ON THE REGULATION OF HYDRAULIC FORCES.

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that would be practically convenient: and it is obvious, on the other hand,that a certain velocity may be procured from a wheel moving rapidly, withless machinery than from another which moves more slowly. In general thevelocity of the surface of the wheel is between two and six feet in a second ;and whether it be greater or smaller, the force actually applied will alwaysbe equal in effect to the weight of a portion of the stream employed, equal inlength to the height of the wheel. In order to avoid the resistance whichmight be occasioned by the stagnant water below the wheel, it is a goodpractice to turn the stream backwards upon its nearer half, so that the water,when discharged, may run off in the general direction of its motion. (PlateXXII. Fig. 290.)

If we suffer the stream of water to acquire the utmost velocity that thewhole fall can produce, and to strike horizontally against the floatboards ofan undershot wheel, or if we wish to employ the force of a river running in adirection nearly horizontal, the wheel must move, in order to produce thegreatest effect, with half the velocity of the stream. For the whole quantityof water impelling the floatboards is nearly the same, whatever may be the ve-locity, especially if the wheel is properly inclosed in a narrow channel, andhence it is easy to calculate that the greatest possible effect will be producedwhen the relative velocity of the stream, striking the floatboards, is equal tothe velocity of the wheel itself. The pressure on the floatboards is equal tothat of a stream containing the same quantity of water, and striking a fixedobstacle with half the velocity, that is, such a stream as escapes from thewheel, which must be twice as deep or twice as wide as the original stream,since its motion is only one half as rapid; and a column of such a stream, oftwice the height due to its velocity, that is, of half the height of the fait,being, as we have already seen, the measure of the hydraulic pressure, thisforce will be precisely half as great as that of a similar column, acting on anovershot wheel, which moves with the same velocity. But the stream thusretarded will not retain the other half of its mechanical power; since itsgreatest effect will be in the same proportion to that of an equal stream actingon an overshot wheel with one fourth of the fall of the former : and the rc- \maining fourth of the power is lost in producing the change of form of thewater and in overcoming its friction. Tn whatever way we apply theforce of water, we shall find that the mechanical power which it possesses

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