Initial Pressure, Initial Flow Velocity, and the Time Dependence of Crater Depth in Fluid Impacts

An explicit expression for the velocity potential governing the flow produced by impact of a liquid drop against a liquid is given. With use of this velocity potential, an equation is derived from which the cavity depth and the velocity of the cavity wall, for various times after the instant of impact, can be obtained. With use of this velocity potential an expression for the initial pressure in the fluid is also obtained. Good agreement is found between calculated and observed values of cavity depth at various times after the instant of impact and between the calculated initial pressure and the water-hammer pressure.