Abstract
Abstract
This chapter explains the relationship between vector fields and complex integration. It begins by defining the concepts of flux and work. Although the chapter primarily focuses on two-dimensional flows, it is important to mention the concept of flux in three dimensions. If a fluid is flowing through ordinary space, it no longer makes sense to speak of the flux across a curve, but it does make sense to speak of the rate at which the fluid crosses a surface. The total flux is then obtained by integrating this quantity over the whole surface. Just as in two dimensions, the incompressibility of a three-dimensional flow is equivalent to the statement that all closed surfaces (that do not contain sources or sinks) have vanishing flux. The chapter then considers the complex potential.
Publisher
Oxford University PressOxford
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