Filed under: Water Power | Tags: measure water power, water powered farm, water wheels, weir
Since a steady flow of water, and a constant head, bring about this
ideal condition in the water wheel, the first problem that faces the
farmer prospector is to determine the amount of water which his stream
is capable of delivering. This is always measured, for convenience,
in _cubic feet per minute_. (A cubic foot of water weighs 62.5 pounds,
and contains 7-1/2 gallons.) This measurement is obtained in several
ways, among which probably the use of a weir is the simplest and most
accurate, for small streams.
A weir is, in effect, merely a temporary dam set across the stream in
such a manner as to form a small pond; and to enable one to measure
the water escaping from this pond.
It may be likened to the overflow pipe of a horse trough which is
being fed from a spring. To measure the flow of water from such a
spring, all that is necessary is to measure the water escaping through
the overflow when the water in the trough has attained a permanent
level.
[Illustration: Detail of home-made weir]
[Illustration: Cross-section of weir]
The diagrams show the cross-section and detail of a typical weir,
which can be put together in a few minutes with the aid of a saw and
hammer. The cross-section shows that the lower edge of the slot
through which the water of the temporary pond is made to escape, is
cut on a bevel, with its sharp edge upstream. The wing on each side of
the opening is for the purpose of preventing the stream from narrowing
as it flows through the opening, and thus upsetting the calculations.
This weir should be set directly across the flow of the stream,
perfectly level, and upright. It should be so imbedded in the banks,
and in the bottom of the stream, that no water can escape, except
through the opening cut for that purpose. It will require a little
experimenting with a rough model to determine just how wide and how
deep this opening should be. It should be large enough to prevent
water flowing over the top of the board; and it should be small
enough to cause a still-water pond to form for several feet behind the
weir. Keep in mind the idea of the overflowing water trough when
building your weir. The stream, running down from a higher level
behind, should be emptying into a still-water pond, which in turn
should be emptying itself through the aperture in the board at the
same rate as the stream is keeping the pond full.
Your weir should be fashioned with the idea of some permanency so that
a number of measurements may be taken, extending over a period of
time–thus enabling the prospector to make a reliable estimate not
only of the amount of water flowing at any one time, but of its
fluctuations.
Under expert supervision, this simple weir is an exact
contrivance–exact enough, in fact, for the finest calculations
required in engineering work. To find out how many cubic feet of water
the stream is delivering at any moment, all that is necessary is to
measure its depth where it flows through the opening. There are
instruments, like the hook-gauge, which are designed to measure this
depth with accuracy up to one-thousandth of an inch. An ordinary foot
rule, or a folding rule, will give results sufficiently accurate for
the water prospector in this instance. The depth should be measured
not at the opening itself, but a short distance back of the opening,
where the water is setting at a dead level and is moving very slowly.
With this weir, every square inch of water flowing through the opening
indicates roughly one cubic foot of water a minute. Thus if the
opening is 10 inches wide and the water flowing through it is 5 inches
deep, the number of cubic feet a minute the stream is delivering is 10
x 5 = 50 square inches = 50 cubic feet a minute. This is a very small
stream; yet, if it could be made to fall through a water wheel 10 feet
below a pond or reservoir, it would exert a continuous pressure of
30,000 pounds per minute on the blades of the wheel–nearly one
theoretical horsepower.
This estimate of one cubic foot to each square inch is a very rough
approximation. Engineers have developed many complicated formulas for
determining the flow of water through weirs, taking into account fine
variations that the farm prospector need not heed. The so-called
Francis formula, developed by a long series of actual experiments at
Lowell, Mass., in 1852 by Mr. James B. Francis, with weirs 10 feet
long and 5 feet 2 inches high, is standard for these calculations and
is expressed (for those who desire to use it for special purposes) as
follows:
Q = 3.33 L H^(3/2) or, Q = 3.33 L H sqrt(H),
in which Q means _quantity_ of water in cubic feet per second, L is
length of opening, in feet; and H is height of opening in feet.
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 1/4 1/2 3/4
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 6-1/4
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 “1/4″.
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 x 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.
