Diffraction of Water on a Body of Revolution Along Several Meridians - Application to a Tank in the Sea

Abstract

This paper was prepared for the SPE-European Spring Meeting 1974 of the Society of Petroleum Engineers of AIME, held in Amsterdam, the Netherlands, May 29–30, 1974. Permission to copy is restricted to an abstract of not more than 300 words. Illustrations may not be copied. The abstract should contain conspicuous acknowledgment of where and by whom the paper is presented. Publication elsewhere after publication in the JOURNAL OF PETROLEUM TECHNOLOGY or the SOCIETY OF publication in the JOURNAL OF PETROLEUM TECHNOLOGY or the SOCIETY OF PETROLEUM ENGINEERS JOURNAL is usually granted upon request to the Editor PETROLEUM ENGINEERS JOURNAL is usually granted upon request to the Editor of the appropriate journal provided agreement to give proper credit is made. Discussion of this paper is invited. Three copies of any discussion should be sent to the Netherland Section of the Society of Petroleum Engineers, P. O. Box 228, The Hague, the Netherlands. Such discussion may be presented at the above meeting and, with the paper, may be considered for publication in one of the two SPE magazines. Abstract It is advantageous for tank or platform builders to be able to calculate platform builders to be able to calculate pressure distribution on a body of any pressure distribution on a body of any shape set on the bottom of floating. This model is an initial approach to the problem. It can be used to calculate pressure problem. It can be used to calculate pressure distribution, total force or moments on a solid of revolution set on the bottom or floating. For this, the fluid is assumed to be perfect, irrotational and non-viscous. We are thus working with linear conditions. The solution is calculated in a functional space of splines in the domain between the body and an arbitrary cylinder encompassing it. The solution is continued outside the cylinder as a Bessel function series. Introduction For offshore structures, it appears more and more necessary to be in possession of sufficiently accurate and possession of sufficiently accurate and reliable mathematical models. The existence of very powerful computers such as the CDC 7600, for which this model has been programmed, thus makes it possible to programmed, thus makes it possible to consider methods which, although requiring relatively extensive calculating, give more accurate and complete results than in the past. This study was made for the Association de Recherche "Action des Elements" which we hereby thank for having allocated to us the necessary funds and for authorizing publication. PHYSICAL HYPOTHESIS PHYSICAL HYPOTHESIS The fluid is assumed to be: * Irrotational, incompressible, nonviscous. * The pressure at the free surface is also assumed to be constant. Under such conditions, there exists a velocity potential phi (x, y, z). So that : in which u, v, w are the velocities components on x, y and z axis. One can show 1 that phi thus checks out: delta phi = 0 which is associated with the Bernoulli's equation :