Actual horsepower = (207 × 230.1 × 62.5) / 33,000 = 90.21 × .80 = 72.168 Hp.
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 metwith 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.
PipeDiameterVelocity in Feet per Second2.02.22.42.62.83.03.23.43.63.84.04.24.417.120.025.628.332.037.340.945.850.456.062.368.174.93"5.96.57.17.78.38.99.410.010.611.211.812.413.011.013.015.017.320.223.226.229.633.036.541.045.449.24"10.511.512.613.614.715.716.817.818.819.921.022.023.07.79.411.012.914.916.919.521.624.027.029.832.936.05"16.418.019.621.222.924.526.127.829.531.032.734.336.06.07.28.69.911.713.014.616.619.021.523.425.527.86"23.525.928.230.632.935.337.740.042.444.747.149.551.84.96.97.08.19.310.612.013.615.217.019.021.023.07"32.035.338.541.744.948.151.354.557.760.964.167.370.54.04.96.06.97.89.110.010.213.014.415.917.219.28"41.946.150.254.458.662.867.071.275.479.683.787.992.13.44.25.15.96.77.78.99.811.012.213.815.016.09"53.058.363.668.974.279.584.890.195.41011061111162.93.74.45.15.96.77.58.69.510.612.113.114.110"65.472.078.585.191.698.21051111181241311371442.63.23.84.45.15.96.67.58.49.510.310.112.511"7987951031111191271341421501581661742.362.93.43.94.55.25.96.77.58.59.410.011.012"94103113122132141151160169179188198207
PipeDiameterVelocity in Feet per Second4.64.85.05.25.45.65.86.07.08.09.010.078.182.089.598.9105.0113.2120.8130.0162.8216.0270.323.3"13.614.214.815.315.916.517.117.720.623.526.529.552.357.061.568.072.578.283.189.5121.155.198.242.4"24.125.126.227.228.329.330.431.536.641.947.252.439.242.346.049.853.558.062.067.089.118.148.182.5"37.639.240.942.544.145.847.549.157.165.473.782.030.633.135.639.041.644.648.051.669.089.0114.140.6"54.156.558.961.263.665.968.370.782.494.310611825.127.329.532.034.537.140.043.058.075.095.0116.7"73.776.980.283.386.689.893.096.211212814516120.022.524.927.028.830.632.835.547.561.278.695.18"96.310110510911311712112514616818921017.119.221.022.924.626.228.030.140.152.166.682.09"12212713213814314815415918521223826514.816.717.919.921.022.724.325.934.845.958.070.110"15015716317017718319019622926129532713.014.715.917.118.220.121.322.630.740.050.862.011"18219019820621422222923727731635639611.613.014.015.116.117.819.120.227.135.945.455.912"217226235245254264273283330377425472
EXAMPLE
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'
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-revolutionof 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, asits 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 reactionturbine 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.
A typical vertical turbine
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 determinedquantityandhead, 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.
Two wheels on a horizontal shaft(Courtesy of the C. P. Bradway Company, West Stafford, Conn.)
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, whenfilled 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.
Bird's-eye view of a developed water-power plant
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 orsolid 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-inchchestnut, 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.
Cross-section of a rock and timber dam
This dam forms a pond from which the racedraws 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 requiredwithout 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.
Detail of bulkhead gate
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 or½-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 thecost 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 ownland, 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.
ELECTRICITY
THE DYNAMO; WHAT IT DOES, AND HOW
Electricity compared to the heat and light of the Sun—The simple dynamo—The amount of electric energy a dynamo will generate—The modern dynamo—Measuring power in terms of electricity—The volt—The ampere—The ohm—The watt and the kilowatt—Ohm's Law of the electric circuit, and some examples of its application—Direct current, and alternating current—Three types of direct-current dynamos: series, shunt, and compound.
Electricity compared to the heat and light of the Sun—The simple dynamo—The amount of electric energy a dynamo will generate—The modern dynamo—Measuring power in terms of electricity—The volt—The ampere—The ohm—The watt and the kilowatt—Ohm's Law of the electric circuit, and some examples of its application—Direct current, and alternating current—Three types of direct-current dynamos: series, shunt, and compound.
What a farmer really does in generating electricity from water that would otherwise run to waste in his brook, is to install a private Sun of his own—which is on duty not merely in daylight, but twenty-four hours a day; a private Sun which is under such simple control that it shines or provides heat and power, when and where wanted, simply by touching a button.
This is not a mere fanciful statement. When you come to look into it you find thatelectricity actually is the life-giving power of the Sun's rays, so transformed that it can be handily conveyed from place to place by means of wires, and controlled by mechanical devices as simple as the spigot that drains a cask.
Nature has the habit of traveling in circles. Sometimes these circles are so big that the part of them we see looks like a straight line, but it is not. Even parallel lines, according to the mathematicians, "meet in infinity." Take the instance of the water wheel which the farmer has installed under the fall of his brook. The power which turns the wheel has the strength of many horses. It is there in a handy place for use, because the Sun brought it there. The Sun, by its heat, lifted the water from sea-level, to the pond where we find it—and we cannot get any more power out of this water by means of a turbine using its pressure and momentum in falling, than the Sun itself expended in raising the water against the force of gravity.
Once we have installed the wheel to change the energy of falling water into mechanicalpower, the task of the dynamo is to turn this mechanical power into another mode of motion—electricity. And the task of electricity is to change this mode of motion back into the original heat and light of the Sun—which started the circle in the beginning.
Astronomers refer to the Sun as "he" and "him" and they spell his name with a capital letter, to show that he occupies the center of our small neighborhood of the universe at all times.
