Page:Aerial Flight - Volume 1 - Aerodynamics - Frederick Lanchester - 1906.djvu/143

Rh § 94. Discontinuous Flow.—Up to this point the assumption has been made that the continuity of the fluid cannot be broken. As a working hypothesis, the fluid has been defined as capable of sustaining stress in tension; it has at the same time been pointed out that the equivalent result may be obtained by supposing the fluid to be subjected from without to a hydrostatic pressure superior to the greatest negative pressure (tension) due to its motion at any point throughout the region.

We will now suppose that the fluid is not capable of sustaining tension, and that the external hydrostatic pressure is either wanting or is insufficient to prevent cavitation.

The importance of studying these conditions does not rest so much upon the possibility of actual cavitation, as upon the general resemblance of the resulting systems of flow to those encountered where real fluids are concerned. It is evident that the void regions in the examples we are about to discuss may be supposed filled either with some different fluid, or even with inert masses of the same fluid as that in which the motion is taking place.

§ 95. Efflux of Liquids.—A typical example of motion with a free surface is presented in the efflux of liquids. When a liquid escapes from an orifice under pressure, the surfaces of the jet so formed, and its interior a short distance away from the point of discharge, are at atmospheric pressure (presuming the experiment is conducted under ordinary conditions), and the velocity can therefore be predicted, knowing the pressure within the vessel. If we suppose the pressure to be applied by a head of liquid in the vessel, then whatever quantity of liquid passes out of the jet disappears from the region of the free surface, so that if we assume the “principle of work,” and suppose there to be no loss of energy, the velocity of the jet will be that due to a body falling freely from the height of the column of fluid measured from the point of discharge to the free surface. This is the theorem of Torricelli.