1 - Brief review of basic hydrodynamic theory

Summary

An extensive, highly mathematical literature exists dealing with fluidmechanical aspects of ship propellers.

Invariably, the mathematical developments are only outlined, impeding easy comprehension even by knowledgeable readers. Our aim is to elucidate the mathematical theory in much greater detail than is generally available in extant papers. In this context, the first three chapters are provided as aids for those who have not had extensive practice in the application of classical hydrodynamical theory to flows induced in fluids by the motions of bodies. The fluid of interest is water which is taken to be incompressible and inviscid. Modifications arising from viscosity are described in a later chapter (Chapter 7) through reference to experimental observations.

This review begins with the derivation of the concept of continuity or conservation of mass at all points in sourceless flow and proceeds to the development of the Euler equations of motion. In the restricted but important class of irrotational motions (zero vorticity) Laplace's equation for the velocity potential is obtained. The remainder of this chapter is devoted to derivations of fundamental solutions of Laplace's equation in two and three dimensions.

It is emphasized that these first two chapters are necessarily limited in scope, being directed to our needs in subsequent chapters. There are many excellent books which should be consulted for those seeking greater depth and broader description of hydrodynamic theory. Among these we suggest Batchelor (1967), Lamb (1963), Lighthill (1986), Milne-Thomson (1955), and Yih (1988), and Newman (1977) for modern applications.