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; t
In general, there are two types of water wheels, the impulse wheel and the reaction wheel. Both are called turbines, although the name belongs, more properly, to the reaction wheel alone.
Impulse wheels derive their power from the momentum of falling water. Reaction wheels derive their power from the momentum and pressure of falling water. The old-fashioned undershot, overshot, and breast wheels are 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 the turbine, 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 is limited, 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.
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 completely absorb 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 each bucket 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 the flume. 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, the tangential 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 water motors; 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 mains when 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 the effective head, and determines the amount of power delivered at the nozzle.
The tables on pages 66-67 show the friction loss 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:
To calculate what the horsepower of this tube 12 inches in diameter and 900 feet long, would be without a nozzle, under a head of 240 feet, introduces a new element of friction losses, which is too complicated to figure here. Such a condition would not be met with in actual practice, in any event. The largest nozzles used, even in the jumbo plants of the Far West, rarely exceed 10 inches in diameter; and the pipe conveying water to such a nozzle is upwards of eight feet in diameter.
PIPE FRICTION TABLES
INDICATING THE CALCULATED LOSS OF HEAD DUE TO FRICTION IN RIVETED STEEL PIPE WITH VARIOUS WATER QUANTITIES AND VELOCITIES
[Courtesy of the Pelton Water Wheel Company]
Heavy-faced figures = Loss of head in feet for each one thousand feet of pipe.
Light-faced figures = Water quantity in cubic feet per minute.
|Velocity in Feet per Second|
|Velocity in Feet per Second|
Assume the surveyed head as 240 feet, the water quantity as 207 cubic feet per minute and a pipe line 12 inches in diameter 900 feet long. To ascertain the friction loss, refer to column of pipe diameter and follow across the column for 12 inches diameter to the quantity, 207 cubic feet per minute. The heavy-faced figures above 207 indicate that the loss per 1000 feet of pipe length is 11 feet. Therefore, since the pipe in the example is 900 feet long, the loss will be 11.' × 900/1000 or 9.9 feet, and the effective head will be 240' - 9.9' = 230.1'
Steel tubing for supply pipes, from 3 to 12 inches in diameter is listed at from 20 cents to $1.50 a foot, according to the diameter and thickness of the material. Discounts on these prices will vary from 25 to 50 per cent. The farmer can cut down the cost of this pipe by conveying his supply water from its natural source to a pond, by means of an open race, or a wooden flume. An ingenious mechanic can even construct his own pipe out of wood, though figuring labor and materials, it is doubtful if anything would be saved over a riveted steel pipe, purchased at the regular price. This pipe, leading from the pond, or forebay, to the water wheel, should be kept as short as possible; at the same time, the fall should not be too sharp. An angle of 30° will be found very satisfactory, although pipe is frequently laid at angles up to 50°.
Other Types of Impulse Wheels
In recent years more efficient forms of the old-fashioned overshoot, pitch-back breast, and undershoot wheels have been developed, by substituting steel or other metal for wood, and altering the shape of the buckets to make better use of the power of falling water.
In some forms of overshoot wheels, an efficiency of over 90 per cent is claimed by manufacturers; and this type offers the additional advantage of utilizing small quantities of water, as well as being efficient under varying quantities of water. They utilize the falling weight of water, although by giving the water momentum at the point of delivery, by means of the proper fall, impulse too is utilized in some measure. The modern steel overshoot wheel receives water in its buckets from a spout set a few degrees back of dead center; and its buckets are so shaped that the water is retained a full half-revolution of the wheel. The old-style overshoot wheel was inefficient principally because the buckets began emptying themselves at the end of a quarter-revolution. Another advantage claimed for these wheels over the old style is that, being made of thin metal, their buckets attain the temperature of the water itself, thus reducing the danger of freezing to a minimum. They are manufactured in sizes from 6 feet in diameter to upwards of fifty feet; and with buckets of from 6 inches to 10 feet in width. In practice it is usual to deliver water to the buckets by means of a trough or pipe, through a suitable spout and gate, at a point two feet above the crown of the wheel. For this reason, the diameter of the wheel corresponds very closely to the head in feet.
The Reaction Turbine
The reaction turbine is best adapted to low heads, with a large supply of water. It is not advisable, under ordinary circumstances, to use it under heads exceeding 100 feet, as its speed is then excessive. It may be used under falls as low as two feet. Five thousand cubic feet of water a minute would give approximately 14 actual horsepower under such a head. A sluggish creek that flows in large volume could thus be utilized for power with the reaction turbine, whereas it would be useless with an impulse wheel. Falls of from five to fifteen feet are to be found on thousands of farm streams, and the reaction turbine is admirably adapted to them.
