PRACTICAL MECHANICS FOR BOYS TEXT

down, so it is at B, it moves four times farther than the short end moves upwardly, as the distance from C to D is just one-fourth that from A to B. The energy expended in moving four times the distance balances the power gained. POWER VS. DISTANCE TRAVELED.--From this the following law is deduced: That whatever is gained in power is lost in the distance traveled. Second: Using the same figure, supposing it was necessary to raise the short end of the lever, from C to D, in one second of time. In that case the hand pressing down the long end of the lever, would go from A to B in one second of time; or it would go four times as far as the short end, in the same time. POWER VS. LOSS IN TIME.--This means another law: That what is gained in power is lost in time. Distinguish clearly between these two motions. In the first case the long end of the lever is moved down from A to B in four seconds, and it had to travel four times the distance that the short end moves in going from C to D. In the second case the long end is moved down, from A to B, in one second of time, and it had to go that distance in one-fourth of the time, so that four times as much energy was expended in the same time to raise the short end from C to D. WRONGLY DIRECTED ENERGY.--More men have gone astray on the simple question of the power of the lever than on any other subject in mechanics. The writer has known instances where men knew the principles involved in the lever, who would still insist on trying to work out mechanical devices in which pulleys and gearing were involved, without seeming to understand that those mechanical devices are absolutely the same in principle. This will be made plain by a few illustrations. In Fig. 128, A is a pulley four times larger, diametrically, than B, and C is the pivot on which they turn. The pulleys are, of course, secured to each other. In this case we have the two weights, one of four pounds on the belt, which is on the small pulley (B), and a one-pound weight on the belt from the large pulley (A). [Illustration: _Fig. 128. The Pulley_] THE LEVER AND THE PULLEY.--If we should substitute a lever (D) for the pulleys, the similarity to the lever (Fig. 127) would be apparent at once. The pivot (C) in this case would act the same as the pivot (C) in the lever illustration. In the same manner, and for like reasons, the wedge, the screw and the incline plane, are different structural applications of the principles set forth in the lever. Whenever two gears are connected together, the lever principle is used, whether they are the same in size, diametrically, or not. If they are the same size then no change in power results; but instead, thereof, a change takes place in the direction of the motion. [Illustration: _Fig. 129. Fig. 130. Change of Direction_] When one end of the lever (A) goes down, the other end goes up, as shown in Fig. 129; and in Fig. 130, when the shaft (C) of one wheel turns in one direction, the shaft of the other wheel turns in the opposite direction. It is plain that a gear, like a lever, may change direction as well as increase or decrease power. It is the thorough knowledge of these facts, and their application, which enables man to make the wonderful machinery we see on every hand. SOURCES OF POWER.--Power is derived from a variety of sources, but what are called the _prime movers_ are derived from heat, through the various fuels, from water, from the winds and from the tides and waves of the ocean. In the case of water the power depends on the head, or height, of the surface of the water above the discharging orifice. WATER POWER.--A column of water an inch square and 28 inches high gives a pressure at the base of one pound; and the pressure at the lower end is equal in all directions. If a tank of water 28 inches high has a single orifice in its bottom 1" x 1" in size, the pressure of water through that opening will be only one pound, and it will be one pound through every other orifice in the bottom of the same size. CALCULATING FUEL ENERGY.--Power from fuels depends upon the expansion of the materials consumed, or upon the fact that heat expands some element, like water, which in turn produces the power. One cubic inch of water, when converted into steam, has a volume equal to one cubic foot, or about 1,700 times increase in bulk. Advantage is taken of this in steam engine construction. If a cylinder has a piston in it with an area of 100 square inches, and a pipe one inch square supplies steam at 50 pounds pressure, the piston will have 50 pounds pressure on every square inch of its surface, equal to 5,000 pounds. THE PRESSURE OR HEAD.