CHAPTER III

HOW TO MEASURE WATER-POWER

What is a horsepower?--How the Carthaginians manufactured horsepower--All that goes up must come down--How the sun lifts water up for us to use--Water the ideal power for generating electricity--The weir--Table for estimating flow of streams, with a weir--Another method of measuring--Figuring water horsepower--The size of the wheel--What head is required--Quant.i.ty of water necessary.

If a man were off in the woods and needed a horsepower of energy to work for him, he could generate it by lifting 550 pounds of stone or wood, or whatnot, one foot off the ground, and letting it fall back in the s.p.a.ce of one second. As a man possesses capacity for work equal to one-fifth horsepower, it would take him five seconds to do the work of lifting the weight up that the weight itself accomplished in falling down. All that goes up must come down; and by a nice balance of physical laws, a falling body hits the ground with precisely the same force as is required to lift it to the height from which it falls.

The Carthaginians, and other ancients (who were deep in the woods as regards mechanical knowledge) had their slaves carry huge stones to the top of the city wall; and the stones were placed in convenient positions to be tipped over on the heads of any besieging army that happened along. Thus by concentrating the energy of many slaves in one batch of stones, the warriors of that day were enabled to deliver "horsepower" in one ma.s.s where it would do the most good. The farmer who makes use of the energy of falling water to generate electricity for light, heat, and power does the same thing--he makes use of the capacity for work stored in water in being lifted to a certain height.

As in the case of the gasoline engine, which burns 14 pounds of air for every pound of gasoline, the engineer of the water-power plant does not have to concern himself with the question of how this natural source of energy happened to be in a handy place for him to make use of it.

The sun, shining on the ocean, and turning water into vapor by its heat has already lifted it up for him. This vapor floating in the air and blown about by winds, becomes chilled from one cause or another, gives up its heat, turns back into water, and falls as rain. This rain, falling on land five, ten, a hundred, a thousand, or ten thousand feet above the sea level, begins to run back to the sea, picking out the easiest road and cutting a channel that we call a brook, a stream, or a river. Our farm lands are covered to an average depth of about three feet a year with water, every gallon of which has stored in it the energy expended by the heat of the sun in lifting it to the height where it is found.

The farmer, prospecting on his land for water-power, locates a spot on a stream which he calls Supply; and another spot a few feet down hill near the same stream, which he calls Power. Every gallon of water that falls between these two points, and is made to escape through the revolving blades of a water wheel is capable of work in terms of foot-pounds--an amount of work that is directly proportional to the _quant.i.ty_ of water, and to the _distance_ in feet which it falls to reach the wheel--_pounds_ and _feet_.

_The Efficient Water Wheel_

And it is a very efficient form of work, too. In fact it is one of the most efficient forms of mechanical energy known--and one of the easiest controlled. A modern water wheel uses 85 per cent of the total capacity for work imparted to falling water by gravity, and delivers it as rotary motion. Compare this water wheel efficiency with other forms of mechanical power in common use: Whereas a water wheel uses 85 per cent of the energy of its water supply, and wastes only 15 per cent, a gasoline engine reverses the table, and delivers only 15 per cent of the energy in gasoline and wastes 85 per cent--and it is rather a high-cla.s.s gasoline engine that can deliver even 15 per cent; a steam engine, on the other hand, uses about 17 per cent of the energy in the coal under its boilers and pa.s.ses the rest up the chimney as waste heat and smoke.

There is still another advantage possessed by water-power over its two rivals, steam and gas: It gives the most even flow of power. A gas engine "kicks" a wheel round in a circle, by means of successive explosions in its cylinders. A reciprocating steam engine "kicks" a wheel round in a circle by means of steam expanding first in one direction, then in another. A water wheel, on the other hand, is made to revolve by means of the pressure of water--by the constant force of gravity, itself--weight. Weight is something that does not vary from minute to minute, or from one fraction of a second to another. It is always the same. A square inch of water pressing on the blades of a water wheel weights ten, twenty, a hundred pounds, according to the height of the pipe conveying that water from the source of supply, to the wheel. So long as this column of water is maintained at a fixed height, the power it delivers to the wheel does not vary by so much as the weight of a feather.

