Chapter 12 - Flow of Ideal Fluid

Abstract

When the Reynolds number Re is large, because the diffusion of vorticity is now small and the boundary layer is very thin, the overwhelming majority of the flow is the main flow. Consequently, although the fluid itself is viscous, it can be treated as an ideal fluid subject to Euler's equation of motion, thus disregarding the viscous term. In other words, the applicability of ideal flow is large. For an irrigational flow, the velocity potential can be defined, so this flow is called potential flow. Originally the definition of potential flow did not distinguish between viscous and nonviscous flows. In the case of two-dimensional flow, a stream function can be defined from the continuity equation, establishing a relationship where the Cauchy–Riemann equation is satisfied. This fact allows theoretical analysis through the application of the theory of complex variables. Then, velocities in x and y directions can be obtained, and the nature of the flow is revealed.