The internal ballistics of a leaking gun

The dynamical problem of the motion of the shot in the gun, which is rendered complicated as it has to take account of  the irreversible processes in the gun such as the physical shot-start pressure, the bore resistance and the heat-loss to the barrel, and the flow of the gas behind the shot. In the theory of an orthodox gun, the effect of the gas-flow is taken, account of by the so-called ‘Lagrange corrections.