Measuring a small stream with a weir
In your neighborhood there is a creek three or four feet wide, toiling along day by day, at its task of watering your fields. Find a wide board a little longer than the width of this creek you have scorned. Set it upright across the stream between the banks, so that no water flows around the ends or under it. It should be high enough to set the water back to a dead level for a few feet upstream, before it overflows. Cut a gate in this board, say three feet wide and ten inches deep, or according to the size of a stream. Cut this gate from the top, so that all the water of the stream will flow through the opening, and still maintain a level for several feet back of the board.
This is what engineers call a weir, a handy contrivance for measuring the flow of small streams. Experts have figured out an elaborate system of tables as to weirs. All we need to do now, in this rough survey, is to figure out the number of square inches of water flowing through this opening and falling on the other side. With a rule, measure the depth of the overflowing water, from the bottomof the opening to the top of the dead level of the water behind the board. Multiply this depth by the width of the opening, which will give the square inches of water escaping. For every square inch of this water escaping, engineers tell us that stream is capable of delivering, roughly, one cubic foot of water a minute.
Thus, if the water is 8 inches deep in an opening 32 inches wide, then the number of cubic feet this stream is delivering each minute is 8 times 32, or 256 cubic feet a minute. So, a stream 32 inches wide, with a uniform depth of 8 inches running through our weir is capable of supplying the demands of the average farm in terms of electricity. Providing, of course, that the lay of the land is such that this water can be made to fall 10 feet into a water wheel.
Go upstream and make a rough survey of the fall. In the majority of instances (unless this is some sluggish stream in a flat prairie) it will be found feasible to divert the stream from its main channel by means of a race—anartificial channel—and to convey it to a not far-distant spot where the necessary fall can be had at an angle of about 30 degrees from horizontal.
If you find there istwiceas much water as you need for the amount of power you require, a five-foot fall will give the same result. Or, if there is onlyone-halfas much water as the 250 cubic feet specified, you can still obtain your theoretical five horsepower if the means are at hand for providing a fall of twenty feet instead of ten. Do not make the very common mistake of figuring that a stream is delivering a cubic foot a minute to each square inch of weir opening, simply because itfillsa certain opening. It is the excess water, fallingoverthe opening, after the stream has set back to a permanent dead level, that is to be measured.
This farmer who spends an idle day measuring the flow of his brook with a notched board, may say here: "This is all very well. This is the spring of the year, when my brook is flowing at high-water mark. What am I going to do in the dry months of summer, whenthere are not 250 cubic feet of water escaping every minute?"
There are several answers to this question, which will be taken up in detail in subsequent chapters. Here, let us say, even if this brook does flow in sufficient volume only 8 months in a year—the dark months, by the way,—is not electricity and the many benefits it provides worth having eight months in the year? My garden provides fresh vegetables four months a year. Because it withers and dies and lies covered with snow during the winter, is that any reason why I should not plow and manure and plant my garden when spring comes again?
A water wheel, the modern turbine, is a circular fan with curved iron blades, revolving in an iron case. Water, forced through the blades of this fan by its own weight, causes the wheel to revolve on its axis; and the fan, in turn causes a shaft fitted with pulleys to revolve.
The water, by giving the iron-bladed fan a turning movement as it rushes through, impartsto it mechanical power. The shaft set in motion by means of this mechanical power is, in turn, belted to the pulley of a dynamo. This dynamo consists, first, of a shaft on which is placed a spool, wound in a curious way, with many turns of insulated copper wire. This spool revolves freely in an air space surrounded by electric magnets. The spool does not touch these magnets. It is so nicely balanced that the weight of a finger will turn it. Yet, when it is revolved by water-power at a predetermined speed—say 1,500 revolutions a minute—it generates electricity, transforms the mechanical power of the water wheel into another form of energy—a form of energy which can be carried for long distances on copper wires, which can, by touching a button, be itself converted into light, or heat, or back into mechanical energy again.
If two wires be led from opposite sides of this revolving spool, and an electric lamp be connected from one to the other wire, the lamp will be lighted—will grow white hot,—henceincandescent light. The instant this lamp is turned on, the revolving spool feels a stress, the magnets by which it is surrounded begin to pull back on it. The power of the water wheel, however, overcomes this pull. If one hundred lights be turned on, the backward pull of the magnets surrounding the spool will be one hundred times as strong as for one light. For every ounce of electrical energy used in light or heat or power, the dynamo will require a like ounce of mechanical power from the water wheel which drives it.
