this is represented diagrammatically in Fig. 88. It is evident that the plane that causes the greater displacement of the lines of flow will experience the greater pressure.
Fig. 88.
(3) The viscous drag on the dead water will be greater when the periphery is greater. Thus, the pressure on the rear face of the plane will be less, that is, the vacuum will be greater for planes of elongate or erratic form.
§ 140. Comparison with Efflux Phenomena.—An analogous case illustrating the foregoing principles is to be found in the efflux of fluids under pressure (§§ 95–96). In the case of a jet issuing from a simple circular orifice we have a case of three-dimensional motion, and as the flow takes place inwardly the layers of fluid in the vicinity of the orifice will be fed by a greater stream area than would be the case if the orifice had the form of a slit and the motion in two dimensions; the “spurting” at the edge will therefore be more vigorous and the contraction of the jet will be greater. This is found experimentally to be the case, the coefficient of contraction being usually taken, for the circular aperture, as from .615 to .620, whereas for a slit aperture it is found to be about .635, On the principles discussed in § 95, the greater the jet contraction the less the pressure is relieved on the wall of the vessel in the vicinity of the orifice.
We may follow the comparison further. In the case of the Borda nozzle the access of the fluid to the jet is improved by the arrangement of an inwardly projecting “lip” so that the pressure on the wall of the vessel undergoes next to no reduction, and the coefficient of contraction becomes (theoretically) = .5 or by experiment .515.
