TABLE III.-COEFFICIENTS OF DISCHARGE OF VERTICAL, THIN-LIPPED, RECTANGULAR ORIFICES, WITH COMPLETE CONTRACTION. THE HEADS OF WATER MEASURED IMMEDIATELY OVER THE ORIFICE. Thence we derive this rule for estimating the discharge of water from thin-lipped orifices; seek in Table I. the velocity corresponding to the head of water measured from the centre of the effluent vein; multiply this by the area of the orifice in square feet, and the product is the theoretical discharge. Fiveeighths of the theoretical discharge will give the actual discharge in cubic feet a second, if a rough approximation only is required. If the estimation is to be accurate, seek in Tables II. and III. the coefficient of discharge most nearly corresponding to the given head and area of orifice, and multiply the theoretical discharge by the coefficient so found. Thus the following table has been calculated : : TABLE IV.—THEORETICAL AND ACTUAL DISCHARGE FROM A THIN-LIPPED ORIFICE OF A SECTIONAL AREA OF ONE SQUARE FOOT. The above table is given as a sample of the method of calculation according to the above rule. For other areas and different heads the calculation may very easily be performed. 3rd. Discharge with incomplete contraction.-It is very freFig. 99A. quently the case in practice that one of the sides of a thin-lipped orifice is prolonged, so that the vein of fluid no longer contracts upon all sides, as in fig. 99A. In this case the coefficients in Tables II. and III. give too low a result. M. Morin gives the following rule for discharge with incomplete contraction : Multiply the coefficient of discharge for complete contraction found as above by 1.035 when the vein contracts on 3 sides only in order to obtain the true coefficient by which the theoretical discharge must be multiplied to give the actual discharge. Hence, for an approximate calculation, we may multiply the theoretical discharge (a xv) by 0.63, when the orifice is = longed upon one side; by 0.66 when it is prolonged on two sides, and by 0.69 when it is prolonged on three sides. When all four sides are prolonged, the thick-lipped orifice, fig. 94, is formed of which the coefficient of efflux is 0.8. 4th. Discharge from rectangular notches, waste boards, and weirs. In this case the theoretical discharge = where discharge in cubic feet per second. b = breadth of notch or weir. h = head of water, measured at some distance behind the crest of the weir. v = velocity in feet per second = √2 gh... a = area of effluent vein = b xh. (2) The actual discharge is found by multiplying the theoretical discharge by the coefficient of efflux m, which varies under different circumstances. The millwright must select this coefficient from the following tables, so as to suit the particular case to which it is to be applied. TABLE V.-COEFFICIENT OF DISCHARGE FOR WEIRS, FROM EXPERIMENTS ON NOTCHES 8 INCHES BROAD, BY PONCELET AND LESBROS. Head of Water in inches. 0.89 0.78 1.18 1.57 2.36 3.15 3.93 5.90 7.86 8.65 0.424 0.417 0-412 0407 0-401 0·397 0.395 0.393 0.390 0.385 This gives a mean value of 0·4 or ths for 3m, and hence we may approximately find the discharge from a waste board by multiplying the head in feet by the breadth of the notch in feet, and by the velocity due to the head found by equation (2) or Table I. Two-fifths of this product will be the discharge in cubic feet per second. In 1852 the council of the Institution of Civil Engineers awarded to Mr. Blackwell a premium for a valuable series of experiments on the discharge of water from weirs made on a very large scale, and with various conditions of head and with different kinds of overfall bars. What constitutes the principal value of Mr. Blackwell's paper is the scale on which the experiments were made, and their close approximation to actual practice. It must be borne in mind, however, that in calculating the quantity of water discharged in the flow of rivers over weirs, reference must be had to the form of the top, in order to ascertain the state of the overfall as compared with those in the following table, from which the coefficient is taken for calculation. The most important of the generalisations from this table are 1st. That the discharge is decreased in proportion to the breadth and inclination of the crest, being least when the crest is level. 2nd. That converging wing walls, above the overfall, increase the discharge. Where, as in the case of a river, the water approaches the weir with a certain velocity, it should be taken separately into account, the above coefficients being deduced from experiments on reservoirs so large that the water was approximately stag nant. Let k = height of head due to velocity v of water as it approaches the weir; that is, let k= the effective discharge is then = v2 64.38 Q = } m. b. √ 2 g [(h+k)* − k3] ... (6). 2g TABLE VII.-EXAMPLES OF ESTIMATION OF DISCHARGE FROM WEIRS. According to the above formula I have computed the following table showing at a glance the velocity in feet, the theoretical discharge in cubic feet per second, and the actual discharge of water over a thin-edged notch or weir for various heads from an inch to 6 feet-the water approaching the weir with no perceptible current. * Weisbach. |