the indicated horse power. But the rate at which the shaft of the engine supplies energy to other machinery is called the brake horse power, because it is what would be measured by some sort of dynamometer or Prony brake. If, instead of the total energy developed, the delivered energy is used in computing the efficiency, the result is called the overall efficiency. Thermal efficiencies of about 25 per cent have been obtained with multiple-expansion engines. In a steam plant the efficiency of the boiler is an important item. The boiler efficiency is defined as the ratio of the heat energy in steam generated per hour to the energy in fuel used per hour. In good plants this will usually run about 60 per cent, although 85 per cent has been reached. It is often convenient to group the engine and boiler together as one unit and define the efficiency of the combination as the ratio of the mechanical work per hour to the energy in fuel used per hour. Instead of stating this as a percentage, it is quite common to state this efficiency by the number of pounds of coal required for each horse-power hour or for each kilowatt-hour. An efficiency of about 1 pound of coal per horse-power hour has been reached; some modern plants develop 1 kilowatt-hour for each 1 pounds of coal used. 307. Steam turbines. The steam turbine has in recent years come into common use in power plants where large or moderately large units are needed. The simplest form is the impulse, or velocity, type. Steam issues from one or more nozzles at a very high speed, from 1000 to 4000 feet per second. These high-speed jets strike the vanes of a wheel and set it in rotation, in much the same manner as water turbines are given energy by jets of water. The wheel acquires a very high speed, which is most efficient when the vanes have about one half the speed of the jet. In this form of engine the energy of the steam in the boiler is changed into kinetic energy of the jet, and this in turn gives up energy to the moving vanes. Many of the more modern types are much more complicated. In these the steam, instead of losing its pressure at one place, passes through a number of stages, in each of which it loses part of its initial pressure, acquiring kinetic energy and then acting on moving blades. Since the steam expands more gradually in this type of engine, it does not acquire such a high velocity, and the turbine does not need to have the very high velocity which the simple impulse type must have. For the same horse power a turbine occupies less space than a reciprocating engine. It has, also, greater freedom from vibration. It is not so efficient as the best reciprocating engine when high-pressure steam is used, but it is more efficient than an engine for low-pressure steam. In large sizes the turbine costs less than a reciprocating engine of the same horse power. To run electrical generators large turbines of from 20,000 to 30,000 horse power have been constructed which give an efficiency, from fuel to the electrical energy developed, of about 23 per cent, a result close to that of the best internal-combustion engine. 308. Maximum theoretical efficiency. In the subject of thermodynamics two important theorems are proved for the Carnot engine. This is not an actual engine, but an imaginary one in which all processes are carried on under ideal conditions, without losses of heat energy by radiation, conduction, etc. The "working substance" receives all its heat energy at a certain high temperature T1; and when it does work in the engine, it is cooled down to the temperature T2. The first of these theorems is as follows: No engine can have an efficiency greater than that of the Carnot engine when working through the same range of temperature. The second theorem is stated thus: The thermal efficiency of a Carnot engine is equal to 2 1 where T1 and T2 are the high and low temperatures, in the absolute scale, between which the engine works. It follows from these two theorems that no engine can have an efficiency greater than this fraction. For example, suppose that a given steam engine received steam from a boiler the temperature of which is 200° C. (or 473° K.), and delivers this steam to a condenser at a temperature of 40° C. (or 313° K.). The thermal efficiency of a Carnot engine working between these limits is Hence an actual engine working between these temperatures cannot have an efficiency greater than 34 per cent. The actual efficiency attained for these temperatures is about 25 per cent. This formula for the efficiency shows that an engine can be made more efficient by increasing the difference between the high and the low temperature. The high temperature is often increased by superheating the steam; that is, by heating it further after it has left the boiler. Lower temperatures are obtained by producing better vacua in the condensers, thereby condensing the steam at a lower temperature. 