Magnets and Magnetism
The dynamo is a mechanical engine, like the steam engine, the water turbine or the gas engine; and it converts the mechanical motion of the driven wheel into electrical motion, with the aid of a magnet. Many scientists say that the full circle of energy that keeps the world spinning, grows crops, and paints the sky with the Aurora Borealis, begins and ends with magnetism—that the sun's rays are magnetic rays. Magnetism is the force that keeps the compass needle pointing northand south. Take a steel rod and hold it along the north and south line, slightly inclined towards the earth, and strike it a sharp blow with a hammer, and it becomes a magnet—feeble, it is true, but still a magnet.
Take a wire connected with a common dry battery and hold a compass needle under it and the needle will immediately turn around and point directly across the wire, showing that the wire possesses magnetism encircling it in invisible lines, stronger than the magnetism of the earth.
A direct-current dynamo or motor, showing details of construction(Courtesy of the Crocker-Wheeler Company)
Insulate this wire by covering it with cotton thread, and wind it closely on a spool. Connect the two loose ends to a dry battery, and you will find that you have multiplied the magnetic strength of a single loop of wire by the number of turns on the spool—concentrated all the magnetism of the length of that wire into a small space. Put an iron core in the middle of this spool and the magnet seems still more powerful. Lines of force which otherwise would escape in great circles into space, are now concentrated in the iron. The iron core is a magnet. Shut off the current from the battery and the iron is still a magnet—weak, true, but it will always retain asmall portion of its magnetism. Soft iron retains very little of its magnetism. Hard steel retains a great deal, and for this reason steel is used for permanent magnets, of the horseshoe type so familiar.
A Simple Dynamo
A dynamo consists, first, of a number of such magnets, wound with insulated wire. Their iron cores point towards the center of a circle like the spokes of a wheel; and their curved inner faces form a circle in which a spool, wound with wire in another way, may be spun by the water wheel.
Now take a piece of copper wire and make a loop of it. Pass one side of this loop in front of an electric magnet.
As the wire you hold in your hands passes the iron face of the magnet, a wave of energy that is called electricity flows around this loop at the rate of 186,000 miles a second—thesame speed as light comes to us from the sun. As you move the wire away from the magnet, a second wave starts through the wire, flowing in the opposite direction. You can prove this by holding a compass needle under the wire and see it wag first in one direction, then in another.
A wire "cutting" the lines of force of an electro-magnet
This is a simple dynamo. A wire "cutting" the invisible lines of force, that a magnet is spraying out into the air, becomes "electrified." Why this is true, no one has ever been able to explain.
The amount of electricity—its capacity for work—which you have generated with the magnet and wire, does not depend alone on the pulling power of that simple magnet. Let us say the magnet is very weak—has not enough power to lift one ounce of iron. Nevertheless,if you possessed the strength of Hercules, and could pass that wire through the field of force of the magnet many thousands of times a second, you would generate enough electricity in the wire to cause the wire to melt in your hands from heat.
Cross-section of an armature revolving in its field
Forms of annealed steel discs used in armature construction
This experiment gives the theory of the dynamo. Instead of passing only one wire through the field of force of a magnet, we have hundreds bound lengthwise on a revolving drum called an armature. Instead of one magnetic pole in a dynamo we have two, orfour, or twenty according to the work the machine is designed for—always in pairs, a North pole next to a South pole, so that the lines of force may flow out of one and into another, instead of escaping in the surrounding air. If you could see these lines of force, they would appear in countless numbers issuing from each pole face of the field magnets, pressing against the revolving drum like hair brush bristles—trying to hold it back. This drum, in practice, is built up of discs of annealed steel, and the wires extending lengthwise on its face are held in place by slots to prevent them from flying off when the drum is whirled at high speed. The drum does not touch the face of the magnets, but revolves in an air space. If we give the electric impulses generated in these wires a chance to flow in acircuit—flow out of one end of the wires, and in at the other, the drum will require more and more power to turn it, in proportion to the amount of electricity we permit to flow. Thus, if one electric light is turned on, the drum will press back with a certain strength on the water wheel; if one hundred lights are turned on it will press back one hundred times as much. Providing there is enough power in the water wheel to continue turning the drum at its predetermined speed, the dynamo will keep on giving more and more electricity if asked to, until it finally destroys itself by fire. You cannot take more power, in terms of electricity, out of a dynamo that you put into it, in terms of mechanical motion. In fact,to insure flexibility and constant speed at all loads, it is customary to provide twice as much water wheel, or engine, power as the electrical rating of the dynamo.
An armature partly wound, showing slots and commutator
We have seen that a water wheel is 85 per cent efficient under ideal conditions. A dynamo's efficiency in translating mechanical motion into electricity, varies with the type of machine and its size. The largest machines attain as high as 90 per cent efficiency; the smallest ones run as low as 40 per cent.
Measuring Electric Power
The amount of electricity any given dynamo can generate depends, generally speaking, on two factors, i. e., (1) the power of the water wheel, or other mechanical engine that turns the armature; and (2) the size (carrying capacity) of the wires on this drum.
Strength, of electricity, is measured inamperes. An ampere of electricity is the unit of the rate of flow and may be likened to a gallon of water per minute.
In surveying for water-power, in ChapterIII, we found that the number of gallons or cubic feet of water alone did not determine the amount of power. We found that the number of gallons or cubic feet multiplied by the distance in feet it falls in a given time, was the determining factor—pounds (quantity) multiplied by feet per second—(velocity).