Navier-Stokes equations

Abstract

System (17.1) can be derived by the analogous system for compressible flows introduced in Chapter 16 by assuming ρ constant, using the continuity equation (which, under current assumptions, takes the simplified form divu = 0) to simplify the various terms, and finally dividing the equation by ρ. Note that in the incompressible case (17.2) the energy equation has disappeared. Indeed, even though such an equation can still be written for incompressible flows, its solution can be found independently once the velocity field is obtained from the solution of (17.1).