ON fUK FItICTION OF FLUIDS,

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the fluids, which, where it exists, is a force nearly uniform, like that offriction, bat principally from the irregular motions and mutual collisions oftheir particles ; and in this case, according to the laws of mechanics, it mustvary nearly in proportion to the square of the velocity. For when a body>s moving in a line of a certain curvature, the centrifugal force is always asthe. square of the velocity; and the particles of water in contact with the sidesand bottom of a river or pipe, must be deflected, in consequence of theminute irregularities of the surfaces on which they slide, into nearly the samecurvilinear paths, whatever their velocity may be,so that the resistance, which18 in great measure occasioned by this centrifugal force, must also vary as thesquare of the velocity. Thus also the curvature assumed by the outline of astream of water issuing from a simple orifice, which constitutes the contrac-tion already described, is very nearly the same, whatever the velocity maybe: nor does the friction increase with the pressure, as is demonstrated bya n experiment of Professor Robison on the oscillations of a fluid through abent tube, terminated by two bulbs, which were performed in the same time,Whether the tube was in a horizontal or in a vertical position. Mr. Coulombbas also proved the same fact by experiments on the vibrations of bodies'mmersed in fluids, and suspended by twisted wires; he finds that preciselya t the surface, the friction is somewhat greater than at any depth below it:be also considers a certain part of the friction as simply proportional to thev elocity, and a very small portion only, in common fluids, as perfectly inde-pendent of it.

It is obvious that wherever the friction varies as the square of the velocity,

0r even when it increases in any degree with the velocity, there must alwaysa limit, which the velocity can never exceed, by means of any constant*°vce, and this limit must be the velocity at which the resistance would be-c °nie equal to the force. It is for this reason that a light body, descendingtrough the air, soon acquires a velocity nearly uniform ; and if it be caused,

V any external force, to move for a time more rapidly, it will again be speed-retarded, until its velocity be restored very nearly to its original state.

11 the same manner the weight of the water in a river, which has once aofluued a stationary velocity, is wholly employed in overcoming the frictionInduced by the bottom and the banks.

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