1140

THEORY AND PRACTICE OF ENGINEERING.

Book II.

On the Quantity of Water discharged by Orifices of different Forms from Vessels keptconstantly full. — In making these experiments M. Bossut employed very clear waterrunning through holes made in plates of copper half aline in thickness; the tempera-ture of the water is not given; the time was exactly measured, as well as the quantity ofwater discharged, and the result was, that the quantity of water discharged in equal timesby the same orifices, from the same head of water, is very nearly as the areas of the orifices ;and, that the quantities of water discharged in equal times by the same orifices, underdifferent heads of water, are nearly as the square roots of the corresponding heights ofthe water in the reservoir above the centre of the orifices. If we call Q, 9, the quantitiesof water discharged in the same time from the two orifices A, A', under the same heightof water in the reservoir ; q and Q', the quantities of water discharged during the sametime by the same aperture A, under the different heads of water h, h '; we have by thefirst of the above results,

Q : q = A : A', and by the second q : Q= v'A : \/h ';

c ... lt . A'xQ , Q Whfrom which we obtain q = —, and q ■

. A'xQ Qf \/h . . ..

then, since -7—= — 777-, we have Q : Q' = A vh : A vh.

A v h’

The quantities of water discharged during the same time by different apertures, underdifferent heights of water in the reservoir, are to one another in the compound ratio of theareas of the apertures and of the square roots of the heights in the reservoirs.

M. Michelotti made on this subject a series of experiments on a great scale, and withthe utmost accuracy. The apertures extended to 3 inches both square and circular, andat considerable altitudes : the reservoir was 20 feet high, and 3 feet square; the waterflowed from it into a cistern whose area was 289 square feet, and the results correspondednearly with the experiments by Du Buat on the quantity of water discharged over weirs :the depth may be considered as the upper edge of a plank placed below the upper surfaceof the water in the river or reservoir: one of the orifices was 18£ inches English inlength.

Depth of the Discharge of Discharge

Oritice in English Water in cubic calculated by

feet. feet. the Formula.

1-778

3199

4-665

506

1222

2153

524

1218

2155

6-753

3750

3772

Du Buat has given the following formula reduced to English inches, by which the thirdcolumn is calculated, and is very accurate. This formula, as altered by Dr. Robinson, is

D = / </130-032“lI*, or

D = 11 *4172 /id:

where D is the quantity of water discharged in cubic feet, l the length of the waste-board,and H its depth; that is, multiply the square root of the cube of the depth of the upperedge of the waste board below the surface by II’, and by the length of the waste-board,and the product will be the quantity discharged in English inches.

Dr. Robison found by his experiments that the discharge was one-sixteenth more thanthat produced by Du Buat’s formula.

For the Quantity of Water discharged over a Weir t we cannot do better than select a tabic,drawn up and revised by Dr. Robison, from experiments made in Scotland , which showedsome slight variations from the formula given by Du Buat. The water from which thedischarge was made was perfectly quiet, hut when it was suffered to reach the opening overwhich it passed with any velocity, it was necessary that the area of the section should bemultiplied by the velocity of the stream.

Since the publication of 44 Traite theorique et experimental d’Hydronamique ” by theAbbe Bossut in 1771, this subject has been justly regarded as important, and has receivedthe attention of the most eminent philosophers. Bossut’s experiments were made upon agrand scale, and his formulae are more to be relied on than those given by Michelotti;and in order to determine the motion of the particles of a fluid which was in the act ofbeing discharged from an orifice, Bossut employed a glass cylinder, 8 inches in height and6 inches in diameter, to the bottom of which he adapted several contrivances for the effluxof the water.

Chevalier Buat, Colonel of Engineers, in 1779, adopted the theory of Bossut, and paidparticular attention to the motion of water in rivers and canals, and to him we are indebtedfor the observation, that if water possessed perfect fluidity, and flowed in a channel infi-nitely smooth, its motion would be constantly accelerated, like that of heavy bodies de-scending upon an inclined plane. But the velocity of a river is not accelerated ad