EXAMPLE.-What horsepower will a 3-inch wrought-iron shaft transmit which makes 100 revolutions per minute, there being no pulleys between bearings? SOLUTION.-H= D3 X R Substituting, we have H= 3 × 3 × 3 × 100 70 38.57 horsepower. Ans. If there were the usual amount of power taken off, as mentioned 27 × 100 above, we should take C = 95. Then, H= 95 power. Ans. =28.42 horse 654. To compute the number of revolutions a shaft must make to transmit a given horsepower: Rule 128.-The number of revolutions necessary for a given horsepower equals the product of the value of C for the given material and the number of horsepower, divided by the cube of the diameter. Cx H EXAMPLE.-How many revolutions must a 3-inch wrought-iron shaft make per minute to transmit 28.42 horsepower, power being taken off at intervals between the bearings? СХН SOLUTION.-R = ᎠᏰ Substituting, we have R = 95 X 28.42 = 100 revolutions. Ans. 655. To compute the diameter of a shaft that will transmit a given horsepower, the number of revolutions the shaft makes per minute being given: Rule 129.—The diameter of a shaft equals the cube root of the quotient obtained by dividing the product of the value of C for the given material and the number of horsepower by the number of revolutions. That is, D = √ CX H R EXAMPLE. What must be the diameter of a wrought-iron shaft to transmit 38.57 horsepower, the shaft to make 100 revolutions per minute, no power being taken off between bearings? As the speed of shafting is used as a multiplier in the calculations of the horsepower of shafts, a shaft having a given diameter will transmit more power in proportion as its speed is increased. Thus, a shaft which is capable of transmitting 10 horsepower when making 100 revolutions per minute, will transmit 20 horsepower when making 200 revolutions per minute. We may, therefore, say the horsepowers transmitted by two shafts are directly proportional to the number of revolutions. EXAMPLES FOR PRACTICE. 1. What horsepower will a 24′′ wrought-iron shaft transmit when running at 110 revolutions per minute, it being used for transmission only? Ans. 24.55 horsepower. 2. A 6" cast-iron shaft transmits 150 horsepower; how many revolutions per minute must it make, no power being taken off between bearings? Ans. 62 R. P. M. 3. What should be the diameter of a wrought-iron shaft to transmit 100 horsepower at 150 revolutions per minute, power being taken off between bearings? Ans 4 in., nearly. 4. The diameter of a steam-engine shaft is 8"; what horsepower will it transmit, if made of steel, when making 150 revolutions per minute? Ans. 1,181.54 horsepower. 5. The machines driven by a certain line of wrought-iron shafting take their power from various points between the bearings; and, if all were working together at their full capacity, they would require 65 horsepower to drive them. What diameter should the shaft be if it runs at 150 revolutions per minute? Ans. 8 in. STEAM AND STEAM BOILERS. HEAT. It is, in fact, a It was stated 656. Heat is a form of energy. motion of the molecules composing matter. in Art. 434 that all matter is composed of molecules; now, these molecules are not in a state of rest, but are moving, or vibrating back and forth, with a greater or less velocity, and it is this movement of the molecules that causes the sensations of warmth or cold. If the motion is slow, the body appears cold to the touch; when the vibrations are rapid, the body becomes warm or hot. It was shown in Art. 545, rule 100, that a body in motion has kinetic energy, the amount of which is measured in foot-pounds, and is found by multiplying the weight of the body by the square of its velocity and dividing by 64.32. Since the molecules composing matter are in motion, they must possess kinetic energy, and we are justified, therefore, in saying that heat, this motion of the molecules, is a form of energy. 657. Temperature is a term used to indicate how hot or cold a body is; i. e., to indicate the rate of vibration of the molecules of a body. A hot body has a high temperature; a cold body, a low temperature. When a body, as, for example, an iron bar, receives heat from any source, its temperature rises; on the other hand, when a body loses heat, its temperature falls. The temperature is not a measure of the quantity of heat a body possesses. Temperature may be considered to be a measure of the velocity of the molecules of a body as they vibrate to and fro, while the quantity of heat may be considered to be the kinetic energy of the molecules composing the body. A small iron rod may be heated to whiteness and yet possess a very small quantity of heat. For notice of the copyright, see page immediately following the title page. Its temperature is very high, which simply indicates that the molecules of the rod are vibrating with an extremely high velocity. Temperature is measured by an instrument called the thermometer, which is so familiar as to scarcely need description. It consists of a thin glass tube, at one end of which is a bulb filled with mercury. Upon being heated the mercury expands in proportion to its temperature. Thermometers are graduated in different ways. In the Fahrenheit thermometer, which is generally used in this country, the point where the mercury stands when the instrument is placed in melting ice is marked 32°. The point indicated by the mercury when the thermometer is placed in water boiling in the open air at the level of the sea is marked 212°. The tube between these two points is divided into 180 equal parts called degrees. 658. Effects of Heat.-Suppose we take a vessel filled with water. Let the vessel be a cylinder fitted with a piston, as shown in Fig. 142. The water is say at the freezing point, and the millions of molecules composing the water are moving to and fro with a comparatively small velocity. Place the vessel in a fire or furnace. Heat is communicated to the molecules of water, and they begin to move faster and faster and faster. That is, their kinetic energy increases, and, if a thermometer were inserted in the vessel, it would be found that the temperature of the water rises. Consequently, one effect of heat is to raise the temperature of the body to which it is applied. But, after reaching a certain temperature, the molecules of the water not only move faster, but they move further from each other and their paths are longer. It is plain that if the molecules are further apart than they were originally, the whole body of them must take up more space. In other words, after reaching a certain temperature, the water expands as heat is added. Hence, another effect of heat is to expand bodies to which it is applied. Common examples of the expansion of bodies by heat are seen in the setting of tires, the expansion of the rails of a railway in summer, etc. 659. The heat supplied to the vessel of water has so far done three things: 1. Raised the temperature of the water and thus increased the kinetic energy of the molecules. (Let the amount of heat expended for this purpose be denoted by S.) 2. A certain quantity of heat has been used in expanding the water; that is, in pushing its molecules further apart against the force of cohesion. (Denote the amount of heat so expended by I.) 3. Since the water expands, it must raise the piston Pagainst the pressure of the atmosphere, and, consequently, more heat must be used to expand the water than would be required if there were no pressure on the upper side of the piston. (Call this extra quantity of heat, W.) If we denote by Q the total heat given up to the vessel of water, we have Q = S+I+ IV. 660. Ordinarily, the greater part of the heat given to a body is spent in raising its temperature, and but little is used in expanding the body. That is, the quantity S is nearly equal to the quantity Q, while the quantities I and W are extremely small. Suppose that the piston is removed from the cylinder of Fig. 142 and a thermometer inserted. As the vessel becomes more and more heated, the temperature indicated by the thermometer will rise until it reaches 212°. So far most of the heat has been used to raise the temperature of the water. But now, no matter how much heat is added to the water, the thermometer stands at 212° and can not be made to rise higher. This is the reason: When the temperature reaches 212° the molecules of water have been set into such rapid motion that the force of cohesion is no longer able to hold them and they tend to separate. In other words, |