The story is told of a canny Scotch engineer, who, in the first days of dynamos, not so very long ago, scoffed at the suggestion that such a spool, spinning in free air, in well lubricated bearings, could bring his big Corliss steam engine to a stop. Yet he saw it done simply by belting this "spool," a dynamo, to his engine and asking the dynamo for more power in terms of light than his steam could deliver in terms of mechanical power to overcome the pull of the magnets.
Electricity must be consumed the instant it is generated (except in rare instances where small amounts are accumulated in storage batteries by a chemical process). The pressure of a button, or the throw of a switch causes the dynamo instantly to respond with just enough energy to do the work asked of it, always in proportion to the amount required. Having this in mind, it is rather curious to think of electricity as being an article of export, an item in international trade. Yet in 1913 hydro-electric companies in Canada "exported" by means of wires, to this country over 772,000,000 kilowatt-hours (over one billion horsepower hours) of electricity for use in factories near the boundary line.
This 250 cubic feet of water per minute then, which the farmer has measured by means of his notched board, will transform by means of its falling weight mechanical power into a like amount of electrical power—less friction losses, which may amount to as much as 60% in very small machines, and 15% in largerplants. That is, the brook which has been draining your pastures for uncounted ages contains the potential power of 3 and 4 young horses—with this difference: that it works 24 hours a day, runs on forever, and requires no oats or hay. And the cost of such an electric plant, which is ample for the needs of the average farm,is in most cases less than the price of a good farm horse—the $200 kind—not counting labor of installation.
It is the purpose of these chapters to awaken the farmer to the possibilities of such small water-power as he or his community may possess; to show that the generating of electricity is a very simple operation, and that the maintenance and care of such a plant is within the mechanical ability of any American farmer or farm boy; and to show that electricity itself is far from being the dangerous death-dealing "fluid" of popular imagination. Electricity must be studied; and then it becomes an obedient, tireless servant. During the past decade or two, mathematical wizards have studied electricity, explored its atoms,reduced it to simple arithmetic—and although they cannot yet tell uswhyit is generated, they tell ushow. It is with this simple arithmetic, and the necessary manual operations that we have to do here.
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—Quantity of water necessary.
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—Quantity 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 space 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 ofphysical 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 mass 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 thisnatural 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 toescape 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 thequantityof water, and to thedistancein feet which it falls to reach the wheel—poundsandfeet.
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-class gasoline engine that can deliver even 15 per cent; a steam engine, onthe other hand, uses about 17 per cent of the energy in the coal under its boilers and passes 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 ismaintained 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 analyzed, 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, incubic feet per minute. (A cubic foot of water weighs 62.5 pounds, and contains 7½ 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.
Detail of home-made weir
Cross-section of weir
The diagrams show the cross-section and detail of a typical weir, which can be puttogether 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 theboard; 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 areinstruments, 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, 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 meansquantityof 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
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 isnecessary 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 ofQuantitycan easily be determined. The next problem is to determine whatHeadcan be obtained.Headis 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 tohead, just as it is directly proportional toquantity. Thus the typical weir measured above was 30 inches wide and 6¼ deep, giving 189 cubic feet of water a minute—Quantity.Since such a stream is of common occurrence on thousands of farms, let us analyze briefly its possibilities for power: One hundred and eighty-nine cubic feet of waterweighs 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.
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 withquantityandhead, it is obvious that a streamone-halfas big fallingtwiceas far, would still give one horsepower at the wheel; or, a stream of 189 cubic feet a minute fallingten timesas far, 30 feet, would giveten timesthe power, ortenhorsepower; a stream fallingone hundred timesas far would giveone hundredhorsepower. Thus small quantities of water falling great distances, or large quantities 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 Quantity and Head are known, is as follows:
(A) Theoretical Horsepower = (Cu. Ft. per minute × Feet head × 62.5) / 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: H.P. = (Cu. ft. p. m. 376 × head 13.5 × pounds 62.5) / 33,000 = 9.614 horsepower
This istheoretical horsepower. To determine theactualhorsepower 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.
