Page:Aerial Flight - Volume 1 - Aerodynamics - Frederick Lanchester - 1906.djvu/421

Rh the fluid as incompressible, we suppose the enclosure to possess some degree of elasticity so as to exert on the fluid a pressure sufficient to prevent cavitation, then the peripheral pressure will undergo no change in consequence of the vortices, for a change of pressure on the walls of an elastic enclosure must be accompanied by a compression or dilatation of the fluid contents. Under these conditions the greater the energy of the vortex system set up in the fluid the lower will become the pressure in the internal part of the region, so that the plus and minus momentum of the equal and opposite flow taking place across any imaginary barrier plane is accounted for by the ordinary static pressure on the confines of the region, and does not give rise to any added pressure.

If we suppose the enclosure rigid and the fluid elastic, the change of pressure due to the vortices on the boundary walls depends upon the  law of elasticity, and is not a function of the magnitude or energy of the vortex system alone. The result of the above reasoning is not at all in harmony with accepted views as to the behaviour of vortices as expounded in the Vortex Atom theory. According to the highest authorities the individual vortices carry momentum just as if they were bodies of greater density than the fluid that contains