Page:Aerial Flight - Volume 1 - Aerodynamics - Frederick Lanchester - 1906.djvu/81

Rh this law is capable of more general demonstration, in which case the form of the curve (in an infinite region) will be limited to a minimum index of 1.5 and the straight line stage will disappear.

It is to be expected in any case that in actual experiment the ordinary viscous law will be found to apply for very low velocities on account of the fact that the size of the vessel containing fluid in which the experiment is performed cannot be made infinite, and for very low velocities the viscous stress or part thereof will be carried across to the walls of the vessel. Under these circumstances the condition that the reaction of the viscous substance shall be borne by its own inertia will not apply; it is consequently of importance that experiments should be conducted in as large a tank as can be conveniently employed.

§ 45. Consequences of interchangeability of V and l.—It is evident that the general results relating to the form of the curve which have been deduced from the obvious relations of resistance and velocity apply to the less obvious relationship of resistance and linear dimension, owing to the interchangeability of V and l previously demonstrated (§ 42); we therefore see that—

For small similar bodies, obeying the viscous law, the resistance varies with the linear dimension, that is as the square root of their area.

For bodies of larger size, the resistance may be found to vary as the 1.5 power of the linear dimension, that is as the .75 power of the area.

For bodies of very large size, the resistance will approach to vary as the linear dimension squared, that is directly as the area.

For planes moving tangentially it would appear possible that the latter condition is never attained but that some lower power may prove to be the limiting condition.

§ 46. Comparison of Theory with Experiment.—The foregoing theory receives substantial support from the experimental work of Froude, Dines, Allen and others.