Effects of a water hammer and cavitation on jet formation in a test tube

We investigate the motion of a gas-liquid interface in a test tube induced by a large acceleration via impulsive force. We conduct simple experiments in which the tube partially filled with a liquid falls under gravity and hits a rigid floor. A curved gas-liquid interface inside the tube reverses and eventually forms a so-called focused jet. In our experiments, there arises either vibration of the interface or an increment in the velocity of the liquid jet, accompanied by the onset of cavitation in the liquid column. These phenomena cannot be explained by a considering pressure impulse in a classical potential flow analysis, which does not account for finite speeds of sound or phase changes. Here we model such water-hammer events as a result of the one-dimensional propagation of a pressure wave and its interaction with boundaries through acoustic impedance mismatching. The method of characteristics is applied to describe pressure-wave interactions and the subsequent cavitation. The model proposed is found to be able to capture the time-dependent characteristics of the liquid jet.