INTRODUCTION 



In the work of the David Taylor Model Basin a need was felt some twenty 

 years ago for a collection of the known types of the potential flow of frictionless 

 fluids having a uniform and invariable density. The following report was intended 

 to meet that need in a form convenient for reference. 



In Chapter I the chief principles needed in dealing with the potential flow 

 of a frictionless fluid are described. In this chapter, but not elsewhere, variation 

 of the fluid density is sometimes allowed. In Chapter II the use of mathematical 

 complex functions in dealing with two-dimensional problems is explained. Then 

 Chapter III deals with two-dimensional cases and Chapter IV with three-dimensional 

 cases. Sometimes boundary conditions in the form of vortices or vortex lines are 

 allowed. Chapter V lists coefficients of inertia. 



The fluid velocity in potential flow is assumed to equal the negative grad- 

 ient of the velocity potential, as in the textbooks of Lamb and of Milne-Thomson. 

 An older assumption was that the velocity equals the -positive gradient of the 

 potential. The formulas given in this report can be adapted to this older assump- 

 tion by reversing in all formulas either the potential or all of the fluid velocities 

 wherever these occur. 



It was found necessary, however, to limit somewhat the field that is covered. 

 The extensive literature in which incidental use is made of potential flow in treating 

 'practical flow problems is not even listed. Curved line vortices have not been 

 included, nor interacting spherical boundaries, nor the thin curved stratum that is 

 discussed in Article 80 of Lamb's Hydrodynamics. 



This report was finished during the last war, but its great volume was con- 

 sidered to make publication impractical at that time. Publication has finally been 

 effected. No additions have been made, however, to take account of literature 

 published since the war. 



