diving mask or helmet with an air space between the viewport and the eyes, humans can see clearly under water. Light entering from water into the flat window changes direction minimally within the window material itself, But when the light exits the window into the air space between the flat window and the eye, the refraction is quite noticeable. Objects underwater will appear 33% bigger (34% bigger in salt water) and 25% closer than they actually are. The field of view is also affected. Also pincushion distortion and lateral chromatic aberration may be noticeable. Dome ported masks can restore natural sized underwater vision and field of view, with certain limitations.

Diving masks can be fitted with lenses for divers needing optical correction to improve vision. corrective lenses are ground flat on one side and optically cemented to the inside face of the mask lens. This provides the same amount of correction above and below the surface of the water. Bifocal lenses are also available for this application.

### Light in water

Close to the surface, in-water visibility is affected by the amount of daylight and the angle at which sunlight strikes the surface. When the sun is low, in winter in the higher latitudes or in the early morning or late evening, the sun strikes the surface at a low angle and a large proportion of the light is reflected. If the sea is rough, reflection in the surface layer is increased. After the diffused light has entered the water it is absorbed, scattered and reflected. The longer wavelengths of light (red, orange, yellow) are absorbed first as the light passes through the water. At about 10 m only green and blue wavelengths remain and the diver is effectively colour blind without artificial light. Scattering and reflection depend on the turbidity of the water. This is a measure of the number of fine particles suspended in the water. These particles may be sediment, plankton or any solid material. There may be seasonal or daily variations in turbidity. Plankton growth is greatest in the summer, the amount of sediment may vary with the strength and direction of the tidal current, or variations in the flow of a large river. The diver’s work can also affect turbidity by disturbing sediments. There are also variations with depth. The visibility of an object to the diver depends on the amount of light reaching his eyes and the contrast of the object with its background. In monochromatic conditions, where the diver has no artificial light to assist him, contrast depends solely on the relative brightness of object and background.

#### Colour

Comparison of penetration of light of different wavelengths in the open ocean and coastal waters

Water attenuates light due to absorption which varies as a function of frequency. In other words, as light passes through a greater distance of water color is selectively absorbed by the water. Color absorption is also affected by turbidity of the water and dissolved material.

Water preferentially absorbs red light, and to a lesser extent, yellow, green and violet light, so the color that is least absorbed by water is blue light. As a result of this, most of the natural light available at depth in clean water is blue. Particulates and dissolved materials may absorb different frequencies, and this will affect the color at depth, with results such as the typically green color in many coastal waters, and the dark red-brown color of many fresh water rivers and lakes due to dissolved organic matter.

Table of Light Absorption in pure water
Color Average wavelength Approximate depth of total absorption
Ultraviolet 300 nm 25 m
Violet 400 nm 100 m
Blue 475 nm 275 m
Green 525 nm 110 m
Yellow 575 nm 50 m
Orange 600 nm 20 m
Red 685 nm 5 m
Infra-red 800 nm 3 m

The best colors to use for visibility in water were shown by Luria et al. and quoted from Adolfson and Berghage below:

A. For murky, turbid water of low visibility (rivers, harbors, etc.)

1. With natural illumination:
a. Fluorescent yellow, orange, and red.(Fluorescence is the emission of light by a substance that has absorbed light or other electromagnetic radiation. It is a form of luminescence. In most cases the emitted light has a longer wavelength than the absorbed radiation, therefore a different colour, which results in greater contrast underwater.)
b. Regular yellow, orange, and white.
2. With incandescent illumination:
a. Fluorescent and regular yellow, orange, red and white.
3. With a mercury light source:
a. Fluorescent yellow-green and yellow-orange.
b. Regular yellow and white.

B. For moderately turbid water (sounds, bays, coastal water).

1. With natural illumination or incandescent light source:
a. Any fluorescent in the yellows, oranges, and reds.
b. Regular yellow, orange, and white.
2. With a mercury light source:
a. Fluorescent yellow-green and yellow-orange.
b. Regular yellow and white.

C. For clear water (southern water, deep water off shore, etc.).

1. With any type of illumination fluorescent paints are superior.
a. With long viewing distances, fluorescent green and yellow-green.
b. With short viewing distances, fluorescent orange is excellent.
2. With natural illumination:
a. Fluorescent paints.
b. Regular yellow, orange, and white.
3. With incandescent light source:
a. Fluorescent paints.
b. Regular yellow, orange, and white.
4. With a mercury light source:
a. Fluorescent paints.
b. Regular yellow, white.

