Page:Encyclopædia Britannica, Ninth Edition, v. 12.djvu/481

465 HYDRAULICS.] HYDROMECHANICS 465 hi in feet. ho hi in feet. 0856 164 328 650 1-640 3-28 4-02 6 56 9-84 A ) 480 511 542 574 599 601 601 601 601 B } 0-656 480 510 538 566 592 600 602 602 601 of 527 553 574 592 607 610 610 609 608 A) 488 577 624 631 625 624 619 613 606 B } 0164 487 571 606 617 626 628 627 623 618 oj 585 614 633 645 652 651 650 650 649 24. Inversion of the Jet. &quot;When a jet issues from a horizontal orifice, or is of small size compared with the head, it presents no marked peculiarity of form. But if the orifice is in a vertical surface, and if its dimensions are not small compared with the head, it undergoes a series of singular changes of form after leaving the orifice. These were first investigated by Bidone ; subsequently Magnus measured jets from different orifices; and lately Lord Rayleigh (Proc. Roy. Soc., xxix. 71) has investigated them anew. Fig. 28 shows some remarkable forms, the upper row giving the shape of the orifices, and the others sections of the jet. The jet first contracts as described above, in consequence of the convergence c Fig. 27. of the fluid streams within the vessel, retaining, however, a form similar to that of the orifice. Afterwards it expands into sheets in planes perpendicular to the sides of the orifice. Thus the jet from a triangular orifice expands into three sheets, in planes bisecting at right angles the three sides of the triangle. Generally a jet from an orifice, in the form of a regular polygon of n sides, forms n sheets in planes perpendicular to the sides of the polygon. Bidone explains this by reference to the simpler case of meeting streams. If two equal streams having the same axis, but moving in opposite directions, meet, they spread out into a thin disk nov- e Fig. 28. mal to the common axis of the streams. If the directions of two streams intersect obliquely they spread into a symmetrical sheet perpendicular to the plane of the streams. - -{-=^|=5S Now those portions of f a jet which y&amp;gt;roceed ~ from different portions of an orifice are con ceived to behave in some degree like in dependent meeting streams. Let fflj, a. 2 (fig. 29) be two points in an ori fice at depths h :, h 2 from the free surface. The filaments issuing ata,, a. 2 will have the Fig- 29. different velocities f2gh } and /2gh. 2 . Consequently they will tend to describe parabolic paths a^ and a 2 c& 2 of different horizontal range, and intersecting in the point c. But since two filaments cannot simultaneously flow through the same point, they must exercise mutual pressure, and will be deflected out of the paths they tend to describe. It is this mutual pressure which causes the ex pansion of the jet into sheets. Lord Rayleigh has pointed out that, when the orifices are small and the head is not great, the expansion of the sheets in directions per pendicular to the direction of flow reaches a limit. Sections taken at greater distance from the orifice show a contraction of the sheets until a compact form is reached similar to that at the first contrac tion. This is shown in the elevation of the jet c. Beyond this point, if the jet retains its coherence, sheets are thrown out again, but in directions bisecting the angles between the previous sheets. Lord Rayleigh accepts an explanation of this contraction first suggested by Buff, namely, that it is due to surface tension or capillarity. The fluid is enclosed in an envelope of constant tension, and the recurrent form of the jet is due to vibrafionsof the fluid column, about a circular figure of equilibrium, superposed on the general progressive motion. Since the phase of vibration de pends on the time elapsed, it is always the same at the same point in space, and thus the motion is steady and the boundary of the jet is a fixed surface.