380

LECTURE XXIII.

stream contracts itself, after it has passed the orifice, for the distance of abouthalf its diameter, so that at this point its thickness is only four fifths asgreat as at its passage; and the quantity discharged is only five eighths asgreat as that which the whole orifice would furnish, according to the preced-ing calculation: instead,therefore,of multiplying the square root of the heightby 8, we may employ the multiplier 5 for determining the actual discharge.But the velocity, where the stream is most contracted, is only one thirtiethless than that which is due to the whole height; and when the jet is dis-charged in a direction nearly perpendicular, it rises almost as high as the sur-face of the thud in the reservoir.

This contraction of the stream, and the consequent diminution of thedischarge, is unquestionably owing to the interference of the particles of thefluid coming from the parts on each side of the orifice, with those which aremoving directly towards it; and the effect is more perceptible when the orificeis made by a pipe projecting within the reservoir, so that some of the particlesapproaching it must acquire in their path a motion contrary to that of thestream. It would be possible to obtain an approximate calculation of themagnitude of this contraction, from the equilibrium which must subsist be-tween the centrifugal forces of the particles, as they pass out of the orifice,describing various curves, according to their various situations, and the pres-sure required for the contraction of the internal parts of the stream, whichobliges the particles to move more rapidly as they proceed, and which mustbe proportional to the height required for producing this acceleration.(Plate XX. Fig. 255.)

When a short cylindrical tube is added to the orifice, it is probable that themotion of the fluid within the tube is still in some measure similar : but thevessel must now be supposed to be prolonged, and to have a new orifice at theend of the tube, at which the particles cannot arrive by any lateral motions,and which will, therefore, not be liable to a second contraction : the dischargemay, therefore, be estimated nearly according to the true measure of thisorifice; the original pressure of the fluid continuing to act until the strearuescapes.

The effect of a short pipe, in increasing the discharge, ceases when the