LECTURE XXIV.

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glides along the convex surface, because it finds a readier passage in the neigh-bourhood of the solid, towards which it is urged by the impulse of the parti-cles of the air approaching it on one side, and by the delect of pressure on theother side, occasioned by the removal of a certain portion of the air which itcarries with it. (Plate XXI. Pig. 270, 271.)

Prom considerations similar to those by which the velocity of a river is de-termined, we may calculate the quantity of water discharged from a pipe olany given dimensions, and in any position. The same expressions will servefor estimating the magnitude of the friction in both cases; the pipe beingconsidered as a small-river, of which the mean depth is one fourth of its dia-meter: but a part only of the force of gravity is now expended in overcomingthe friction, the rest being employed in producing the momentum of thewater. We may obtain a sufficiently accurate determination of the velocity,by supposing the height of the reservoir above the orifice of the pipe to bediminished in the same proportion as the diameter of the pipe would be in-creased by adding to it one fiftieth part of the length, and finding the wholevelocity corresponding to four fifths of this height. Thus, if the diameterof the pipe were one inch, and its length 100 inches, we must suppose theeffective height to be reduced to one third by the friction,and the discharge mustbe calculated from a height four fifths as great as this,which may be consideredas a reduction derived from the interference of the particles, entering the pipe,with each other’s motions. If the diameter of the pipe had been two inches,the height must only have been supposed to be reduced to one half by thefriction; such a pipe would, therefore, discharge about five times as mu ehwater as the former, although of only twice the diameter; and this circum-stance requires the attention of all those who are concerned in regulating thedistribution of water by pipes for domestic use, or for any other purpose.

In such cases it becomes also frequently necessary to attend to the ang^ cin which a small pipe is inserted into a larger; whenever a pipe is bent, the ,cis a loss of force according to the degree of flexure, and to the velocity of fh ewater, which may be calculated, if it be required; but if a pipe be fixed i nt °another through which the water is moving very rapidly, in a direction co 11trary to that of the stream, its discharge will not only be much smaller tl>:mif the directions more nearly coincided, hut sometimes such a pipe will <h*