DISCHARGE OF APERTURES, PIPES, &C. (1.) "Velocity of Efflux."-The velocity with which water issues from the side of a vessel, as at A, Fig. 1, is the same as that of a body falling freely by gravity from the height H, or the distance from the centre of the orifice to the surface of the In which H = the height or head of water in feet, and V = the In which H = the head of water in feet, d = the diameter of the orifice in inches, and G = gallons discharged per minute. Table 1 has been calculated by this rule. These rules give the theoretical velocity and discharge; for application to practice, they may require some modification to adapt them to the particular form of the orifice. (2.) "Discharge by an Orifice in a Thin Plate."-It has been found by experiment that, when the discharging orifice is made in a thin plate, the converging currents of water approaching the aperture cause a contraction in the issuing stream, so that instead of a parallel or cylindrical jet, it becomes a conical one of the form shown by Fig. 2, the greatest contraction being at B 2.32 3.275 4.01 4.63 5.18 5.67 1785 1915 2030 2134 2333 2534 2707 2865 3024 3170 3312 4508 5888 7.32 8.03 8.67 9.27 9.83 10 36 10.87 11 35 the point C, whose distance from the plate is half the diameter of the orifice, and its diameter 784, that of the orifice being 1. The form from B to C may be taken as a curve, whose radius is 1.22 times the diameter of the orifice. Now, the foregoing rule gives the maximum velocity, or that at the point of greatest contraction C, and if the diameter be taken there, the rules would give the true velocity and discharge without correction. But it is obvious that the velocity at the aperture itself (or at B) would be less than at C in the ratio of the respective areas at the two points, or as 12 to -7842 or 1 to ·615, and in that case, the diameter being taken at B, the velocity there would become V √H× 8 × ·615 and the discharge G√Hx √x dx 16.3 x 615. From this we get for apertures in a thin plate, the rules : = = Thus, with 3 inches diameter and 16 feet head, the discharge would be 16 x 32 x 10, or 4 x 9 x 10 = 360 gallons per minute. The head for 150 gallons per minute with 2 inches (3.) "Discharge by Short Tubes."-When the aperture is of considerable thickness, or has the form of a short tube, not less in length than twice the diameter, the amount of contraction is found to be less, and the discharge greater, than with a thin plate. Fig. 3 shows a tube 1 inch diameter and 2 inches long; the greatest contraction is in that case 9 inch diameter, and its ṛ portional area 92 81, or say 8 of the area of the tube. For short tubes therefore the rules become : Table 2 has been calculated by these rules; thus, for a 7-inch pipe discharging 450 gallons, the Table shows that the head necessary to generate the velocity at entry is 6 inches; this is irrespective of friction, which, in fact, for so short a tube as the rule supposes, would be practically nothing. This Table applies to all cases of pipes; for instance, Fig. 4 shows the inlet end of a main from a reservoir, which will require for the velocity at entry alone the amount of head shown by the Table. When, as is usually the case, the pipe is of considerable length, the head due to friction must also be allowed for. (4.) "Friction of Long Pipes."-With a long pipe there is not only the loss of head due to the velocity at entry, but also another loss due simply to the friction of the water against the sides of the pipe, so that in all cases the head consumed may be considered as composed of two portions :-one, the amount due to velocity of entry, irrespective of friction; and the other, the amount due to friction alone. Thus, in Fig. 8 the head h gives a certain velocity of discharge by the short pipe A; but to give the same velocity in the long main B C, the head H' is necessary, of which h' is consumed in generating the velocity at entry, being the same as for A, and the rest, or H, in the friction of the long pipe: the total head is, of course, the sum of the two. (5.) The loss of head by friction may be calculated by the |