foot of some substance, we must multiply the weight of the unit of water by the specific gravity of the substance. Example: The specific gravity of alcohol is .8. How many pounds would there be to a gallon of alcohol? One gallon of water =83 lb. One gallon of alcohol = .8×83=63 lb., Answer. If a substance has a specific gravity less than 1, it will float in water, because it is lighter than the same volume of water. If the specific gravity is greater than 1, the substance is heavier than water and will sink. A substance that will float in water may sink in some other liquid if it has a greater specific gravity than the liquid in question. For example, a piece of apple-wood will float in water but will sink when placed in gasoline, the specific gravity of the wood being about .76 and that of gasoline about .71. A piece of iron will sink in water but will float when placed in mercury (quick silver), the specific gravity of mercury being 13.6 and that of iron about 7.21. One of the 117. Transmission of Pressure Through Fluids. most useful properties of all fluids is the ability to transmit W FIG. 73. pressure in all directions. If we have a vessel filled with water, as shown in Fig. 73, and apply a pressure to the water by means of a piston, as shown, this pressure will be transmitted through the water in all directions. If the sides of the vessel are flat, they will bulge out, showing that there is a pressure on the sides; and if the piston is loose, the water will escape upward around it, showing that there is a pressure in this direction also. If the total force on the piston is W lb. and the area on the bottom of the piston is A sq. in., then there will be a pressure W A of lb. exerted on each square inch of the water beneath the piston. This pressure will be transmitted equally in all directions and the pressure on each square inch of the top, sides, and W A bottom of the vessel will be lb. Example: If the piston of Fig. 73 is 6 in. in diameter, and has a total weight of 1000 lb., what would be the water pressure per square inch? W 1000 = Ρ A .7854×62 1000 28.27 Explanation: As the piston rests on the water, the pressure of the water on the bottom of the piston must be sufficient to -35.4 lb. per sq. in., Answer. support the weight. The area of the bottom is 28.27 sq. in., 1000 and the pressure on each sq. in. will be or 35.4 lb. persquare inch. 28.27 This pressure is transmitted throughout the water and is exerted by it with equal force in all directions. 118. The Hydraulic Jack. This property of water of transmitting pressure in any direction is made use of in many ways. The same property is, of course, common to other fluids such as P W FIG. 74. oil, air, etc. Wherever we find a powerful, slow-moving force required in a shop, we usually find some hydraulic machine. (The word "hydraulic" refers to the use of water but it is often applied to machines using any liquid-water, oil, or alcohol.) Fig. 74 shows the principle of all these hydraulic machines. A small force P is exerted on a small piston and this produces a certain pressure in the water. This pressure is transmitted to the larger cylinder where the same pressure per square inch is exerted on the under side of the large piston. If the large piston has 100 times the area of the small piston, the weight supported (W) will be 100 times P. If the water pressure produced by P is 100 lb. per square inch and the large piston has an area of 100 sq. in., then the weight W that can be raised will be 10,000 lb. Like the lever, the jackscrew, and the pulley, this increase in force is obtained only by a decrease in the distance the weight is moved. The work done on the small piston is theoretically the same as the work obtained from the large piston. For example, suppose that the large piston has 100 times the area of the small one and we shove the small piston down 1 in.; the water that is thus pushed out of the small cylinder will have to spread out over the entire area of the large piston; the large piston will, therefore, be raised only one one-hundredth of the distance that the small piston was moved. Thus, we have, here also, an application of the law that the work put into a machine is equal, neglecting friction, to the work done by it. ForceX distance moved = weight distance raised. The Mechanical Advantage of such a machine will be seen to be the ratio of the areas of the pistons. In the case just mentioned, the ratio of the areas of the pistons was 100:1; hence, the mechanical advantage was 100. In Fig. 74, the motion that can be given to W is very limited, but by using a pump with valves, instead of the simple plunger P, we can continue to force water into the large cylinder and thus secure a considerable motion to W. Fig. 75 shows a common form of hydraulic jack which operates on this principle. The top part contains a reservoir for the liquid, and also has a small pump operated by a hand lever on the outside of the jack. By working the lever, the liquid is pumped into the lower part of the jack between the plunger and the casing, thus raising the load. The load may be lowered by slacking the lowering screw Y. This opens a passage to the reservoir, and the load on the jack forces the liquid to flow back through this passage to the reservoir. In calculating the mechanical advantage of a hydraulic jack, we must consider the mechanical advantage of the lever which operates the pump as well as the advantage due to the relative sizes of the pump and the ram. FIG. 75. Example: If the ram of Fig. 75 is 3 in. in diameter and the pump is 1 in. in diameter, while the lever is 15 in. long and is connected to the pump at a distance of 11⁄2 in. from the fulcrum, what is the mechanical advantage of the entire jack? Explanation: The areas of the ram and pumps are as 9:1, hence their mechanical advantage is 9. The lever has a mechanical advantage of 10. Hence, that of the whole jack is 9×10=90, and a force applied at the end of the lever would be multiplied 90 times. This force would, however, move through a distance 90 times as great as the distance the load would be raised. The hydraulic jack has usually an efficiency of over 70% and is, therefore, a much more efficient lifting device than the jack screw. A mixture containing one-third alcohol and two-thirds water should be used in jacks. The alcohol is added to prevent freezing. 119. Hydraulic Machinery.—In the shop, we often find water pressure used to operate presses, punches, shears, riveters, hoists, and sometimes elevators. These machines are seldom operated by hand power but have water supplied under pressure from a central pumping plant. The admission of the water and the consequent motion of the machine is controlled by hand operated valves. Most of these hydraulic machines are used where tremendous forces are required. Therefore, very high water pressures are used, occasionally as high as 3000 lb. per square inch. 1500 lb. per square inch is a common working pressure for hydraulic machines. Fig. 76 shows a press operated by hydraulic pressure. It will be noticed that the movable head is connected to two pistonsa large one for doing the work on the down stroke, and a smaller one above, used only for the idle or return stroke of the press. 120. Hydraulic Heads.-Quite often we use a high tower or |