Зображення сторінки
PDF
ePub

may be rectangular, the crest being truly horizontal, and using either of the formulæ mentioned above according to the conditions specified. The two examples following will point out the manner of proceeding, and furnish an opportunity of adding some practical details, elucidating what has been laid down in § 63 to § 66.

71. EXAMPLES.-1st. Let us suppose it necessary to gauge the discharge of a small river or water-course: we must search for a part suitable for the construction of an overfall. This will probably be found at a point where the bed has become contracted, and the banks are somewhat steep, and immediately below a wide part of the stream; at such locality the width at the surface of the water is found to be 11.808 feet, and the greatest depth 2.62 feet. After a preliminary examination of the transverse section, and of the surface velocity, measured by means of some light body thrown into the current, we find, approximately, multiplying the assumed section by the velocity, that the stream is discharging nearly 35 cubic feet per second. Since the width is 11.808 feet, we may give 3.936 feet to that of the overfall for gauging (i. e. 11.8083); the charge H will then be above o.1968 feet, for the formula Q=3.21 IHH gives

[blocks in formation]

which, for the assumed discharge, gives in this case,

[blocks in formation]

From this preliminary inspection we may construct a suitable partition of plank about o.1 feet thick on the upper edge, and of such figure as nearly to fit the sides and bottom of the water-course. It must be carefully stanched, being sunk into the bottom and sides, and puddled on the up-stream face. From out of its upper edge we must cut an opening 3.936 feet long and 2.132 ft. deep, so that its sill being o.488 feet above the bottom of the bed (2.62 - 2.132), the water may flow off freely. The section of the presumed discharge (3.936 feet x 1.969 7.746 square feet) being not the fifth nor even the seventh part of the transverse section of the river, which exceeds 55 square feet, all the conditions for the application of the formula Q3.21 IHH are present. Everything being duly prepared for the gauging of the water-such as, all leakage having been stopped, and the current restored to its

=

ordinary and uniform flow, we proceed to measure H by stretching a cord across the opening, whose ends are fastened to points in the sides, marked at the level of still water (deduction being made for capillarity), and about a foot from the vertical side of the overfall. The depth of the sill below this line at the centre of the opening is carefully measured, and found to be 2.01 ft., and the length also, intended to be 3.936 feet, is found to be 3.92 feet. The discharge is, therefore, Q = 3.21 × 3.92 × 2.01 √ 2.01 = 29.128 cubic feet.

72. 2nd. A question of law requires that the exact quantity of water flowing down a stream when the surface is level with the top of a certain fixed mark be determined. The gauging must evidently be effected by a dam across the course. About 170 feet above the mark a temporary dam is placed, at a part where, from its regular width and inclination, the river-bed is suitable, having, when the water is at the height above named, a breadth of 64.94 feet, and a mean depth of 4.1 feet; the overfall being a plank well squared, and 0.1312 feet thick, the upper edge being placed truly horizontal, and 0.656 feet above the bench-mark. At each extremity a vertical piece is raised, so that the length of the overfall is 63.6 feet; close to the vertical pieces two others are placed, on which a scale is drawn whose zero is the upper edge of the plank. These arrangements being made, it is only necessary

to observe when the surface of the water down stream is level with the fixed mark, and then read the height of the water upon each scale. This last has been found to be 2.34 feet. As this height is nearly the half of that of the temporary dam (4.1 +0.656 4.756), we cannot apply with confidence the formula 3.558 LH √ H, § 64, p. 44, and we must use

=

3.488 LHH + 0.0349 w2, § 66, p. 47.

To obtain the value of w, the velocity of the surface of the current on arriving at the overfall, we must take a distance of, say, 165 feet on each bank, above the point where the surface of the current begins to curve towards the overfall, and, marking these points, we must place in the current, about 60 or 70 feet above them, some floating body of the same specific gravity as water, and mark carefully the time which it may take to flow along the 165 feet: a mean of six observations gave 48 seconds; whence

[blocks in formation]

3.4 feet per second, and 0.0349 w2 = 0.40344.

Hence

Q = 3.488 × 63.6 × 2.34 √ 2.34 + 0.40344 = 859.78 cubic feet,

the formula 3.558 LH √ H would give 810.63 cubic feet. Thus we may certify, that at the given height of surface the river discharges about 850 cubic feet of water per second.

