Rocket Science, Part 2
The Ideal Gas Law
An English physicist, named Robert Boyle (a contemporary of Newton) worked with the compression and expansion of gases during the mid 1600’s and discovered that there was a direct proportionality between the pressure in a sealed container and it’s volume. For example if we took a sealed cylinder with a movable piston in one end and started with some initial pressure, after we compressed the gas to half it’s volume by pressing the piston into the cylinder, the final pressure would be twice the original starting pressure. This relationship can be written as:
 Figure 1 Larger volume, lower pressure.
Smaller volume, higher pressure. |
where P1 is the initial pressure, P2 is the final pressure, V1 is the initial volume of gas, and V2 is the final volume of gas. Solving for the final pressure, P2 gives us:
If we expel a small amount of water, dV from the rocket, the volume of air inside the bottle will expand by the same amount. Therefore:
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which we can substitute into the previous equation to yield:
This gives us a way of calculating the pressure in the bottle at any time during the launch. All we need to know is the starting pressure, P1 , the starting volume of compressed air in the bottle, V1 , and how much water has been ejected, dV , in the amount of time since the rocket has been launched.
