Boyle's Law

Air is a gas. Gases have various properties which we can observe with our senses, including the gas pressure (p), temperature, mass, and the volume (V) which contains the gas. Scientific observation has determined that these variables are related to one another, and the values of these properties determine the state of the gas.

In the mid 1600's, Robert Boyle studied the relationship between the pressure p and the volume V of a confined gas held at a constant temperature. Boyle observed that the product of the pressure and volume are observed to be nearly constant. The product of pressure and volume is exactly a constant for an ideal gas.

p * V = constant

This relationship between pressure and volume is called Boyle's Law in his honor.

In diving Boyle's Law applies to the expansion and contraction of gases within the body due to external pressure changes.

If the pressure starts out as one atmosphere at the surface, it increases linearly with depth under water depending upon the density of the water:

P_ATA = 1 + (depth/kappa)
where kappa depends on the density of the water and units of depth:

	Value of kappa
	Depth in feet	Depth in meters
fresh water	33.8	10.3
sea water	33.1	10.1

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Dalton's Law

Dalton's Law states that in a mixture of n gases the partial pressure of each gas [Pi] is proportional to the molar fraction of each gas [Yi] that makes up the total:

P_Total = P₁ + P₂ + ... + P_n = Y₁P_Total + Y₂P_Total + ... + Y_nP_Total

Dalton's Law can be used to determine how much nitrogen, oxygen, or carbon dioxide is in the ambient air at any hyperbaric pressure underwater.

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Henry's law

Henry's Law states a gas will dissolve into a liquid in proportion to its partial pressure in the air and its solubility in the liquid.

A formula for Henry's Law is:

eP = ekC
where P is the partial pressure of the gaseous solute above the solution, C is the concentration of the gas in mol/L and k is the Henry's Law constant, which has the units L*atm/mol.

Henry's Law can predict the body's absorption of inert gases into and back from the body at any pressure or depth.

Table 1 Increasing severity of nitrogen narcosis symptoms with depth in feet and pressures in atmospheres.(1,3,6)
Depth	P Total	P N2	Symptoms
100	4.0	3.0	Reasoning measurably slowed.
150	5.5	4.3	Joviality; reflexes slowed; idea fixation.
200	7.1	5.5	Euphoria; impaired concentration; drowsiness.
250	8.3	6.4	Mental confusion; inaccurate observations.
300	10.	7.9	Stupefaction; loss of perceptual faculties.

Table 2 Symptoms and terminology of DCS.
Location of Bubbles	Symptom(s)	DCS Type	Common Term
Joints	Pain upon flexure.	I	Bends
Skin	Altered skin sensation, itching, or rash.	I
Brain-spine	Dizziness, headache, loss of coordination, weakness.	II	Staggers
Chest	Cough, dyspnea, pain upon breathing.	II	Chokes

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Buoyancy

Buoyancy is a physical law that was discovered by the Greek mathematician and inventor Archimedes in the third century BC. The principle, called Archimedes' principle, states that any body floating or submerged in a fluid (gas or liquid) is buoyed upward by a force equal to the weight of the displaced fluid. Balloons rise because the air pressure acting upward against it is greater than the pressure above that is pushing downward.

The buoyancy is numerically equal to the weight of the fluid (air in the case of a balloon) displaced. An object surrounded by air (like a balloon) is buoyed upward by a force equal to the weight of the air displaced. If the mass of the object is less than the weight of an equal volume of air, the object rises. If the weight of the object is greater than the mass of an equal volume of air, it falls.

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