--In addition to that there will also be 50 pounds pressure on each square inch of the head, as well as on the sides of the cylinder. Fig. 131 shows a cylinder (A), a piston (B) and a steam inlet port (C), in which is indicated how the steam pressure acts equally in all directions. As, however, the piston is the only movable part, the force of the steam is directed to that part, and the motion is then transmitted to the crank, and to the shaft of the engine. [Illustration: _Fig. 131. Steam Pressure_] [Illustration: _Fig. 132. Water Pressure_] This same thing applies to water which, as stated, is dependent on its head. Fig. 132 represents a cylinder (D) with a vertically movable piston (E) and a standpipe (F). Assuming that the pipe (F) is of sufficient height to give a pressure of 50 pounds to the square inch, then the piston (E) and the sides and head of the cylinder (D) would have 50 pounds pressure on every square inch of surface. FUELS.--In the use of fuels, such as the volatile hydrocarbons, the direct expansive power of the fuel gases developed, is used to move the piston back and forth. Engines so driven are called _Internal Combustion Motors_. POWER FROM WINDS.--Another source of power is from the wind acting against wheels which have blades or vanes disposed at such angles that there is a direct conversion of a rectilinear force into circular motion. In this case power is derived from the force of the moving air and the calculation of energy developed is made by considering the pressure on each square foot of surface. The following table shows the force exerted at different speeds against a flat surface one foot square, held so that the wind strikes it squarely: -------------------------------------------------------------------- -----------------+--------------++-------------------+-------------- SPEED OF WIND | PRESSURE || SPEED OF WIND | PRESSURE -----------------+--------------++-------------------+-------------- 5 Miles per hour | 2 oz. || 35 miles per hour | 6 lb. 2 oz. 10 " " | 8 " || 40 " " | 8 " 15 " " | 1 lb. 2 " || 45 " " | 10 " 2 " 20 " " | 2 " || 50 " " | 12 " 2 " 25 " " | 3 " 2 " || 55 " " | 15 " 2 " 30 " " | 4 " 8 " || 60 " " | 18 " -----------------+--------------++-------------------+-------------- VARYING DEGREES OF PRESSURE.--It is curious to notice how the increase in speed changes the pressure against the blade. Thus, a wind blowing 20 miles an hour shows 2 pounds pressure; whereas a wind twice that velocity, or 40 miles an hour, shows a pressure of 8 pounds, which is four times greater than at 20 miles. It differs, therefore, from the law with respect to water pressure, which is constant in relation to the height or the head--that is, for every 28 inches height of water a pound pressure is added. POWER FROM WAVES AND TIDES.--Many attempts have been made to harness the waves and the tide and some of them have been successful. This effort has been directed to the work of converting the oscillations of the waves into a rotary motion, and also to take advantage of the to-and-fro movement of the tidal flow. There is a great field in this direction for the ingenious boy. A PROFITABLE FIELD.--In no direction of human enterprise is there such a wide and profitable field for work, as in the generation of power. It is constantly growing in prominence, and calls for the exercise of the skill of the engineer and the ingenuity of the mechanic. Efficiency and economy are the two great watchwords, and this is what the world is striving for. Success will come to him who can contribute to it in the smallest degree. Capital is not looking for men who can cheapen the production of an article 50 per cent., but 1 per cent. The commercial world does not expect an article to be 100 per cent, better. Five per cent. would be an inducement for business. CHAPTER XII ON MEASURES HORSE-POWER.--When work is performed it is designated as horse-power, usually indicated by the letters H. P.; but the unit of work is called a _foot pound_. If one pound should be lifted 550 feet in one second, or 550 pounds one foot in the same time, it would be designated as one horse-power. For that reason it is called a foot pound. Instead of using the figure to indicate the power exerted during one minute of time, the time is taken for a minute, in all calculations, so that 550 multiplied by the number of seconds, 60, in a minute, equals 33,000 foot pounds. FOOT POUNDS.