This is due to theacceleration of gravityon falling bodies. A rifle bullet shot into the air with a muzzle velocity of 3,000 feet a second begins to diminish its speed instantly on leaving the muzzle, and continues to diminish in speed at the fixed rate of 32.16 feet a second, until it finally comes to a stop, and starts to descend. Then, again, its speed accelerates at the rate of 32.16 feet a second, until on striking the earth it has attained the velocity at which it left the muzzle of the rifle, less loss due to friction.
The acceleration of gravity affects falling water in the same manner as it affects a falling bullet. At any one second, during its course of fall, it is traveling at a rate 32.16 feet a second in excess of its speed the previous second.
In figuring the size wheel necessary under given conditions or to determine the power of water with a given nozzle opening, it is necessary to take this into account. The table on page 51 gives velocity per second of falling water, ignoring the friction of the pipe, in heads from 5 to 1000 feet.
The scientific formula from which the table is computed is expressed as follows, for those of a mathematical turn of mind:
Velocity (ft. per sec.) = sqrt(2gh); or, velocity is equal to the square root of the product (g = 32.16,—times head in feet, multiplied by 2).
SPOUTING VELOCITY OF WATER, IN FEET PER SECOND, IN HEADS OF FROM 5 TO 1,000 FEET
In the above example, we found that 376 cubic feet of water a minute, under 13.5 feet head, would deliver 7.2 actual horsepower. Question: What size wheel would it be necessary to install under such conditions?
By referring to the table of velocity above, (or by using the formula), we find that water under a head of 13.5 feet, has a spouting velocity of 29.5 feet a second. This means that a solid stream of water 29.5 feet long would pass through the wheel in one second.What should be the diameter of such a stream, to make its cubical contents 376 cubic feet a minute or 376/60 = 6.27 cubic feet a second?The following formula should be used to determine this:
(B) Sq. Inches of wheel = (144 × cu. ft. per second) / (Velocity in ft. per sec.)
Substituting values, in the above instance, we have:
Answer: Sq. Inches of wheel = (144 × 6.27 Cu. Ft. Sec.) / (29.5 Velocity in feet.) = 30.6 sq. in.
That is, a wheel capable of using 30.6 square inches of water would meet these conditions.
What Head is Required
Let us attack the problem of water-power in another way.A farmer wishes to install a water wheel that will deliver 10 horsepower on the shaft, and he finds his stream delivers 400 cubic feet of water a minute. How many feet fall is required?Formula:
(C) Head in feet = (33,000 × horsepower required) / (Cu. Ft. per minute × 62.5)
Since a theoretical horsepower is only 75 per cent efficient, he would require 10 × 4/3 = 13.33 theoretical horsepower of water, in this instance. Substituting the values of the problem in the formula, we have:
Answer: Head = (33,000 × 13.33) / (400 × 62.5) = 17.6 feet fall required.
What capacity of wheel would this prospect (400 cubic feet of water a minute falling 17.6 feet, and developing 13.33 horsepower) require?
By referring to the table of velocities, we find that the velocity for 17.5 feet head (nearly) is 33.6 feet a second. Four hundredfeet of water a minute is 400/60 = 6.67 cu. ft. a second. Substituting these values, in formula (B) then, we have:
Answer: Capacity of wheel = (144 × 6.67) / 33.6 = 28.6 sq. in. of water.
Quantity of Water
Let us take still another problem which the prospector may be called on to solve:A man finds that he can conveniently get a fall of 27 feet. He desires 20 actual horsepower. What quantity of water will be necessary, and what capacity wheel?
Twenty actual horsepower will be 20 × 4/3 = 26.67 theoretical horsepower. Formula:
(D) Cubic feet per minute = (33,000 × Hp. required) / (Head in feet × 62.5)
Substituting values, then, we have:
Cu. Ft. per minute = (33,000 × 26.67) / (27 × 62.5) = 521.5 cubic ft. a minute.
A head of 27 feet would give this stream a velocity of 41.7 feet a second, and, fromformula (B) we find that the capacity of the wheel should be 30 square inches.
It is well to remember that the square inches of wheel capacity does not refer to the size of pipe conveying water from the head to the wheel, but merely to the actual nozzle capacity provided by the wheel itself. In small installations of low head, such as above a penstock at least six times the nozzle capacity should be used, to avoid losing effective head from friction. Thus, with a nozzle of 30 square inches, the penstock or pipe should be 180 square inches, or nearly 14 inches square inside measurement. A larger penstock would be still better.