Reaction turbines consist of an iron "runner" which is in effect a rotary fan, the pressure and momentum of the column of water pressing on the slanted blades giving it motion and power. These wheels are manufactured in a great variety of forms and sizes; and are to be purchased either as the runner (set in bearings) alone, or as a runner enclosed in an iron case. In case the runner alone is purchased, the owner must enclose it, either with iron or wood. They vary in price according to size, and the means by which the flow of water is controlled. A simple 12-inch reaction turbine wheel, such as would be suitable for many power plants can be had for $75. A twelve-inch wheel, using 18 or 20 square inches of water, would generate about 7½ horsepower under a 20-foot head, with 268 cubic feet of water a minute. Under a 30-foot head, and with 330 cubic feet of water such a wheel will give 14 horsepower. A 36-inch wheel, under a 5-foot head, would use 2,000 cubic feet of water, and give 14 horsepower. Under a 30-foot head, this same wheel, using 4,900 cubic feet of water a minute, would develop over 200 horsepower. If the farmer is confronted by the situation of a great deal of water and small head, a large wheel would be necessary. Thus he could secure 35 horsepower with only a 3-foot head, providing his water supply is equal to the draft of 8,300 cubic feet a minute.
From these sample figures, it will be seen that the reaction turbine will meet the requirements of widely varying conditions up to, say a head of 100 feet. The farmer prospector should measure first the quantity of water to be depended on, and then the number of feet fall to be had. The higher the fall, with certain limits, the smaller the expense of installation, and the less water required. When he has determined quantity and head, the catalogue of a reputable manufacturer will supply him with what information is necessary to decide on the style and size wheel he should install. In the older settled communities, especially in New England, a farmer should be able to pick up a second-hand turbine, at half the price asked for a new one; and since these wheels do not depreciate rapidly, it would serve his purpose as well, in most cases, as a new one.
Reaction turbines may be either horizontal or vertical. If they are vertical, it is necessary to connect them to the main shaft by means of a set of bevel gears. These gears should be substantially large, and if the teeth are of hard wood (set in such a manner that they can be replaced when worn) they will be found more satisfactory than if of cast or cut metal.
The horizontal turbine is keyed to its shaft, like the impulse wheel, so that the wheel shaft itself is used for driving, without gears or a quarter-turn belt. (The latter is to be avoided, wherever possible.) There are many forms of horizontal turbines; they are to be had of the duplex type, that is, two wheels on one shaft. These are arranged so that either wheel may be run separately, or both together, thus permitting one to take advantage of the seasonal fluctuation in water supply. A convenient form of these wheels includes draft tubes, by which the wheel may be set several feet above the tailrace, and the advantage of this additional fall still be preserved. In this case the draft tube must be airtight so as to form suction, when filled with escaping water, and should be proportioned to the size of the wheel. Theoretically these draft tubes might be 34 feet long, but in practice it has been found that they should not exceed 10 or 12 feet under ordinary circumstances. They permit the wheel to be installed on the main floor of the power station, with the escape below, instead of being set just above the tailrace level itself, as is the case when draft tubes are not used.
Reaction turbines when working under a variable load require water governors (like impulse wheels) although where the supply of water is large, and the proportion of power between water wheel and dynamo is liberal—say two to one, or more—this necessity is greatly reduced. Reaction wheels as a rule govern themselves better than impulse wheels, due both to the fact that they use more water, and that they operate in a small airtight case. The centrifugal ball governor is the type usually used with reaction wheels as well as with impulse wheels. This subject will be discussed more fully later.
Installing a Power Plant
In developing a power prospect, the dam itself is usually not the site of the power plant. In fact, because of danger from flood water and ice, it is better to locate it in a more protected spot, leading the water to the wheel by means of a race and flume.
A typical crib dam, filled with stone, is shown in section in the diagram, and the half-tone illustration shows such a dam in course of construction. The first bed of timbers should be laid on hard-pan or solid rock in the bed of the stream parallel to its flow. The second course, across the stream, is then begun, being spiked home by means of rods cut to length and sharpened by the local blacksmith, from ¾-inch Norway iron. Hemlock logs are suitable for building the crib; and as the timbers are finally laid, it should be filled in and made solid with boulders. This filling in should proceed section by section, as the planking goes forward, otherwise there will be no escape for the water of the stream, until it rises and spills over the top timbers. The planking should be of two-inch chestnut, spiked home with 60 penny wire spikes. When the last section of the crib is filled with boulders and the water rises, the remaining planks may be spiked home with the aid of an iron pipe in which to drive the spike by means of a plunger of iron long enough to reach above the level of the water. When the planking is completed, the dam should be well gravelled, to within a foot or two of its crest. Such dams are substantial, easily made with the aid of unskilled labor, and the materials are to be had on the average farm with the exception of the hardware.
