ON THE REGULATION OF HYDRAVLIC FORCES. ~ 3ii 1 



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, with 

 less machinery than from another which moves more slowly. In general the 

 velocity 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 always 

 be equal in effect to the weight of a portion of the stream employed, equal in 

 length to the height of the wheel. In order to avoid the resistance which 

 might be occasioned by the stagnant water below the wheel, it is a good 

 practice 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. (Plate 

 XXII. Fig. 290.) 



If we suffer the stream of water to acquire the utmost velocity that the 

 whole fall can produce, and to strike horizontally against the floatboards of 

 an undershot wheel, or if we wish to employ the force of a river running in a 

 direction nearly horizontal, the wheel must move, in order to produce the 

 greatest effect, with half the velocity of the stream. For the whole quantity 

 of 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, and 

 hence it is easy to calculate that the greatest possible effect will be produced 

 when the relative velocity of the stream, striking the floatboards, is equal to 

 the velocity of the wheel itself. The pressure on the floatboards is equal to 

 that of a stream containing the same quantity of water, and striking a fixed 

 obstacle with half the velocity, that is, such a stream as escapes from the 

 wheel, 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, of 

 twice the height due to its velocity, that is, of half the height of the fall, 

 being, as we have already seeri, the measure of the hydraulic pressure, this 

 force Avill be precisely half as great as that of a similar column, acting on an 

 overshot wheel, which moves with the same velocity. But the stream thu.s 

 retarded will not retain the other half of its mechanical power; since its 

 greatest effect will be in the same proportion to that of an equal stream acting 

 on an overshot wheel with one fourth of the fall of the former : and the re- 

 maining fourth of the power is lost in producing the change of form of the 

 water and in overcoming its friction. In whatever way we apply the 

 4brce of water, we shall find that the mechanical power which.it possesses 



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