We have this fax completely neglected the fact that all fluids possess viscosity. This property gives rise to tangential frictional forces at the boundaries of a moving fluid and to dissipation within the fluid as the “lumps” of fluid shear against one another. The regions where viscosity significantly alters the flow from that given by inviscid irrotational theory are confined to narrow or thin domains termed boundary layers along the surfaces moving through the fluid or along those held fixed in an onset flow. The tangential component of the relative velocity is zero at the surface held fixed in a moving stream and for the moving body in still fluid all particles on the moving boundary adhere to the body.

The resulting detailed motions in the thin shearing layer are complicated, passing from the laminar state in the extreme forebody through a transitional regime (due to basic instability of laminar flow) to a chaotic state referred to as turbulent. We do not calculate these flows.

In what follows we show that viscous effects are a function of a dimensionless grouping of factors known as the Reynolds number and review the significant influences of viscosity in terms of the magnitude of this number upon the properties of foils as determined by measurements in windtunnels at low subsonic speeds.

PHENOMENOLOGICAL ASPECTS OF VISCOUS FLOWS

The equations of motion for an incompressible but viscous fluid can be derived in the same way as for a non-viscous fluid, cf. Chapter 1, p. 3 and sequel, but now with inclusion of terms to account for the viscous shear stresses.