The Physics of Diving NOAA Diving Manual Fourth Edition

The Physics of Diving

NOAA Diving Manual

Fourth Edition


• Types of pressure • Buoyancy

• Density • Gases used in diving

• Specific Gravity • Gas Laws

• pH • Humidity

• Properties of water • Light

• Units of measurement • Sound

Overview

• Physics is the field of science dealing with matter and energy and their interactions.

• This presentation explores physical laws and principles that pertain to the diving environment and its influence on the diver.

• The principles of physics provide the keystone for understanding the reasons for employing various diving procedures.

Student Performance

After reviewing this presentation you will be able to:• Define the different types of pressure measurements

associated with diving• Recognize the affect of a variety of environmental factors

and explain how they impact the diver.• List the Gas Laws associated with scuba diving.• Explain each of the Gas Laws; explaining how each

pertains to scuba diving.• Demonstrate your understanding of each of the Gas

Laws by being able to solve problems germane to a scuba diving related scenarios.

Pressure

“Pressure is force acting on a unit area”

• Pressure = force / area• P = F/A• In the USA pressure is typically measured in pounds per

square inch (psi).• Underwater a diver is affected by 2 types of pressure

– The pressure exerted by the atmosphere– The pressure exerted by the surrounding water

• A diver, at any depth, must be in pressure balance (equilibrium) with the forces at that depth.

Atmospheric Pressure

• This is the pressure exerted by the earth’s atmosphere.

• At sea level it is equal to 14.7 psi, or one atmosphere (atm).

• It decreases with altitude above sea level.• For example, at 18,000 ft. atmospheric pressure

is 7.35 psi or half that at sea level.• An pressure inside an individual’s lungs at sea

level are at equilibrium with the surrounding pressure – 1 atm

Hydrostatic Pressure

• This pressure is created by the weight of water - called “hydrostatic pressure”.

• This pressure is cumulative. The deeper the dive, the more water above the diver and the greater the weight of the water.

• Hydrostatic pressure affects the diver from all sides equally.

Hydrostatic Pressure

• In seawater:– hydrostatic pressure increases at a rate of .445 psi

per foot you descend.– One ata (14.7 psi) of hydrostatic pressure is reached

at a depth of 33 feet sea water (fsw) & increases one atm for every additional 33 fsw thereafter.

• In freshwater:– hydrostatic pressure increases at a rate of .432 psi

per foot you descend.– One ata (14.7 psi) of hydrostatic pressure is reached

at a depth of 34 feet fresh water (ffw) & increases one atm for every additional 34 ffw thereafter.

Absolute Pressure

• The sum of atmospheric pressure plus hydrostatic pressure is called “absolute pressure”.

• It can be expressed as: “psia” (pounds per square inch absolute), “ata” (atmospheres absolute), “fswa” (feet of seawater absolute), “ffwa” (feet of freshwater absolute), or “mmHga” (millimeters of mercury absolute.

Gauge Pressure

• The difference between atmospheric pressure and the pressure being measured is “gauge pressure”.

• The “zero psi” reading on a scuba cylinder pressure gauge at sea level is actually equal to 14.7 psi.

• Gauge pressure + 14.7 = ata

Partial PressureDalton’s Law

• In mixture of gases, the proportion of the total pressure contributed by each gas in the mixture is called the “partial pressure”.

• For our purposes air is composed of 21% oxygen and 79% nitrogen.

Density

“Density can be defined as weight per unit volume”

• Density = Weight / Volume or D = W / V• Density is expressed in lbs/ft3 or g/cm3

• Gas density is related to absolute pressure.• Density is directly proportional to pressure

– As depth increases, the density of the breathing gas and becomes heavier per unit volume.

Density

• Seawater has a density of 64 pounds per cubic foot.

• Freshwater has a density of 62.4 pounds per cubic foot.

• As a result, freshwater floats on top of seawater – a diver is more buoyant, given the same

conditions, in seawater than in freshwater.

Specific Gravity

• Specific gravity is the ratio of the weight of a given volume of a substance (density) to that of an equal volume of another substance.– Water is the standard for liquids and solids.– Air is the standard for gases.