This dam forms a pond from which the race draws its supply of water for the wheel. It also serves as a spillway over which the surplus water escapes. The race should enter the pond at some convenient point, and should be protected at or near its point of entrance by a bulkhead containing a gate, so that the supply of water may be cut off from the race and wheel readily. The lay of the land will determine the length and course of the race. The object of the race is to secure the required head by carrying a portion of the available water to a point where it can escape, by a fall of say 30° to the tailrace. It may be feasible to carry the race in a line almost at right angles to the stream itself, or, again, it may be necessary to parallel the stream. If the lay of the land is favorable, the race may be dug to a distance of a rod or so inshore, and then be permitted to cut its own course along the bank, preventing the water escaping back to the river or brook before the site of the power plant is reached, by building suitable retaining embankments. The race should be of ample size for conveying the water required without too much friction. It should end in a flume constructed stoutly of timbers. It is from this flume that the penstock draws water for the wheel. When the wheel gate is closed the water in the mill pond behind the dam, and in the flume itself should maintain an approximate level. Any surplus flow is permitted to escape over flushboards in the flume; these same flushboards maintain a constant head when the wheel is in operation by carrying off what little surplus water the race delivers from the pond.
At some point in the race or flume, the flow should be protected from leaves and other trash by means of a rack. This rack is best made of ¼ or ½-inch battens from 1½ to 3 inches in width, bolted together on their flat faces and separated a distance equal to the thickness of the battens by means of iron washers. This rack will accumulate leaves and trash, varying with the time of year and should be kept clean, so as not to cut down the supply of water needed by the wheel.
The penstock, or pipe conveying water from the flume to the wheel, should be constructed of liberal size, and substantially, of two-inch chestnut planking, with joints caulked with oakum, and the whole well bound together to resist the pressure of the water. Means should be provided near the bottom for an opening through which to remove any obstructions that may by accident pass by the rack. Many wheels have plates provided in their cases for this purpose.
The tailrace should be provided with enough fall to carry the escaping water back to the main stream, without backing up on the wheel itself and thus cutting down the head.
It is impossible to make any estimates of the cost of such a water-power plant. The labor required will in most instances be supplied by the farmer himself, his sons, and his help, during times when farm operations are slack.
Water Rights of the Farmer
The farmer owns the bed of every stream not navigable, lying within the boundary lines of the farm; and his right to divert and make use of the water of such streams is determined in most states by common law. In the dry-land states where water is scarce and is valuable for irrigation, a special set of statutes has sprung up with the development of irrigation in this country.
A stream on the farm is either public or private; its being navigable or "floatable" (suitable for floating logs) determining which. Water rights are termed in law "riparian" rights, and land is riparian only when water flows over it or along its borders.
Green (Law for the American Farmer) says:
"Water is the common and equal property of every one through whose land it flows, and the right of each land-owner to use and consume it without destroying, or unreasonably impairing the rights of others, is the same. An owner of land bordering on a running stream has the right to have its waters flow naturally, and none can lawfully divert them without his consent. Each riparian proprietor has an equal right with all the others to have the stream flow in its natural way without substantial reduction in volume, or deterioration in quality, subject to a proper and reasonable use of its waters for domestic, agricultural and manufacturing purposes, and he is entitled to use it himself for such purposes, but in doing so must not substantially injure others. In addition to the right of drawing water for the purposes just mentioned, a riparian proprietor, if he duly regards the rights of others, and does not unreasonably deplete the supply, has also the right to take the water for some other proper uses."
Thus, the farmer who seeks to develop water-power from a stream flowing across his own land, has the right to divert such a stream from its natural channel—providing it is not a navigable or floatable stream—but in so doing, he must return it to its own channel for lower riparian owners. The generation of water-power does not pollute the water, nor does it diminish the water in quantity, therefore the farmer is infringing on no other owner's rights in using the water for such a purpose.
When a stream is a dividing line between two farms, as is frequently the case, each proprietor owns to the middle of the stream and controls its banks. Therefore to erect a dam across such a private stream and divert all or a part of the water for power purposes, requires the consent of the neighboring owner. The owner of the dam is responsible for damage due to flooding, to upstream riparian owners.