Nonlinear Impulsive Force on an Accelerating Container

The nonlinear theory developed by Chwang [1] is applied to calculate the hydrodynamic pressure force on an accelerating rectangular or circular container. The fluid inside the container is initially at rest and the motion of the container is impulsive. During the initial stage of this impulsive motion, no travelling free-surface waves are present, and the fluid simply piles up on one side of the container and subsides on the opposite side. When the horizontal displacement of the container is small in comparison with the horizontal dimension of the container as well as the undisturbed fluid depth, the small-time expansion method is applied to obtain the velocity potential of the fluid which is accurate up to and including the third-order solution. The second-order free surface elevation is found to be singular along the contact line between the fluid and the container wall.