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to obtain the second, third, &c., we have but to add to this successively 0.18691, and consequently obtain the following numbers:-0.393, 0.580, 0.767, 0.954, 1.141, 1.328, 1.702 1.795; which, being multiplied by their respective square roots, give 0.2468, 0.442, 0.672, 0.932, 1.219, 1.530, 1.864, 2.220.

Hence the eight several discharges through the 40 ft. lengths are found by multiplying the common part of

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the formula (§ 55) m, l, HVH. V2g, that is, 3.558 × 40

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head, we have 6700 cb.

= 142.3 into the values of H√H given above, and, adding these, we have the total discharge over the sloping part of this weir 1299 cb. ft. per sec. And for the length of 780 ft. of level crest with 1.8 ft. ft. per sec. Hence the total discharge is 7999 cb. ft. per sec. As 8 × 40 = 320 ft., and the length of sloping portion is 321 ft., we must add one foot to 779, the length of the level portion.

(XXVIII.) In the weirs on the Shannon constructed by the Commissioners, it was requisite that salmon-gaps should be constructed, so that the fish be able to migrate up stream at the weirs during such periods as might not afford sufficient depth of water if the whole quantity were uniformly distributed over the total length of the weir. These were 10 feet wide, and the crest 1.5 ft. below that of the weir. Calculate the quantity flowing down three of these salmon-gaps, the water on the level part of the crest being 0.6 ft. deep. Here

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3Q3 × 3.558 x 10 x 2.1 2.1 = 324.8 cb. ft.

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(XXIX.) A feeder or water-course along the side of a valley is required to be augmented by the streams and springs above its level. It is required to determine their

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total volume. For this purpose the several courses are dammed up at convenient and suitable places, and a narrow board provided, in which is cut an opening for the overfall 1 ft. long, and 0.5 feet deep; it being reasonably surmised that this would be sufficient to gauge the largest of the streams; and another piece was prepared that, when attached to the former, would reduce the length to 0.5 ft. for the smaller. Calculate the total quantity delivered by the five following streams and springs :

No. 1, on being dammed up, flowed over the 1 ft. opening 0.37 ft. deep. Hence Q 3.558 x 0.37 0.37 = 0.8 √0.37 cb. ft.

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No. 2, at 0.5 ft. in length of overfall, rose to 0.41 ft. in depth. Hence Q = 3.558 × 0.5 x 0.41 √0.41 = 0.467 cb. ft. per second.

No. 3, at 1 ft. length, was 0.29 ft. high on the overfall, and

Q = 3.558 × 0.29 √0.29 = 0.555 cb. ft. per sec.
No. 4, at 0.5 in length, rose o.19 ft. Hence we have
Q = 0.5 × 3.21 × 0.19 √0.19 = 0.133 cb. ft. per sec.

No. 5, being a small spring, was not measured by the overfall; but being banked up, a pipe, 0.0416 ft. in diameter, was let through the dam, and when the surface had become stationary, and consequently the discharge through the pipe equal to the supply from the spring, it was gauged into a vessel marked for 1 and 2, &c., imperial gallons; the time required to reach the former was 32 seconds. Hence the spring gave 0.005 cb. ft. per sec., as 6.25 gallons make one cubic foot.

The total quantity, therefore, received by the aqueduct from the lateral springs and streams above its level amounted to 1.96 cb. ft. per second.

(XXX.) On the Manchester water-works weirs are constructed across some of the lateral mountain streams which supply the reservoirs, so that the higher velocity which the water has when flowing over at the greater depths may separate the turbid water, unfit for the town supply, from the clear. In heavy or sudden rains these streams bring down very rapidly water discoloured by peat and earth, and unfit for domestic use; but in fine weather the quantity is much reduced, and the water clear and suitable for the mains of the town. The wood engraving represents a transverse section of the water-course which is carried through the masonry of the weir, conveying clear water from other streams, across the valley in which the weir is placed, and so serving as an aqueduct; at the top this is open, and when the water flows over at a small depth, that is, when it is clear, it falls into the channel, Fig. 63, and is con

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veyed by it eventually into the main which supplies the town; but if it rise and discharge a greater body of water, the increased velocity projects it beyond the edge of the

opening, Fig. 64, and it thus passes over the longitudinal opening, and flows down to the compensation reser

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voir for the supply of water to the mills situated on the river.

By referring to § 8, we find the means of calculating the curve of any issuing jet of water. But in this case we have a different velocity, and therefore a different parabola for every lamina into which we may suppose the water divided. Fig. 65 represents the different paths taken by each, that for the mean velocity at ths of the depth being drawn in a full line; hence those above will

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Fig. 65.

tend to depress the curve, and those below, on the contrary, to carry it more up towards the horizontal line; we may therefore suppose the whole sheet of water to be carried out in a curve at top and bottom parallel to that

of the mean velocity, Fig. 66. If therefore we put H1

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for this mean velocity, and the curve taken by the lowest lamina is that due to a head H1, for if in the expres

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9

4(H√H-h √ h\2

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we put h = o, the resulting value of 2' is

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67 let x = 1 ft., and y = 0.83 ft.; hence, from § 8, p. 12,

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= 0.1722 .. H1 = 9 x 0.1722 ÷ 4 =0.3874 ft.

So then, when the water flowing over has a depth at

or greater than 0.3874 ft., it is carried completely over the longitudinal opening. We must, then, gauge the stream in wet seasons, and so proportion x to y that the volume of water, from the head necessary to discharge it, have velo

m

n'..0.83... n
y----

Fig. 67.

city sufficient to pass

over the opening mn; at lesser depths it strikes against

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