Page:Aerial Flight - Volume 1 - Aerodynamics - Frederick Lanchester - 1906.djvu/153

Rh (e) Due to imperfection of boundary conditions (as suggested by Kelvin).

(f) Defect of mathematical hypothesis concerning the nature of an inviscid fluid.

(g) The mathematical demonstration in error.

(h) The experimental observations in error.

(j) Some unaccounted physical conditions.

By a process of exhaustion we dispose of (g), (h), and (j) as highly improbable; (c) and (d) must be considered as insufficient in view of the fact that no cavitation is in general manifest, and a surface of gyration or discontinuity or vortex motion without an internal boundary involves rotation. Alternative (e), suggested by Lord Kelvin, does not seem cap)able of accounting for the facts known to experiment. It seems evident, under ordinary circumstances, that the boundary conditions are a sufficient approximation to theory.

§ 104. The Author's View.—The true explanation is probably to be sought in (1) (b). In all real fluids the influence of viscosity accounts for the departure; and the departure is greater the less the viscosity.

This seems paradoxical; it would appear to denote a sudden change in the behaviour of a fluid when viscosity becomes zero. Such a change would involve discontinuity in the physical properties of a substance, which is scarcely admissible; this paradox is only apparent, for the factor of time is involved in the production of the discontinuous system of flow, and, as will be subsequently shown, the continuity of behaviour extends to the fluid of zero viscosity.

The following conclusions may be formulated:

(1) That whatever may be the value of the viscosity, the initial motion from rest obeys the Eulerian equations.