4th. That the depth of water flowing over the weir be not less than 3 nor more than 25 inches.

5th. That the depth of water flowing over the crest be not greater than 1⁄2 the length of the weir.

6th. That the weir opening be not over % the width of the stream approaching it.

7th. That the discharge over the weir should be free and the approach of the water without velocity sufficient to produce eddies.

8th. That the distance from the crest to the bottom of the channel-and from the ends of the weir to the sides of the channel, shall be at least twice as great as the depth of the water flowing over the weir. This is to secure complete contraction.

Weirs may have either partial or complete contraction as illustrated by figures 1 to 5 of Fig. 7.

Fig. 7. Illustrating Contraction on Weirs.

In following over a weir water takes the form shown in Fig 1. The upward movement of the water toward the crest A of the weir A B causing the water to arch upward as shown. The true head, as shown at c, is reduced by the downward curve of the water, as shown at d e. This is called the contraction. If the weir has the form shown in Fig. 2 the contraction of the flow will be but partial; that is, there will be contraction at the crest a c but none at the sides a b and c d past which the water flows as shown in Fig. 4. If the weir has the form shown in Fig. 3 the contraction is said to be complete, for, in addition to the contraction at the crest, there is also contraction at each side, a b and e d, as shown in Fig. 5 where it is seen that the width of the outflowing stream a is less than the width of the opening b. This will illustrate not only the action of flowing water but the meaning of the term "Complete Contraction." which is a requisite to the proper application of the following table of weir measurements.

TO CONSTRUCT A WEIR AND MEASURE THE VOLUME OF A WELL.

Select some convenient point where, by throwing up a low bank, a small pond may be formed by the stream from the well. Across the outlet set a board or plank out of which has been cut a rectangular piece (say 12 inches deep by 4 feet long). Support the board by nailing to stakes driven into the ground taking care that the edge of the

opening is level or horizontal. Make the bank water-tight about the bottom and ends of the weir. Drive a stake several feet back of the weir and near the edge of the pond making the top of the stake level with the crest of the weir either by using a level or by driving the stake to water level at the moment the water begins to spill over the weir.

Fig. 8. Illustrating the construction of a weir and methods of weir measurement.
Used by permission of James Leffel & Co., Springfield. Ohio. (See advertisement P. 229.)

Permit the water to rise to the full height at which it willstand while flowing over the weir. Then measure the depth of water over the stake.

Enter the weir table with this depth (as explained in examples given) and get the quantity for one inch. Multiply this quantity by the length of the weir in inches to get the total volume flowing from the well, in cubic feet per minute.

If possible have the up-stream edges of the weir lined with strips of tin or sheet iron to give a sharp edge for the water to flow over. If this is not at hand then bevel the crest and sides of the weir to a sharp edge on the up-stream side. See, in short, that ALL the conditions mentioned on page 52 have been complied with. The manner of constructing and using a weir is illustrated on the opposite page, where A is the weir board with the beveled notch or opening B. E is the stake driven back to the side of the weir, out of the current, and from which the true depth is taken as shown.

Application of Weir Table No. 17.

This table gives the number of cubic feet of water passing per minute over each inch in width of a weir, and for depths from inch to 25 inches.

The top horizontal line of fractions are the fractions of an inch in depth, and the columns of figures at the rig t and left ends indicate the full inches of depth. The quantities inside the table are the cubic feet discharged.

Thus inch of depth.11 cu. ft. per inch width of weir. See at

*****

10
1014
1618 66

inches "

66

=12.71
=13.19

66

66

66

66

These examples will render clear the use of the table Examples of Use. How many cubic feet and gallons are discharged per minute by a well the water of which, in flowing over a weir 5 feet long, shows a depth of 73% inches?

From table the quantity of water for one inch wide by 73% inches deep-8.05 cubic feet per minute; 5 feet wide=60 inches; therefore 8.05 multiplied by 60-483 cubic feet per minute. Referring to table No. 36 we find that 483 cubic feet 3612.8 gallons. Therefore by this simple process the volume of our well per minute has been found to be 483 cubic feet, or 3612.8 gallons per minute.

The work involved in the construction of a weir is but slight, and the calculation of the flow, as above, is a mere matter of multiplication and addition. Every well owner should see that the volume of his well is accurately determined in this way; and not once alone, but every few months, in order to know whether there is any increase or diminution in the flow. A series of such systematic tests would no doubt result in furnishing valuable information leading up to a correct determination as to the source and supply of the artesian stream.

WEIR TABLE FROM ONE-SIXTEENTH INCH DEPTH TO TWENTY-FIVE INCHES DEPTH.

James Leffel.

WIER MEASUREMENTS.

TABLE NO. 17.

5

4.50 4.58

6

5.90 6.00

4.67 4.75 4.84 4.92 5.01 5.10 5.18 5.27 5.36 5.45 5.54
6.09 6.18 6.28 6.37 6.47 6.56 6.65 6.75 6.85 6.95 7.05
7.44 7.54 7.64 7.74 7.84 7.94 8.05 8.15 8.25 8.35 8.45 8.55 8.66 8.76 8.86 8.97
9.10 9.20 9.31 9.42 9.52 9.63 9.74 9.85 9.96 10.07 10.18 10.29 10.40 10.51 10.62 10.73 10.86
10.86 10.97 11.08 11.19 11.31 11.42 11.54 11.65 11.77 11.88 12.00 12.12 12.23 12.35 12.47 12.59 12.71
*12.71 12.83 13.95 13.07*13.19 13.31 13.43 13.55 13.67 13.80 13.93 14.04 14.16 14.30 14.42 14.55 14.67
14.67 14.79 14.92 15.05 15.18 15.30 15.43 15.56 15.67 15.81 15.96 16.08 16.20 16.34 16.46 16.59 16.73
16.73 16.86 16.99 17.12 17.26 17.39 17.52 17.65 17.78 17.91 18.05, 18.18 18.32 18.45 18.58 18.72 18.87-
18.87 19.01 19.14 19.28 19.42 19.55 19.69 19.83 19.97 20.10 20.24 20.38 20.52 20.66 20.80 20.94 21.09
21.09 21.23 21.37 21.48 21.65 21.79 21.94 22.08 22.22 22.35 22.51 22.65 22.79 22.94 23.08 23.23 23.38
23.38 23.53 23.67 23.82 23.97 24.11 24.26 24.41 24.56 24.71 24.86 25.01 25.16 25.31 25.46 25.61 25.76
25.76 25.91 26.06 26.21 26.36 26.51 26.66 26.81 26.97 27.12 27.27*27.43 27.58 27.73 27.89 28.04 28.20
28.20 28.35 28.51 28.66 28.82 28.98 29.14 29.29 29.45 29.60 29.76 29.92 30.08 30.23 30.39 30.55 30.70
30.70 30.86 31.02 31.18 31.34 31.50 31.66 31.81 31.98 32.15 32.31 32.47 32.63 32.80 32.96 33.12 33.29
33.29 33.45 33.61 33.78 33.94 34.11 34.27 34.44 34.60 34.77 34.94 35.10 35.27 35.44 35.60 35.77 35.94
35.94 36.10 36.27 34.46 36.60 37.87 36.94 37.11 37.28 37.45 37.62 37.79 37.96 38.14 38.31 38.48 38.65
38.65 38.82 39.00 39.17 39.34 39.52 39.69 39.86 40.04 40.21 40.39 40.56 40.73 40.91 41.09 41.26 41.43
41.43 41.60 41.78 41.96 42.13 42.31 42.49 42.67 42.84 43.02 43.20 43.38 43.56 43.74 43-92 44.10 44.28
44.28 44.46 44.64 44.82 45.00 45.18 45.38 45.53 45.71 45.90 46.08 46.26 46.43 46.63 46.81 47.00 47.18
47.18 47.36 47.55 47.72 47.91 48.09 48.28 48.46 48.65 48.83 49.02 49.20 49.39 49.58 49.76 49.93 50.10

5.63

5.72 5.81

5.90

6

7.15 7.25 7.35

7.44

7

9.10

13

15

16

18

20

21

22

25

Certain refinements of calculation enter into the matter of measurement by weirs, but they have not sufficient bearing on the ordinary practice to deserve more than mention here. Tables of weir measurements are constructed wherein these elements have been taken into account, but the table given is sufficiently accurate for our use. In view of the fact that the table given may not meet all the requirements of practice the formula upon which the most accurate weir measurements are based is here given and briefly explained. The weir formula of Francis is as follows:

V=C (L—.2 H) H

Wherein V=Volume in cu ft per sec. flowing over the weir
C=The coefficient of discharge (=3.33) (or 3.3333+)
L=The length of the weir in feet.

H=The head, or depth of water over the weir.
The square root of the cube of H.

Substituting the value of C, the formula becomes,
V=3.33 (L—.2H) H‡

Which reads as follows:

Volume per second=3.33 multiplied by (the length of the weir less two tenths of the head) multiplied by the square root of the cube of the head.

This will be rendered plain by an illustration.

What will be the discharge per second over a weir 10 feet long if the water is 1.5 feet deep?

The total length L of the weir is reduced, by reason of the contractions at the ends, to the calculated amount of of the depth, or head, for each contraction, hence the expression (L-.2H)

In the example the depth=1.5 feet, of which (there being 2 contractions) is=.3, and ten feet the full length— less .3 9.7 feet, or the effective length.

The cube of 1.5 (the head) =3.375 and the square root of 3.375 1.837. We now have the formula thus:

V=3.33×9.7×1.837.

Which multiplied through=59.39 cubic feet per second flowing over the weir.

The cubes and roots in these calculations may be taken directly from the tables given elsewhere herein. This amount is somewhat less than that resulting from the use of the weir table, but the table is sufficiently accurate for all practical uses. The use of the formula may, in some cases, be more convenient and hence it has been given. Ordinarily the formula is given thus.

V=3.33 L H

no account being taken of the loss to L resulting from the end contractions. If a weir is used wherein there are no end contractions then this last form of formula would be used. If the opening is obstructed by a central post there would be 4 contractions and the expression of the formula would be (L-.4H), and so on for any other number of contractions.