h2 − h1
in feet		 h1 in feet.
.0656 .164 .328 .656 1.640 3.28 4.92 6.56 9.84
A 0.656 .480 .511 .542 .574 .599 .601 .601 .601 .601
B .480 .510 .538 .506 .592 .600 .602 .602 .601
C .527 .553 .574 .592 .607 .610 .610 .609 .608
A 0.164 .488 .577 .624 .631 .625 .624 .619 .613 .606
B .487 .571 .606 .617 .626 .628 .627 .623 .618
C .585 .614 .633 .645 .652 .651 .650 .650 .649
Fig. 23.

§ 25. Inversion of the Jet.—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 G. Bidone (1781-1839); subsequently H. G. Magnus (1802-1870) measured jets from different orifices; and later Lord Rayleigh (Proc. Roy. Soc. xxix. 71) investigated them anew.

Fig. 23 shows some forms, the upper figure 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 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 normal 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.

Fig. 24.

Let a1, a2 (fig. 24) be two points in an orifice at depths h1, h2 from the free surface. The filaments issuing at a1, a2 will have the different velocities √ 2gh1 and √ 2gh2. Consequently they will tend to describe parabolic paths a1cb1 and a2cb2 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 expansion of the jet into sheets.

Lord Rayleigh pointed out that, when the orifices are small and the head is not great, the expansion of the sheets in directions perpendicular 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 contraction. 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 H. Buff (1805-1878), namely, that it is due to surface tension.

§ 26. Influence of Temperature on Discharge of Orifices.—Professor VV. C. Unwin found (Phil. Mag., October 1878, p. 281) that for sharp-edged orifices temperature has a very small influence on the discharge. For an orifice 1 cm. in diameter with heads of about 1 to 11⁄2 ft. the coefficients were:—

Temperature F.C.
205°.594
 62°.598