Some Features of Viscous Flows

Abstract

Theoretical investigations into fluid mechanics in the last century were mainly based on the ideal fluid, i.e. a fluid which is inviscid and incompressible. It is only since this century that the effects of viscosity and compressibility have been taken into account in any great way. In the flow of inviscid fluids, no tangential forces (shear stresses) exist between adjacent layers; only normal forces (pressures) do. This is equivalent to saying that an ideal fluid does not oppose a change in its shape with any internal resistance. The theory of flows of ideal fluids is mathematically very highly developed and indeed in many cases gives a satisfactory description of real flows, as for example, in the cases of wave motion and the formation of liquid jets. On the other hand, the theory of ideal fluids is useless when faced with the problem of calculating the drag of a body. It predicts that a body moving subsonically and uniformly through an infinitely extended fluid will experience no drag (D’Alembert’s paradox).