however, that if there is no residuary disturbance there is no necessary expenditure of energy, and this equally implies that the resistance is nil.
The fluid in the vicinity of a streamline body is of necessity in a state of motion and contains energy, but this energy is conserved, and accompanies the body in its travels, just as in the case of the energy of a wave. It adds to the kinetic energy of the body in motion just as would an addition to its mass.
According to the mathematical theory of Euler and Lagrange, all bodies are of streamline form. This conclusion, which would otherwise constitute a redactio ad absurdum, is usually explained on the ground that the fluid of theory is inviscid, whereas real fluids
Fig. 2.
possess viscosity. It is questionable whether this explanation alone is adequate.
§ 10. Froude's Demonstration.—An explanation of the manner of the conservation of kinetic energy, in the case of a stream-line body, has been given by the late Mr. W. Froude.
Referring to Fig. 2, A. B. C. D. E, represents a bent pipe, through which a fluid is supposed to flow, say in the direction of the lettering, the direction at A and at E being in the same straight line; it is assumed that the fluid is frictionless. Now so long as the bends in the pipe are sufficiently gradual, we know that they cause no sensible resistance to the motion of the fluid. We have excluded viscous resistance by hypothesis, and if the areas at the points A and E are equal there is no change in the kinetic energy. Moreover, the sectional area of the pipe between
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