THE WATER WHEEL AND HOW TO INSTALL IT
Different types of water wheels—The impulse and reaction wheels—The impulse wheel adapted to high heads and small amount of water—Pipe lines—Table of resistance in pipes—Advantages and disadvantages of the impulse wheel—Other forms of impulse wheels—The reaction turbine, suited to low heads and large quantity of water—Its advantages and limitations—Developing a water-power project: the dam; the race; the flume; the penstock; and the tailrace—Water rights for the farmer.
Different types of water wheels—The impulse and reaction wheels—The impulse wheel adapted to high heads and small amount of water—Pipe lines—Table of resistance in pipes—Advantages and disadvantages of the impulse wheel—Other forms of impulse wheels—The reaction turbine, suited to low heads and large quantity of water—Its advantages and limitations—Developing a water-power project: the dam; the race; the flume; the penstock; and the tailrace—Water rights for the farmer.
In general, there are two types of water wheels, theimpulsewheel and thereactionwheel. Both are called turbines, although the name belongs, more properly, to the reaction wheel alone.
Impulse wheels derive their power from themomentumof falling water. Reaction wheels derive their power from themomentum and pressureof falling water. The old-fashionedundershot,overshot, andbreastwheelsare familiar to all as examples of impulse wheels. Water wheels of this class revolve in the air, with the energy of the water exerted on one face of their buckets. On the other hand, reaction wheels are enclosed in water-tight cases, either of metal or of wood, and the buckets are entirely surrounded by water.
The old-fashioned undershot, overshot, and breast wheels were not very efficient; they wasted about 75 per cent of the power applied to them. A modern impulse wheel, on the other hand, operates at an efficiency of 80 per cent and over. The loss is mainly through friction and leakage, and cannot be eliminated altogether. The modern reaction wheel, called theturbine, attains an equal efficiency. Individual conditions govern the type of wheel to be selected.
The Impulse, or Tangential Water Wheel
The modern impulse, or tangential wheel (so called because the driving stream of water strikes the wheel at a tangent) is best adapted to situations where the amount of water islimited, and the head is large. Thus, a mountain brook supplying only seven cubic feet of water a minute—a stream less than two-and-a-half inches deep flowing over a weir with an opening three inches wide—would develop two actual horsepower, under a head of 200 feet—not an unusual head to be found in the hill country. Under a head of one thousand feet, a stream furnishing 352.6 cubic feet of water a minute would develop 534.01 horsepower at the nozzle.
Ordinarily these wheels are not used under heads of less than 20 feet. A wheel of this type, six feet in diameter, would develop six horsepower, with 188 cubic feet of water a minute and 20-foot head. The great majority of impulse wheels are used under heads of 100 feet and over. In this country the greatest head in use is slightly over 2,100 feet, although in Switzerland there is one plant utilizing a head of over 5,000 feet.
Runner of Pelton wheel, showing peculiar shape of the buckets
The Fitz overshoot wheel
Efficient Modern Adaptations of the Archaic Undershot and Overshot Water Wheels
The old-fashioned impulse wheels were inefficient because of the fact that their buckets were not constructed scientifically, and much of the force of the water was lost at the moment of impact. The impulse wheel of to-day, however, has buckets which so completelyabsorb the momentum of water issuing from a nozzle, that the water falls into the tailrace with practically no velocity. When it is remembered that the nozzle pressure under a 2,250-foot head is nearly 1,000 pounds to the square inch, and that water issues from this nozzle with a velocity of 23,000 feet a minute, the scientific precision of this type of bucket can be appreciated.
A typical bucket for such a wheel is shaped like an open clam shell, the central line which cuts the stream of water into halves being ground to a sharp edge. The curves which absorb the momentum of the water are figured mathematically and in practice become polished like mirrors. So great is the eroding action of water, under great heads—especially when it contains sand or silt—that it is occasionally necessary to replace these buckets. For this reason the larger wheels consist merely of a spider of iron or steel, with eachbucket bolted separately to its circumference, so that it can be removed and replaced easily. Usually only one nozzle is provided; but in order to use this wheel under low heads—down to 10 feet—a number of nozzles are used, sometimes five, where the water supply is plentiful.