73. Experiments on weirs on a large scale have been undertaken by Mr. T. E. Blackwell. The first set are contained in the following Table, which has been arranged from the detailed experiments, as published in the Civil Engineer and Architects' Journal, vol. xiv., p. 642:

Length of

Overfalls.

Feet.

FIRST SET OF EXPERIMENTS-T. E. BLACKWELL.

COEFFICIENTS under their respective Charges.

Feet. Feet. Feet. Feet. Feet. Feet. Feet. Feet. Feet. Feet. Feet. Feet.
.083.1660.25.333.4160.50.583.6660.75.833 1.00 1.166

Overfall being a Thin Plate .0052 Feet.

[blocks in formation]
[blocks in formation]

534.534.556

459.561.597.574.601.607 607.589.568.538.525.549.565 435.585.568.601.609.576.571 547-558

Same Overfall, with Wingboards, converging at Angle 64°.

[merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][ocr errors][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small]

This Table is the result of a series of 243 experiments, made on overfalls of 3 feet, 6 feet, and 10 feet in width, with heads from 0.0833 feet to 1.166 feet, and with the varying circumstances of having for the overfall bar,-first, a thin plate; secondly, a plank 0.166 feet thick, square on the top; and thirdly, a crest 3 feet in breadth. The thin plate spoken of as forming one of the overfall bars was a piece of iron fender plate, barely 0.0052 feet thick; and the broad crest used was an apron formed of deal boards 3 feet long, roughly planed over, and fastened on to the outer edge of the vertical overfall plank, so as to form an uninterrupted continuation of it, the object being to approximate towards the case of well-constructed wide-crested weirs, such as may be found in actual use in rivers, &c.: the position of this planking was, in some of the experiments, horizontal, and in others sloped at 1 in 18 and I in 12.

The second set consisted of a series of 70 experiments on an overfall about 10 feet in length, the width of the bar being in every case o.166 feet.

74. In both, special circumstances which influenced the coefficients obtained were present; and in employing them in actual practice, a careful judgment must be formed as to their exact degree of applicability. The former were made upon a side pond or reservoir of the Kennet and Avon Canal, the area of which was 106,200 square feet; and as to these the author remarks, first, that the pond was supplied with water, not continuously, as drawn off in the experiments, but three or four times a day, or as often as might be requisite: however, even if during an experiment no water had been admitted, the decrease of the "head" must have been inappreciable, for the largest discharge measured in any experiment was barely 444 cubic feet, which gives a fall of (444÷106200 =) 0.00418 feet over the whole surface, between the beginning and end of it, and the half of this, or 0.00209 feet, deducted from the head,-measured at the commencement,-for the approximate mean head, could not be perceived. Secondly, at some little distance above the overfall the depth of water was reduced by a submerged course of masonry (Fig. 23), which rose to within 18 or 20 inches of the surface: the width of the approach to the overfall being about 40 feet, we have a transverse area of 60 square feet. Thirdly, the overfall was placed upon the outer line of the dam, in order to obtain the requisite free fall; and the depth of water immediately contiguous to it and on the dam would seem, from the section given, to be a little more than 2 feet; the average depth between the submerged course and the dam

being about 3 feet. The line of the overfall, moreover, was not exactly in the direction of one of the sides of the reservoir; and from the measurements given of the head, taken at still water, and the corresponding depth of the sheet of water flowing off, as given in the following Table, it would appear that some degree of resistance opposed the motion of the water up to the overfall.

75. Actual depth at point of discharge.-In this Table the actual heads were measured at the outer edge of the boarded crests and edges of the overfalls. The upper line of figures gives the head, H, at still water, in feet; the other figures the heads at the outer edge of overfalls or crests, also in feet.

[merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][ocr errors][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small]

The general arrangements at these, the first set of experiments, would seem fairly to represent the case of the discharge of water by an overfall from a large still reservoir.

76. In the second set of experiments-those at Chew Magna -we have an area of reservoir of 5717 square feet kept constantly full by a pipe 2 feet diameter, discharging from a head of 19 feet. The distance between the mouth of this pipe and the overfall was only about 100 feet; the water must, therefore, have retained some of its velocity on approaching the overfall; and indeed, with charges above 0.417 or 0.5 feet, this was perceptible to the eye, but could not, the author states, be accurately determined, from the peculiar form of the reser

« НазадПродовжити »