Modeling the exit velocity of a compressed air cannon

The use of compressed air cannons in an undergraduate laboratory provides a way to illustrate the connection between diverse physics concepts, such as conservation of momentum, the work-kinetic energy theorem, gas expansion, air drag, and elementary Newtonian mechanics. However, it is not clear whether the expansion of the gas in the cannon is an adiabatic or an isothermal process. We built an air cannon that utilizes a diaphragm valve to release the pressurized gas and found that neither process accurately predicts the exit velocity of our projectile. We discuss a model based on the flow of air through the valve, which is in much better agreement with our data.