--The calculation of horse-power is in a large measure arbitrary. It was determined in this way: Experiments show that the heat expended in vaporizing 34 pounds of water per hour, develops a force equal to 33,000 foot pounds; and since it takes about 4 pounds of coal per hour to vaporize that amount of water, the heat developed by that quantity of coal develops the same force as that exercised by an average horse exerting his strength at ordinary work. All power is expressed in foot pounds. Suppose a cannon ball of sufficient weight and speed strikes an object. If the impact should indicate 33,000 pounds it would not mean that the force employed was one horse-power, but that many foot pounds. If there should be 60 impacts of 550 pounds each within a minute, it might be said that it would be equal to 1 horse-power, but the correct way to express it would be foot pounds. So in every calculation, where power is to be calculated, first find out how many foot pounds are developed, and then use the unit of measure, 33,000, as the divisor to get the horse-power, if you wish to express it in that way. It must be understood, therefore, that horse-power is a simple unit of work, whereas a foot pound is a compound unit formed of a foot paired with the weight of a pound. ENERGY.--Now _work_ and _energy_ are two different things. Work is the overcoming of resistance of any kind, either by causing or changing motion, or maintaining it against the action of some other force. Energy, on the other hand, is the power of doing work. Falling water possesses energy; so does a stone poised on the edge of a cliff. In the case of water, it is called _kinetic_ energy; in the stone _potential_ energy. A pound of pressure against the stone will cause the latter, in falling, to develop an enormous energy; so it will be seen that this property resides, or is within the thing itself. It will be well to remember these definitions. HOW TO FIND OUT THE POWER DEVELOPED.--The measure of power produced by an engine, or other source, is so interesting to boys that a sketch is given of a Prony Brake, which is the simplest form of the Dynamometer, as these measuring machines are called. [Illustration: _Fig. 133. Prony Brake_] In the drawing (A) is the shaft, with a pulley (A'), which turns in the direction of the arrow (B). C is a lever which may be of any length. This has a block (C'), which fits on the pulley, and below the shaft, and surrounding it, are blocks (D) held against the pulley by a chain (E), the ends of the chain being attached to bolts (F) which pass through the block (C') and lever (C). Nuts (G) serve to draw the bolts upwardly and thus tighten the blocks against the shaft. The free end of the lever has stops (H) above and below, so as to limit its movement. Weights (I) are suspended from the end of the lever. [Illustration: _Fig. 134. Speed Indicator_] THE TEST.--The test is made as follows: The shaft is set in motion, and the nuts are tightened until its full power at the required speed is balanced by the weight put on the platform. The following calculation can then be made: For our present purpose we shall assume that the diameter of the pulley (A') is 4 inches; the length of the lever (C), 3 feet; the speed of the shaft (A) and the pulley, 210 revolutions per minute; and the weight 600 pounds. Now proceed as follows: (1) Multiply the diameter of the pulley (A') (4 inches) by 3.1416, and this will give the circumference 12.5664 inches; or, 1.0472 feet. (2) Multiply this product (1.0472) by the revolutions per minute. 1.0472 x 210 = 219.912. This equals the _speed_ of the periphery of the pulley. (3) The next step is to get the length of the lever (C) from the center of the shaft (A) to the point from which the weights are suspended, and divide this by one-half of the diameter of the pulley (A'). 36" / 2" = 18", or 1-1/2 feet. This is the _leverage_. (4) Then multiply the _weight_ in pounds by the _leverage_. 600 x 1-1/2 = 900. (5) Next multiply this product (900) by the _speed_, 900 x 219.912 = 197,920.8, which means _foot pounds_. (6) As each horse-power has 33,000 foot pounds, the last product should be divided by this figure, and we have 197,920.8 / 33,000 = 5.99 H. P. THE FOOT MEASURE.--How long is a foot, and what is it determined by? It is an arbitrary measure. The human foot is the basis of the measurement. But what is the length of a man's foot? It varied in different countries from 9 to 21 inches. In England, in early days, it was defined as a measure of length consisting of 12 inches, or 36 barleycorns laid end to end. But barleycorns differ in length as well as the human foot, so the standard adopted is without any real foundation or reason. WEIGHT.--To determine weight, however, a scientific standard was adopted. A gallon contains 8.33 pounds avoirdupois weight of distilled water. This gallon is divided up in two ways; one by weight, and the other by measurement. Each gallon contains 231 cubic inches of distilled water. As it has four quarts, each quart has 57-3/4 cubic inches, and as each quart is comprised of two pints, each pint has nearly 29 cubic inches. THE GALLON.