Response of Liquid in a Rectangular Container

On ignition of the rocket engines of the Saturn V Rocket, a surge wave is created at the discharge side of a large reservoir of liquid of a sound suppressor system. For the design of this system, the wave motion and the pressure distributions, as well as the liquid forces and moments, have to be known to approximately describe the effect of the suction created by the firing of the rocket engines at the discharge side. One container side wall performs a single pulse motion. The response of the ideal liquid in a rectangular container to a rectangular double and sinusoidal pulse has therefore been treated. This was accomplished by first obtaining the response of the liquid to harmonic excitation of one container wall, thus obtaining the admittance with which the pulse excitation could be determined with the help of Fourier integrals. After obtaining the velocity potential, the free surface elevation, pressure distributions, liquid forces, and moments were determined by differentiation and integration with respect to time and spatial co-ordinates. The results are represented for a rectangular double pulse in graphical form.