309. Internal-combustion engines. The most commonly used type of internal-combustion engine is the four-cycle gas engine. In Fig. 180 are shown the four stages in the operation of a singlecylinder engine. For simplicity many details are omitted. In Fig. 180, a, is shown the intake stroke; the explosive mixture is being drawn into the cylinder. The intake valve I is open; the exhaust E is closed. The compression stroke is shown in Fig. 180, b. This motion compresses the gas into the end of the cylinder, where, by an electric spark, the gas is exploded, driving the piston forward. This stage is shown in Fig. 180, c. The exhaust stroke (Fig. 180, d) is for the purpose of driving out of the cylinder the gases which result from the combustion. After this is done the operation is repeated. The axle of the engine makes two complete revolutions for each explosion. In order to keep the engine running between explosions, a heavy flywheel is mounted on the axle. In many engines more than one cylinder is used. Thus the four-cylinder engine is one in which four cylinders are connected to the same axle. These are usually so set that there is one explosion for each half-revolution of the axle. The best four-cycle gas engine is able to convert about 30 per cent of the fuel energy into mechanical energy. The two-cycle engine explodes once for each revolution. There is not a separate stroke used for the exhaust, but the explosive mixture rushing in under pressure drives out the exploded gases. The Diesel oil engine differs from the gas engine in many respects. In this engine air is compressed in the cylinder by a return stroke of the piston until heated to a temperature higher than the firing point of the fuel. The oil under pressure is then blown in the form of a fine spray into this compressed air. At the high temperature of the air the oil begins at once to burn. There is no sudden explosion, but the oil burns as admitted. The gases resulting from this combustion exert, as in the case of the ordinary gas engine, large pressures; for at ordinary pressures they occupy a much greater volume than the materials which were burned. Formerly, Diesel engines were made only in stationary units and not in small sizes. Their use in locomotives, automobiles, and the like is still in an experimental stage. Large Diesel engines may convert 40 per cent of the fuel energy into mechanical energy. PROBLEMS 1. The average resultant pressure on the piston of a steam engine was 60 lb./sq. in., the length of the stroke 10 in., the area of the piston 60 sq. in., and the number of revolutions per minute 200. Compute the horse power. 2. How many pounds of coal per horse-power hour will be needed for a plant which has an efficiency of 15 per cent, if the coal used has a heat of combustion of 14,000 B.T.U./lb.? 3. A large steam plant used 1.5 lb. of coal for each horse-power hour, burning coal which had a heat of combustion of 14,500 B. T.U./lb. What percentage of the total energy was obtained ? 4. The heat of combustion of gasoline is 20,000 B.T. U./lb. If the efficiency of the engine is 20 per cent, how many horse-power hours can be developed from each pound of gasoline? PART III. WAVE-MOTION AND SOUND CHAPTER XXIV WAVE-MOTION AND SOUND Wave-motion, 310. Transverse waves, 311. Longitudinal waves, 312. Transfer of energy in a wave, 313. Water-waves, 314. Relation between velocity, period, frequency, and wave-length, 315. Standing waves, 316. Sound, 317. Sound-waves longitudinal, 318. Speed of sound, 319. Determination of the direction of a source of sound, 320. Sound-ranging, 321. Reflection of sound-waves, 322. Refraction of sound-waves, 323. Musical sounds, 324. Pitch, 325. Intensity, or loudness, 326. Tone quality, 327. Resonance, or sympathetic vibration, 328. Interference, 329. Beats, 330. Doppler's principle, 331. Vibrating strings, 332. Frequency of vibration of strings, 333. Vibrating rods, 334. The Kundt's-tube experiment, 335. Vibrations of air columns, 336. Musical intervals, 337. Law of harmonious combinations, 338. The major scale, 339. 310. Wave-motion. The study of wave-motion is connected, in this text, with that of sound, not because sound is the only form of wave-motion but because there is some advantage in treating them together. It is easier to understand some of the properties of waves in connection with a definite type of wave than by studying them in the abstract. But this coupling of the two subjects must not be permitted to deceive the student. There are many other important applications of wave-motions. The vibrations, or tremors, of buildings, bridges, and other structures are ordinarily wave-motions. In the subject of light, frequent reference will be made to the principles explained here. Telephonic transmission along wires and cables is a special type of wave-motion. Electrical waves in space are now used in wireless telegraphy and telephony. In almost every field of physical science one finds instances of wave-motion. |