Mathematical Analysis of a Vibrating Rigid Water Tank
Amin H. Helou
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The hydrodynamic pressure distribution on the wall of a vibrating water tank is traditionally expressed as a summation of two components; an impulsive component and a convective one obtained by separating the potential function into two parts. This requires solving Laplace's equation in two stages each with a separate set of boundary conditions. The following is one step systematic solution to the problem in a frame moving with the tank. It proves to be simple, compact and could lead to the impulsive, frequency independent and the convective, frequency dependent components of pressure at the water tank wall.