--The legal gallon in the United States is equal to a cylindrical measure 7 inches in diameter and 6 inches deep. Notwithstanding the weights and dimensions of solids and liquids are thus fixed by following a scientific standard, the divisions into scruples, grains, pennyweights and tons, as well as cutting them up into pints, quarts and other units, is done without any system, and for this reason the need of a uniform method has been long considered by every country. THE METRIC SYSTEM.--As early as 1528, Fernal, a French physician, suggested the metric system. Our own government recognized the value of this plan when it established the system of coinage. The principle lies in fixing a unit, such as a dollar, or a pound, or a foot, and then making all divisions, or addition, in multiples of ten. Thus, we have one mill; ten mills to make a dime; ten dimes to make a dollar, and so on. BASIS OF MEASUREMENT.--The question arose, what to use as the basis of measurement, and it was proposed to use the earth itself, as the measure. For this purpose the meridian line running around the earth at the latitude of Paris was selected. One-quarter of this measurement around the globe was found to be 393,707,900 inches, and this was divided into 10,000,000 parts. Each part, therefore, was a little over 39.37 inches in length, and this was called a meter, which means _measure_. A decimeter is one-tenth of that, namely, 3.937 inches; and a decameter 39.37, or ten times the meter, and so on. For convenience the metrical table is given, showing lengths in feet and inches, in which only three decimal points are used. Metrical Table, showing measurements in feet and inches: METRICAL TABLE, SHOWING MEASUREMENTS IN FEET AND INCHES ------------------------------------------ ------------+--------------+-------------- Length | Inches | Feet ------------+--------------+-------------- Millimeter | 0.039 | 0.003 Centimeter | 0.393 | 0.032 Decimeter | 3.937 | 0.328 Meter | 39.370 | 3.280 Decameter | 393.707 | 32.808 Hectometer | 3937.079 | 328.089 Kilometer | 39370.790 | 3280.899 Myriameter | 393707.900 | 32808.992 ------------+--------------+-------------- METRIC SYSTEM, SHOWING THE EQUIVALENTS IN OUR MEASURES 1 Myriameter = 5.4 nautical miles, or 6.21 statute miles. 1 Kilometer = 0.621 statute mile, or nearly 5/8 mile. 1 Hectometer = 109.4 yards. 1 Decameter = 0.497 chain, 1.988 rods. 1 Meter = 39.37 inches, or nearly 3 ft. 3-3/8 inches. 1 Decimeter = 3.937 inches. 1 Centimeter = 0.3937 inch. 1 Millimeter = 0.03937 inch. 1 Micron = 1/25400 inch. 1 Hectare = 2.471 acres. 1 Arc = 119.6 square yards. 1 Centaire, or square meter = 10.764 square feet. 1 Decastere = 13 cubic yards, or about 2-3/4 cords. 1 Stere, or cubic meter = 1.308 cubic yards, or 35.3 cubic feet. 1 Decistere = 3-1/2 cubic feet. 1 Kiloliter = 1 ton, 12 gal., 2 pints, 2 gills old wine measure. 1 Hectoliter = 22.01 Imperial gals., or 26.4 U. S. gals. 1 Decaliter = 2 gallons, 1 pint, 2-2/5 gills, imperial measure, or 2 gals., 2 qts., 1 pt., 1/2 gill, U. S. 1 Liter = 1 pint, 3 gills, imperial, or 1 qt., 1/2 gill U. S. measure. 1 Decileter = 0.704 gill, imperial, or 0.845 gill U. S. measure. 1 Millier = 2,204.6 pounds avoirdupois. 1 Metric quintal = 2 hundredweight, less 3-1/2 pounds, or 220 pounds, 7 ounces. 1 Kilogram = 2 pounds, 3 ounces, 4-3/8 drams avoirdupois. 1 Hectogram = 3 ounces, 8-3/8 drams avoirdupois. 1 Decagram = 154.32 grains Troy. 1 Gram = 15.432 grains. 1 Decigram = 1.542 grain. 1 Centigram = 0.154 grain. 1 Milligram = 0.015 grain. CHAPTER XIII USEFUL INFORMATION FOR THE WORKSHOP To find the circumference of a circle: Multiply the diameter by 3.1416. To find the diameter of a circle: Multiply the circle by .31831. To find the area of a circle: Multiply the square of the diameter by .7854. To find the area of a triangle: Multiply the base by one-half the perpendicular height. To find the surface of a ball: Multiply the square of the diameter by 3.1416. To find the solidity of a sphere: Multiply the cube of the diameter by .5236. To find the cubic contents of a cone: Multiply the area of the base by one-third the altitude. Doubling the diameter of a pipe increases its capacity four times. To find the pressure in pounds per square inch of a column of water: Multiply the height of the column in feet by .434. Standard Horse-power: The evaporation of 30 pounds of water per hour from a feed water temperature of 1,000 degrees Fahrenheit into steam at 70 pounds gauge pressure. To find the capacity of any tank in gallons: Square the diameter in