as it would do in a properly formed streamline body, but shoots past the sharp edge, as indicated in the figure. The region in the rear of the body, Z, is filled with fluid that does not partake of the general flow, and which is termed dead-water.
The resistance experienced by bodies of imperfect form is due to the work done on the fluid, which is not subsequently given back, as is the case with the streamline body. This resistance can be traced to two causes, namely, excess pressure on the surface in presentation and diminished pressure in the dead-water region. The former is of dynamic origin, the energy being
Fig. 7.
expended in directly impressing motion on portions of the fluid; the latter is due to the entrainment or viscous drag experienced by the dead-water at the surface bounded by the live stream. It is generally believed that, in a fluid whose viscosity is negligible, the latter cause would be inoperative, the whole resistance being then due to the excess pressure region in front of the body, the dead-water or wake being at approximately the hydrostatic pressure of the fluid.
The surface separating the live stream and the dead-water constitutes a discontinuity, since the velocity of the fluid, considered as a function of its position in space, is discontinuous. This case is not one of a physical discontinuity, such as discussed in § 12, for the region on either side of the surface is filled with the same kind of fluid; it is rather a kinetic discontinuity, that is to say a discontinuity of motion.
§ 20. The Doctrine of Kinetic Discontinuity.—The theory of kinetic discontinuity is of modern origin, having been introduced
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