12-2 Boyle’s law

BOYLE’S LAW

Boyle’s law states that at constant temperature, the absolute pressure 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.

The formula for expressing Boyle’s law is:

C * V
Where:
 

C   is      constant
P   is      absolute pressure
V  is       volume
 

Boyle’s law can also be expressed as:

P1V1       =     P2V2
 

Where:
P1  = initial pressure
V1  = initial volume
P2  = final pressure
V2  = final volume
 

When working with Boyle’s law, absolute pressure may be measured in atmospheres absolute. To calculate absolute pressure using atmospheres absolute:

Sample Problem 1. The average gas flow requirements of a diver using a MK 21 MOD 1 UBA doing moderate work is 1.4 acfm when measured at the depth of the diver. Determine the gas requirement, expressed in volume per minute at surface conditions, for a diver working at 132 fsw.
                   

1. Rearrange the formula for Boyle’s law to find the initial volume (V1):
   

2. Calculate the final pressure (P2):
   

3. Substitute known values to find the initial volume (V1):
   

4. The gas requirement for a diver working at 132 fsw is 7.0 acfm.
    

Sample Problem 2. TDetermine the gas requirement, expressed in volume per minute at surface conditions, for a diver working at 231 fsw.

1. Rearrange the formula for Boyle’s law to find the initial volume (V1):
   

2. Calculate the final pressure (P2):
   

3. Substitute the known values to find the initial volume (V1):
   

The gas requirement for a diver working at 231 fsw is 11.2 surface acfm.
 

Sample Problem 3. Determine the gas requirement, expressed in volume per minute at surface conditions, for a diver working at 297 fsw.

1. Rearrange the formula for Boyle’s law to find the initial volume (V1):
   

2. Calculate the final pressure (P2):
   

3. Substitute the known values to find the initial volume (V1):
   

The gas requirement for a diver working at 297 fsw is 14.0 surface acfm.
 

Sample Problem 4. An open diving bell of 100-cubic-foot internal volume is to be used to support a diver at 198 fsw. Determine the pressure and total surface equivalent volume of the helium-oxygen gas that must be in the bell to balance the ambient water pressure at depth.

1. Calculate the final pressure (P2):
   

2. Rearrange the formula to solve for the initial volume (V1)::
         

3. Substitute the known values to find the initial volume (V1):

                  

There must be 700 ft3 of helium-oxygen gas in the bell to balance the water pressure at depth.

Sample Problem 5. The open bell described in Sample Problem 4 is lowered to 297 fsw after pressurization to 198 fsw and no more gas is added. Determine the gas volume in the bell at 297 fsw.

1. Calculate the final pressure (P2):
   

2. Rearrange the formula to solve for the final volume (V2):
   

3. Substitute the known values to find the final volume (V2):