• Freshwater has a specific gravity of 1.0– Substances that are more dense than freshwater

have a specific gravity greater than 1.0.

• The specific gravity of seawater is 64/62.4 = 1.026

Water

• Freshwater (H2O):

– is odorless, tasteless and very slightly compressible.

– It freezes at 32oF (0C), and boils at 212oF (100C).

– In its purest form, it is a poor conductor of electricity.

Water

• Seawater:– Contains almost every substance known.– The most abundant chemical is sodium

chloride (common table salt).– Seawater is a good conductor of electricity.

pH

• The pH of an aqueous solution expresses the level of acids or alkalis present.

• The pH of a liquid can range from 0 (strongly acidic) to 14 (strongly alkaline).

• A pH of 7 is considered neutral• The pH level in the blood is what signals the

brain the need to breathe.– Too much CO2 causes the blood to become acidic.

One way the body reduces the acidity is to increase ventilations

Units of Measurement

• There are two systems for specifying force, length and time: the English system and the International System of Units (SI). – also known as Metric.

• The English System is based on the pound, the foot, and the second.– Primarily use in the United States

• The International System of Units is based on the kilogram, the meter, and the second.– Used everywhere else

Length

• 1 meter = 39.37 in = 3.28 ft

• To convert 10 feet to meters:– 10 ft / 3.28 ft/m = 3.05 m

• Convert 10 meters to feet:– 10 m X 3.28 ft/m = 32.8 ft

Area

• In both the English and IS system, area is expressed as a length squared.

• For example: – A room that is 12 feet by 10 feet would have

an area of 120 square feet (12 ft x 10 ft).– A room that is 3.66 m by 3.05 m would have

an area of 11.16 square meters.

Volume

• Volume is expressed in units of length cubed.

• Length x Width x Height = cubic feet (ft3) or cubic meters (m3)– The English System, in addition to ft3, uses

other units of volume such as gallons.– The SI uses the liter (l). A liter = 1000 cubic

centimeters (cm3) or .001 cubic meters (m3), which is one milliliter (ml).

Weight

• The “pound” (lb) is the standard measure of weight in the English System.

• The “kilogram” (kg) is the standard measure of weight in the International System of Units.

• One liter of water at 4C weighs 1 kg or 2.2 lbs.– 1liter (l) = 1 kg = 2.2 lbs

Weight(conversions)

• Convert 180 pounds to kilograms:– 180 lbs / 2.2 lbs/kg = 81.8 kg

• Convert 82 kilograms to pounds:– 82 kg X 2.2 lbs/kg = 180.4 lbs

Temperature

• Heat is associated with the motion of molecules.

• The more rapidly the molecules move, the higher the temperature.

• Temperature is usually measured either with the Fahrenheit (°F) scale or with the Celsius (centigrade) scale (C).

Temperature

• Temperature must be converted to absolute when the gas laws are used.

• The absolute temperature scales, which use Rankine (R) or Kelvin (K), are based on absolute zero (the lowest temperature that can possibly be reached).

• Note that the degree symbol (°) is only used with Fahrenheit temperatures.

Temperature(conversions)

• The Fahrenheit (°F) and Rankine (R) temperature scales are used in the English System.– To convert Fahrenheit to absolute temperature Rankine

• oF + 460 = R

• The Celsius (C) and Kelvin (K) temperature scales are used in the International System of Units.– To convert Celsius to absolute temperature Kelvin

• C + 273 = K

Temperature(conversions)

• To convert from Fahrenheit to Celsius– C = 5/9 X (oF – 32)

• To convert from Celsius to Fahrenheit– oF = (9/5 X C) + 32

Heat

• An often forgotten but extremely important consideration in diving

• Humans can only function effectively in a very narrow range of internal temperatures.

• Maintaining the proper body core temperature is critical– This can be don’t by utilizing the proper

exposure protection suit

BuoyancyArchimedes’ Principle

“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”

Buoyancy

• “Positive” Buoyancy is achieved if the weight of the displaced water (total displacement) is greater than the weight of the submerged object.– Object floats

• “Negative” Buoyancy is achieved if the weight of the displaced water (total displacement) is less than the weight of the submerged object. – Object sinks

• “Neutral” Buoyancy is achieved if the weight of the displaced water (total displacement) is equal to the weight of the water.– Object is suspended)

Buoyancy

• Buoyancy is dependent upon the density of the surrounding liquid.

