Pressure Volume Relationship
Objectives
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Explain Boyle's law.
Define pressure in general terms.
Compare atmospheric, hydrostatic pressure, and
absolute pressure.
Correctly calculate absolute pressure for any depth of
fresh or salt water
Correctly calculate pressure/volume relationships for a
gas in a flexible container at any depth of fresh or salt
water.
Correctly calculate the volume of gas in a cylinder of
known volume, given a change in pressure.
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Boyle’s Law:
– Volume varies inversely with absolute
pressure.
– Density varies directly with absolute
pressure.
Pressure
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Definition
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Force per unit area.
Atmospheric Pressure
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Force exerted by the air column above us.
14.7 psi at sea level = 1 atm.
Hydrostatic Pressure
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Force exerted by the water column above us.
Every 33' of sw = 1atm. (increase per foot of depth = .445 psi)
Every 34' of fw = 1 atm. (increase per foot of depth = .432 psi)
Absolute Pressure
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Sum of atmospheric and hydrostatic pressure.
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Can be expressed as
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Atmospheres absolute (ATA)
Psi absolute (PSIA)
Example 1
• Calculate the Absolute Pressure, in
psia, at 61 feet in the ocean.
Answer:
Hydrostatic Pressure
Atmospheric Pressure
Absolute Pressure
=
.445psi/ft x 61 ft = 27.14 psi
=
14.7 psi
=
41.84psia
Example 2
Calculate the Absolute Pressure at 99' in the ocean in terms of ATA.
Method 1
Use the formula (Depth + 33)/33
Depth = (99+33)/33 = 132/33 =
4ATA
Method 2
Use the formula (Depth/33) + 1 = Depth ATA
Depth ata = (99/33) + 1 = 3atm +1atm = 4ata
Method 3
99 x .445psi = 44.055psi + 14.7psi = 58.7psi/14.7psi= 4ATA
Pressure/Volume Relationship
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Formula
– P1 x V1 = P2 x V2
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P1 = Original Pressure
V1 = Original Volume
P2 = New Pressure
V2 = New Volume
Example 1
A BC has 6 quarts of air at the surface and is submerged
to 49' of fresh water. What will the volume of air be at this
depth?
Answer:
P1 =
Pressure at the surface = 1atm
= 14.7psi
V1 =
Volume at the surface given as
= 6 quarts
P2=
49ffw x .432psi/ffw = 21.162psi + 14.7psi = 35.9psia
V2 = ?
Example 1 continued
Using P1 V1 = P2 V2
14.7psi x 6 quarts = 35.9 psia x V2
(14.7psi x 6 quarts) / 35.9psia = V2
88.2/35.9 = V2
2.45 quarts = V2
Example 2
A BC has 6 quarts of air at the surface and is submerged to
49 ffw. What will the volume of air be at this depth?
P1 =
Pressure at the surface
V1 =
Volume at the surface given as
P2=
(49ffw +34ffw) / 34ffw
V2 = ?
= 1atm
= 6 quarts
= 2.44 atm
Example 2 Continued
Using P1 V1 = P2 V2
1 atm x 6 quarts = 2.44 atm x V2
(1 atm x 6 quarts) / 2.44 atm = V2
6 / 2.44 = V2
2.46 quarts = V2
Volume of air in a cylinder
The volume of air in a cylinder is determined by the pressure of the gas
in the cylinder and the internal volume of the cylinder. As the pressure
in the cylinder drops, the volume of gas decreases. When you know
the working pressure and volume of a cylinder, you can calculate the
volume for any given pressure.
This is done using the formula P1 / V1 = P2 / V2.
Calculations require that we cross multiply and divide
However, you must convert P1 and P2 to absolute pressure by adding
14.7 psi.
Example 1
A cylinder contains 50 cubic feet of air at a pressure of
3000psig. If the temperature remain constant,
approximately how many cubic feet of air remain in the
cylinder at 2000psig
P1 =
3000 psig + 14.7 psi =
3014.7 psia
V1 =
50 cu. ft.
P2 =
2000 psig + 14.7 psi =
2014.7 psia
V2 = ?
Example 1 continued
Use P1/V1 = P2 /V2 (remember to cross multiply and divide)
3014.7 psia = 2014.7 psia
50 cu. ft.
V2
3014.7 psia x V2 = 2014.7 psia x 50 cu. Ft.
3014.7 psia x V2 = 100735
V2 = 100735/3014.7
V2 = 33.4 cu. ft.