The wheel is keyed to a horizontal shaft running in babbited bearings, and this same shaft is used for driving the generator, either by direct connection, or by means of pulleys and a belt. The wheel may be mounted on a home-made timber base, or on an iron frame. It takes up very little room, especially when it is so set that the nozzle can be mounted under the flooring. The wheel itself is enclosed, above the floor, in a wooden box, or a casing made of cast or sheet iron, which should be water-tight.
Since these wheels are usually operated under great heads, the problem of regulating their water supply requires special consideration. A gate is always provided at the upper, or intake end, where the water pipe leaves theflume. Since the pressure reaches 1,000 pounds the square inch and more, there would be danger of bursting the pipe if the water were suddenly shut off at the nozzle itself. For this reason it is necessary to use a needle valve, similar to that in an ordinary garden hose nozzle; and by such a valve the amount of water may be regulated to a nicety. Where the head is so great that even such a valve could not be used safely, provision is made to deflect the nozzle. These wheels have a speed variation amounting to as much as 25 per cent from no-load to full load, in generating electricity, and since the speed of the prime mover—the water wheel—is reflected directly in the voltage or pressure of electricity delivered, the wheel must be provided with some form of automatic governor. This consists usually of two centrifugal balls, similar to those used in governing steam engines; these are connected by means of gears to the needle valve or the deflector.
As the demand for farm water-powers in our hill sections becomes more general, thetangential type of water wheel will come into common use for small plants. At present it is most familiar in the great commercial installations of the Far West, working under enormous heads. These wheels are to be had in the market ranging in size from six inches to six feet and over. Wheels ranging in size from six inches to twenty-four inches are called water motors, and are to be had in the market, new, for $30 for the smallest size, and $275 for the largest. Above three feet in diameter, the list prices will run from $200 for a 3-foot wheel to $800 for a 6-foot wheel. Where one has a surplus of water, it is possible to install a multiple nozzle wheel, under heads of from 10 to 100 feet, the cost for 18-inch wheels of this pattern running from $150 to $180 list, and for 24-inch wheels from $200 to $250. A 24-inch wheel, with a 10-foot head would give 1.19 horsepower, enough for lighting the home, and using an electric iron. Under a 100-foot head this same wheel would provide 25.9 horsepower, to meet the requirements of a bigger-than-average farm plant.
The Pipe Line
The principal items of cost in installing an impulse wheel are in connection with the pipe line, and the governor. In small heads, that is, under 100 feet, the expense of pipe line is low. Frequently, however, the governor will cost more than the water motor itself, although cheaper, yet efficient, makes are now being put on the market to meet this objection. In a later chapter, we will take up in detail the question of governing the water wheel, and voltage regulation, and will attempt to show how this expense may be practically eliminated by the farmer.
To secure large heads, it is usually necessary to run a pipe line many hundreds (and in many cases, many thousands) of feet from the flume to the water wheel. Water flowing through pipes is subject to loss of head, by friction, and for this reason the larger the pipe the less the friction loss. Under no circumstances is it recommended to use a pipe of less than two inches in diameter, even for the smallest watermotors; and with a two-inch pipe, the run should not exceed 200 feet. Where heavy-pressure mains, such as those of municipal or commercial water systems, are available, the problem of both water supply and head becomes very simple. Merely ascertain the pressure of the water in the mainswhen flowing, determine the amount of power required (as illustrated in a succeeding chapter of this book), and install the proper water motor with a suitably sized pipe.
Where one has his own water supply, however, and it is necessary to lay pipe to secure the requisite fall, the problem is more difficult. Friction in pipes acts in the same way as cutting down the head a proportional amount; and by cutting down the head, your water motor loses power in direct proportion to the number of feet head lost. This head, obtained by subtracting friction and other losses from the surveyed head, is called theeffective head, and determines the amount of power delivered at the nozzle.
The tables on pages 66-67 show the frictionloss in pipes up to 12 inches in diameter, according to the amount of water, and the length of pipe.
In this example it is seen that a 240-foot static head is reduced by friction to 230.1 feet effective head. By referring to the table we find the wheel fitting these conditions has a nozzle so small that it cuts down the rate of flow of water in the big pipe to 4.4 feet a second, and permits the flow of only 207 cubic feet of water a minute. The actual horsepower of this tube and nozzle, then, can be figured by applying formula (A), Chapter III, allowing 80 per cent for the efficiency of the wheel. Thus: