The following table is figured according to the Francis formula, and gives the discharge in cubic feet per minute, for openings one inch wide:
TABLE OF WEIRS
| Inches | 0 | ¼ | ½ | ¾ |
|---|---|---|---|---|
| 1 | 0.403 | 0.563 | 0.740 | 0.966 |
| 2 | 1.141 | 1.360 | 1.593 | 1.838 |
| 3 | 2.094 | 2.361 | 2.639 | 2.927 |
| 4 | 3.225 | 3.531 | 3.848 | 4.173 |
| 5 | 4.506 | 4.849 | 5.200 | 5.558 |
| 6 | 5.925 | 6.298 | 6.681 | 7.071 |
| 7 | 7.465 | 7.869 | 8.280 | 8.697 |
| 8 | 9.121 | 9.552 | 9.990 | 10.427 |
| 9 | 10.884 | 11.340 | 11.804 | 12.272 |
| 10 | 12.747 | 13.228 | 13.716 | 14.208 |
| 11 | 14.707 | 15.211 | 15.721 | 16.236 |
| 12 | 16.757 | 17.283 | 17.816 | 18.352 |
| 13 | 18.895 | 19.445 | 19.996 | 20.558 |
| 14 | 21.116 | 21.684 | 22.258 | 22.835 |
| 15 | 23.418 | 24.007 | 24.600 | 25.195 |
| 16 | 25.800 | 26.406 | 27.019 | 27.634 |
| 17 | 28.256 | 28.881 | 29.512 | 30.145 |
| 18 | 30.785 | 31.429 | 32.075 | 32.733 |
Thus, let us say, our weir has an opening 30 inches wide, and the water overflows through the opening at a uniform depth of 6¼ inches, when measured a few inches behind the board at a point before the overflow curve begins. Run down the first column on the left to "6", and cross over to the second column to the right, headed "¼". This gives the number of cubic feet per minute for this depth one inch wide, as 6.298. Since the weir is 30 inches wide, multiply 6.298 × 30 = 188.94—or, say, 189 cubic feet per minute.
Once the weir is set, it is the work of but a moment to find out the quantity of water a stream is delivering, simply by referring to the above table.
Another Method of Measuring a Stream
Weirs are for use in small streams. For larger streams, where the construction of a weir would be difficult, the U. S. Geological Survey engineers recommend the following simple method:
Choose a place where the channel is straight for 100 or 200 feet, and has a nearly constant depth and width; lay off on the bank a line 50 or 100 feet in length. Throw small chips into the stream, and measure the time in seconds they take to travel the distance laid off on the bank. This gives the surface velocity of the water. Multiply the average of several such tests by 0.80, which will give very nearly the mean velocity. Then it is necessary to find the cross-section of the flowing water (its average depth multiplied by width), and this number, in square feet, multiplied by the velocity in feet per second, will give the number of cubic feet the stream is delivering each second. Multiplied by 60 gives cubic feet a minute.
Figuring a Stream's Horsepower