Aerodynamics for Engineers

TLDR

External flow around a low‑resistance body produces large pressure changes that generate most lift and part of drag, though the simplifying assumptions of incompressibility may conflict with experiment, yet engineers still employ graphical methods to solve specific problems. The article investigates steady, incompressible, inviscid external flow around a body, ignoring boundary‑layer effects. The authors analyze the flow analytically in two dimensions, treating the boundary layer as infinitesimally thin so it only permits relative velocity at the surface. They find that air‑flow past a short, low‑resistance body consists of a thin viscous boundary layer and a largely inviscid outer region, with Bernoulli’s equation accurately predicting pressures, leading to a theory that closely matches real aerofoil behavior and has many practical applications.

Abstract

WE found, on experimental grounds in Article I, that the field of air‐flow past a short body of low resistance shape, such as an aerofoil, comprises two dissimilar parts: ( a ) a thin boundary layer enveloping the body and dominated by viscous effects, and ( b ) a motion outside the boundary layer in which viscosity is much less important. It will be remembered that in the external motion occur the large pressure changes, which, transmitted through the boundary layer, account for nearly all the lift and for part of the drag. These pressures we observed to be calculable from the velocities without appreciable error by Bernoulli's equation. In the present Article we confine attention to this external flow, assuming it to be steady, incompressible, and inviscid. Its dependence upon ( a ), already discussed to some extent, we ignore; the boundary layer is conceived to be everywhere very thin, so that the only role it plays is to allow of relative velocity at the surface of the body. The assumptions made, excepting that of incompressibility, will appear drastic, and it will not be surprising if some of our deductions prove discordant with experimental fact. Nevertheless, they lead to a theory which finds many applications and uses in real fluid motion, and, in particular, gives an intimate view of aerofoil flow that is very close to the truth. It is convenient to develop our reasoning in analytical terms and for simplicity to restrict the flow to two dimensions (Article 1, §5). But the engineer will find special scope in this part of aerodynamics for graphical methods in the solution of particular problems.