• Remember:– Seawater has a density of 64 pounds per

cubic foot.– Freshwater has a density of 62.4 pounds per

cubic foot.

Gases Associated with Diving• Atmospheric Air - 21% O2 + 79% N2

• Oxygen - O2

– The most important of all gases.– Usually used for decompression gas

• Nitrogen – N2

• Helium – He– Used extensively in deep diving

• Carbon Dioxide – CO2

– A natural by-product of metabolism • Carbon Monoxide – CO

– A poisonous gas – produced by the incomplete combustion of fuels• Argon – Ar

– Not very common in diving• Neon – Ne

– Not very common in diving• Hydrogen – H2

– Not very common in diving

Gas Laws

• Boyle’s Law

• Charles’/Gay-Lussac’s Law

• Dalton’s Law

• Henry’s Law

• General Gas Law

Gas LawsBoyle’s Law

“For any gas at a constant temperature, the volume of the gas will vary inversely with the pressure”


P1V1 = P2V2

P1= initial pressure surface absolute

V1= initial volume in cubic feet

P2=final pressure absolute

V2=final volume in cubic feet


• Determine the volume (V2) of a 24 ft3 open bottom diving bell with at 66 fsw:

P1 = 1 ata

V1 = 24 ft3

P2 = 3 ata

V2= (P1V1) / P2

V2 = (1 ata x 24 ft3) / 3 ata

V2 = 8 ft3

Gas LawsCharles’/Gay-Lussac’s Law

“For any gas at a constant pressure, the volume of the gas

will vary directly with the absolute temperature or for any gas at a

constant volume, the pressure of the gas will vary directly with the

absolute temperature.”

Gas LawsCharles’ Law

Volume Change

(pressure remains constant)

V1 / V2 = T1 / T2

V1 = volume initial

T1 = temperature initial

V2 = volume final

T2 = temperature final


Volume Change

A balloon with 24 ft3 of air is lowered in water to a depth of 99 fsw. Surface temperature is 80oF; temperature at depth is 45oF. What

will the volume of the balloon be at 99 fsw?

V1 / V2 = T1 / T2 (pressure remains constant)

V1 = volume initial T1 = temperature initial

V2 = volume final T2 = temperature final


Volume Change

Boyle’s law determines that the balloon will have a volume of 6 ft3 at 99 fsw.Determine how temperature affects this volume.

V2 = (V1T2)/T1

V1 = Vol. @ 99 fsw = 6 fsw V2 = unknown

T1 = 80o F + 460 = 540 Rankine T2 = 45o F + 460 = 505 Rankine

V2 = (6 ft3 X 505 R) / 540 R = 5.61 ft3

Gas LawsGay-Lussac’s Law

Pressure Change

(volume remains constant)

P1 / P2 = T1 / T2

P1 = pressure initial

T1 = temperature initial

P2 = pressure final

T2 = temperature final


Pressure Change

A scuba cylinder contains 3000 psig (3014.7 psia) at 64oF. After being left in the Sun the reaches 102oF. What is the new pressure?

P1 / P2 = T1 / T2 (volume remains constant)

P1 = pressure initial = 3014.7 psia

T1 = temperature initial = 64oF + 460 = 524 Rankine

P2 = pressure final = unknown

T2 = temperature final = 102oF + 460 = 562 Rankine


Pressure Change

P2 = (P1T2) / T1

P2 = (3014.7 psia X 562 R) / 524 R

P2 = 3233.3 psia

To convert to gauge pressure

3233.3 psia – 14.7 psi = 3218.6 psig

Gas LawsDalton’s Law

“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.”


Pt = PP1 + PP2 + PP3, etc

Pt = Total Pressure

PP1 = Partial Pressure of first gas

PP2 = Partial Pressure of second gas

PP3 = Partial Pressure of third gas, etc


What is the partial pressure of the nitrogen in a scuba cylinder filled with air to a pressure of 2000 psig?