The most difficult colors at the limits of visibility with a water background are dark colors such as gray or black.

#### Visibility

Visibility is a measure of the distance at which an object or light can be discerned. The standard measurement for underwater visibility is the distance at which a Secchi disc can be seen. In exceptionally clear water visibility may extend as far as about 80m. The range of underwater vision is usually limited by turbidity, and is affected by illumination (amount of light), colour and contrast.

#### Illumination

Illumination is the presence of light, and generally refers to the quality and quantity of light in terms of colour and intensity. Illumination underwater may be by natural or artificial lighting.

##### Natural

Natural light is daylight (sunlight), moonlight, starlight and bioluminescence, the light given off by living organisms. For practical purposes underwater, daylight is useful and moonlight can occasionally be useful, but is seldom bright enough for practical purposes of work. Natural light levels underwater dissipate with depth as described above, but daylight is often adequate for underwater work and navigation.

##### Artificial

Artificial lighting can restore natural colour and provide sufficient light to do necessary work. The capacity to illuminate the underwater worksite is usually limited by the clarity of the water. Artificial light sources may be carried by the diver (head-mounted or hand held), or deployed at the worksite by other means, including lowered on cables, attached to the bell or stage, and carried by a remotely operated vehicle. Often a combination of these methods is used. The advantage of lights carried by the diver is that they can be directed where the diver wants to look. Other methods of deployment may be capable of more intense and widely spread illumination. Monochrome light may be used for special purposes, but white light is most commonly used.

#### Impact on safety

A level of illumination sufficient to allow the diver to see and identify hazards, and to work effectively will improve safety, as the risk of inadvertently approaching a hazard or excessively extending time to do a job are reduced. Conversely, a bright light source directed into the diver's eyes may dazzle the diver and prevent the recognition of a hazard or effective work. This complication is more likely when two or more divers operate together, particularly when they carry head mounted lights, which are directed where the diver looks.

## Effects of the underwater environment on hearing

(Describe the effects of the underwater environment on illumination and visibility and sound and hearing including the impact on the safety of diver)

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### Transmission of sound

• Speed of sound
• Transmission through an interface
• Attenuation by headgear
• Identification of the direction of a sound source

### Noise levels of diving equipment

• difficulty with voice communication, exhalation noise on open circuit, inlet noise in free-flow.
• interference with ability to recognise external sounds
• effects on the environment. scares off some fish.

### Impact on diver safety

• Equipment noise may mask sounds which would alert the diver to hazards
• Reduced effectiveness of voice communications due to background equipment noise increases risk of communication failure in an emergency
• The diver may hear sounds associated with a hazard but not be able to identify the direction or distance of the source

## Buoyancy, Archimedes' principle and the apparent weight of immersed objects

Buoyancy is an upward force exerted by a fluid that opposes the weight of an immersed object.

The pressure in a fluid increases with depth as a result of the weight of the overlying fluid. Thus the pressure at the bottom of an object submerged in a fluid is greater than at the top of the object. This pressure difference results in an upwards force on the object proportional to the pressure difference, and is equivalent to the weight of the fluid that would otherwise occupy the volume of the object, i.e. the displaced fluid. (if the volume was occupied by the fluid it would be in equilibrium, so the forces must be equivalent)

For this reason, an object with an average density greater than that of the fluid in which it is submerged will have a buoyancy less than its weight and will tend to sink. If the object is either less dense than the liquid or is shaped appropriately to decrease its average density by including enough air in the displaced volume (as in a boat), the buoyancy force can keep the object afloat.

Archimedes' principle

Apparent weight of a negatively buoyant object is the net downward force exerted by the object while immersed. Also known as negative buoyancy (quantitative). like weight and buoyancy, it is a force and units of force are applicable. In diving the units used are generally kilogram-force and tonne-force for metric users (pounds and tonnes for Imperial system), but the units substituted in practice are often the kilogram and tonne, which are units of mass. This does not usually cause problems because the effects of gravity are sufficiently consistent to not cause any significant discrepancies. The usual significance of apparent weight to divers, is the amount of buoyancy that must be added to make the object neutrally buoyant.