This property of falling water makes it the ideal power for generating electricity. Electricity generated from mechanical power depends on constant speed for steady pressure--since the electric current, when a.n.a.lyzed, is merely a succession of pulsations through a wire, like waves beating against a sea wall. Water-power delivers these waves at a constant speed, so that electric lights made from water-power do not flicker and jump like the flame of a lantern in a gusty wind. On the other hand, to accomplish the same thing with steam or gasoline requires an especially constructed engine.

_The Simple 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.

[Ill.u.s.tration: Detail of home-made weir]

[Ill.u.s.tration: 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 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, Ma.s.s., 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 _quant.i.ty_ 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 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 quant.i.ty 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_

By one of the above simple methods, the problem of _Quant.i.ty_ can easily be determined. The next problem is to determine what _Head_ can be obtained. _Head_ is the distance in feet the water may be made to fall, from the Source of Supply, to the water wheel itself. The power of water is directly proportional to _head_, just as it is directly proportional to _quant.i.ty_. Thus the typical weir measured above was 30 inches wide and 6-1/4 deep, giving 189 cubic feet of water a minute--_Quant.i.ty._ Since such a stream is of common occurrence on thousands of farms, let us a.n.a.lyze briefly its possibilities for power: One hundred and eighty-nine cubic feet of water weighs 189 62.5 pounds = 11,812.5 pounds. Drop this weight one foot, and we have 11,812.5 foot-pounds. Drop it 3 feet and we have 11,812 3 = 35,437.5 foot-pounds. Since 33,000 foot-pounds exerted in one minute is one horsepower, we have here a little more than one horsepower. For simplicity let us call it a horsepower.

[Ill.u.s.tration: Detail of a water-power plant, showing setting of wheel, and dynamo connection]

Now, since the work to be had from this water varies directly with _quant.i.ty_ and _head_, it is obvious that a stream _one-half_ as big falling _twice_ as far, would still give one horsepower at the wheel; or, a stream of 189 cubic feet a minute falling _ten times_ as far, 30 feet, would give _ten times_ the power, or _ten_ horsepower; a stream falling _one hundred times_ as far would give _one hundred_ horsepower. Thus small quant.i.ties of water falling great distances, or large quant.i.ties of water falling small distances may accomplish the same results. From this it will be seen, that the simple formula for determining the theoretical horsepower of any stream, in which Quant.i.ty and Head are known, is as follows:

Cu. Ft.

per Feet minute head 62.5 (A) Theoretical Horsepower = ---------------------- 33,000

_As an example, let us say that we have a stream whose weir measurement shows it capable of delivering 376 cubic feet a minute, with a head (determined by survey) of 13 feet 6 inches. What is the horsepower of this stream?_

Answer:

Cu. ft. p. m. head pounds 376 13.5 62.5 H.P. = ----------------------------- = 9.614 horsepower 33,000

This is _theoretical horsepower_. To determine the _actual_ horsepower that can be counted on, in practice, it is customary, with small water wheels, to figure 25 per cent loss through friction, etc. In this instance, the actual horsepower would then be 7.2.

_The Size of the Wheel_

Water wheels are not rated by horsepower by manufacturers, because the same wheel might develop one horsepower or one hundred horsepower, or even a thousand horsepower, according to the conditions under which it is used. With a given supply of water, the head, in feet, determines the size of wheel necessary. The farther a stream of water falls, the smaller the pipe necessary to carry a given number of gallons past a given point in a given time.

A small wheel, under 10 13.5 ft. head, would give the same power with the above 376 cubic feet of water a minute, as a large wheel would with 10 376 cubic feet, under a 13.5 foot head.