PN2 = Gas % (decimal) X Pt

PN2 = .78 X 2000 psig

PN2 = 1561.6 psig

Gas LawsHenry’s Law

“The amount of any gas that will dissolve in a liquid at a given

temperature is proportional to the partial pressure of that gas in

equilibrium with the liquid and the solubility coefficient of the gas in

the particular liquid.”


VG / V L = oc P1

VG = Volume of a gas dissolved at STPD

(standard temperature pressure dry)

VL = Volume of gas in the liquid

oc = Solubility coefficient at specific temperature

P1 = Partial pressure of that gas above the gas


• When a gas free liquid is exposed to a gas mixture, gas molecules

diffuse into the solution, pushed by the partial pressure of each

individual gas.

• “Gas Tension” – as the gas molecules enter the liquid they add to a

state of gas tension, a way of identifying the partial pressure of the

gas in the liquid.

• “Pressure Gradient” - The difference between the gas tension and

the partial pressure of the gas outside the liquid.


• When the gradient for diffusion is high combined with low tension

and high partial pressure the rate of absorption into the liquid is

high.

• As the number of gas molecules in the liquid increases, the gas

tension increases until it reaches an equilibrium value equal to the

outside partial pressure.

• “Saturated” - the point of equilibrium described above.

Gas LawsGeneral Gas Law

• Commonly called the “Ideal Gas Law”

• Used to predict the behavior of a given quantity of gas when changes may be expected in any or all of the variables

• Combines– Charles’ Law – Boyle’s Law


(P1 V1) / T1 = (P2 V2) / T2

P1 = initial pressure (absolute)

V1 = initial volume

T1 = initial temperature (absolute)

P2 = final pressure (absolute)

V2 = final volume

T2 = final temperature (absolute)


A open diving bell with an air volume of 24 ft3 is lowered to 99 fsw. Surface temperature is

80oF and temperature at depth is 45oF. What will be the air volume of the bell at depth?


(P1 V1) / T1 = (P2 V2) / T2

or

V2 = (P1 V1 T2) / (T1 P2)

P1 = initial pressure (absolute) = 14.7 psia

V1 = initial volume = 24 ft3

T1 = initial temperature (absolute) = 80o F + 460 = 540 Rankine

P2 = final pressure (absolute) = 4 ata x 14.7 psia = 58.8 psia

V2 = unknown

T2 = final temperature (absolute) = 45o F + 460 = 505 Rankine


V2 = (14.7 psia)(24 ft3)(505 R)

(540 R)(58.8 psia)

V2 = 5.61 ft3

The volume was reduced, due to the drop in temperature and the increase in

ambient pressure.

Humidity

• Water vapor (a gas) behaves in accordance with the gas laws.

• The water vapor condenses at temperatures we are likely to encounter while diving, hence humidity is an important consideration– Mask fogging

Light

• Human eyes can only perceive a very narrow range of wave lengths (visible light)

• Water slows the speed at which light travels. – This causes the light rays to bend or refract– with a mask on the light rays are bent twice

• Objects appear 25 % larger.• Turbidity can also effect vision by making

objects appear farther than it really is.

Light

• Colors– Water absorbs light according to its

wavelength• Red is the first color lost• Blue eventually become the dominant color at

deeper depths

– As depth increases the ability to discern colors decreases until visible objects are distinguishable only by differences in brightness. Contrast becomes the most important factor.

Sound

• Sound is produced by pressure waves triggered by vibration

• The more dense the medium through which sound travels, the faster the speed of sound.

• Sound travels roughly 4 times faster in water than in air– This makes detecting the origin of the sound

very difficult.


Review of the chapter:

• Hydrostatic and atmospheric pressure both influence the diver.

• The density of the water, fresh vs. salt, affects the buoyancy of a diver.

• Depth affects the density of the gas being breathed thus affecting the rate of consumption.

• Measurements can be given in either the English System or the International System of Units.

• There are 5 different gas laws which explain the behavior of gases in a diving environment.

• Humidity, Light and Sound are all affected by the density of water

Documents

The Physics of Diving NOAA Diving Manual Fourth Edition