Page:Aerial Flight - Volume 1 - Aerodynamics - Frederick Lanchester - 1906.djvu/27

Rh If, in place of a real fluid possessing continuity, we had supposed the enclosure filled with the medium of Newton, then momentum would have been communicated in sum to the particles of the medium, and the resistance could be calculated in the manner already demonstrated.

If we take away the condition that the enclosure is fixed and suppose the force applied from without, then the problem is not essentially altered, for though the external force F will now impart momentum to the system en bloc, its action in this respect has no relation to phenomena in the interior, and does not provide any data for the determination of the pressure-velocity relation.

The supposition that the body is a plane evades any question relative to the density of the body itself, and thus simplifies the argument. This question could also be eliminated by supposing the body to possess the same density as the surrounding fluid; in any case a force applied to the body to overcome its inertia is a matter external to, and without influence on, the conditions.

The foregoing proposition cannot depend in any way upon the viscosity or otherwise of the fluid; the existence of viscosity can affect the mode of transmission of the force and the velocity of the body that accompanies its transmission, but can have no influence on the total force transmitted. It is thus apparent that no momentum is imparted to an actual fluid in the sense that it is imparted to the Newtonian medium, and this is the real cause of the difficulty in the application of the Newtonian method.

The principle here demonstrated is referred to in the present work as the "Principle of No Momentum."

§ 6. Illustrations of the Principle of No Momentum.—The foregoing proposition is of moment in connection with several problems in fluid dynamics, and presents the subject in an aspect that is somewhat unfamiliar. Its import may be pointed by the following illustrations.