Wave Motions in Non-Viscous Fluids

Abstract

In Chaps. 9 and 10, fluid flows were considered whose analytical treatment was possible by employing simplified forms of the generally valid basic equations of fluid mechanics. The solution methods required for this are known, i.e. they are at everybody’s disposal, and it is known that they can be successfully employed to solve flow problems. Thus in Chap. 10, for example, the application of methods was shown which permit the solutions of the basic equations of fluid mechanics in order to obtain solutions to one- and two-dimensional flow problems. In particular, in Chap. 10 potential flows were dealt with whose given properties were chosen such that methods of functional theory can be employed to treat analytically two-dimensional and irrotational flow problems. Hence, the special properties of potential flows made it possible to take a fully developed domain of mathematics into fluid mechanics and to employ it for computing potential flows and their potential and streamlines. From these computed quantities, velocity fields of the treated potential flows could be derived. The employment of the mechanical energy equation, in its integral form, finally led to pressure distributions in the considered flow fields. The latter again led to the computations of forces and moments for pre-chosen control volumes. Lift and drag forces were considered that are of particular interest for the solution of engineering problems. Simplifications of the flow properties by introducing two-dimensionality and irrotationality have thus permitted a closed treatment of flow problems with known mathematical methods.