Page:Aerial Flight - Volume 1 - Aerodynamics - Frederick Lanchester - 1906.djvu/420



"Principle of No Momentum," enunciated as a proposition in § 5 of the present work, constitutes so far as the author is aware an innovation in the treatment of problems in fluid dynamics.

The proof of this proposition, indeed the principle itself, is so perfectly simple and obvious, that it is not without some hesitation that it is put forward as new. The consideration of the following examples, involving the simple application of the principle, and leading to results which certainly are not generally recognised, would seem to leave no doubt as to the fact.

Example 1.—The Vortex Atom Theory of Kelvin gives considerable trouble in the light of the Principle of No Momentum.

If the fluid be supposed incompressible and of uniform density in its parts, and if we suppose for example a single vortex ring in motion in a rigidly bounded region, it manifestly cannot carry momentum (§ 5), and equally the momentum of a number of such rings must be zero. It is of course possible that such a ring or number of rings may raise the peripheral pressure of the region, that is, the pressure on the walls of the enclosure, but the case of an incompressible fluid and a rigid enclosure is in this respect an indeterminate problem. Thus if, still regarding