illustrates the effects of lateral pressure. When this vessel is filled with water, the lateral pressures at any two points of the surface of the vessel opposite each other are equal. FIG. 22 Being equal and act ing in opposite direc tions, they balance each other, and no motion can result; but if the stop-cock is opened, there will be no resistance to that pressure acting on the surface equal to the area of the opening, and it will cause the water to flow out, while its equal and opposite force will cause the vessel to move through the water in a direction opposite to that of the spouting water. 32. Since the pressure on the bottom of a vessel due to the weight of the liquid is dependent only on the height FIG. 23 of the liquid, and not on the shape of the vessel, it follows that if a vessel has a number of radiating tubes, as shown in Fig. 23, the water in each tube will be on the same level, no matter what may be the shape of the tubes. For, if the water were higher in one tube than in the others, the downward pressure on the bottom due to the height of the water in this tube would be greater than that due to the height of the water in the other tubes. Consequently, the upward pressure would also be greater, the equilibrium would be destroyed, and the water would flow from this tube into the vessel, and rise in the other tubes until it was at the same level in all, when it would be in equilibrium. This principle is expressed in the familiar saying, water seeks its level. The foregoing principle explains why city water reservoirs are located on high elevations, and why water on leaving the hose nozzle spouts so high. If there where no resistance by friction and air, the water would spout to a height equal to the level of the water in the reservoirs. If a long pipe whose length was equal to the vertical distance between the nozzle and the level of the water in the reservoir were attached to the nozzle, the water would just reach the end of the pipe. If the pipe were lowered slightly, the water would trickle out. Fountains, canal locks, and artesian wells are examples of the application of this principle. EXAMPLE.-The water level in a city reservoir is 150 feet above the level of the street; what is the pressure of the water per square inch on the hydrant? SOLUTION. 1 X 150 X 12 X .03617 65.106 lb. per sq. in. Ans. NOTE. In measuring the height of the water to find the pressure that it produces the vertical height, or distance between the level of the water and the point considered is always taken; this vertical height is called the head. The weight of a column of water 1 inch square and 1 foot high is 62.5 ÷ 144 = .434 pound, nearly. Hence, if the depth (head) is given, the pressure per square inch may be found by multiplying the depth in feet by .434. The constant .434 is the one ordinarily used in practical calculations. 33. In Fig. 24, let the area of the piston a be 1 square inch; of 6, 40 square inches. According to Pascal's law, 1 pound placed on a will balance 40 pounds placed on b. Suppose that a moves downwards 10 inches, then 10 cubic inches of water will be forced into the tube b. This will be distributed over the entire area of the tube b, in the form of = a cylinder whose cubical contents must be 10 cubic inches, whose base has an area of 40 square inches, and whose altitude must be 10 40 inch; that is, a movement of 10 inches of the piston a will cause a movement of inch in the piston b. This is another illustration of the wellknown principle of machines: The force multiplied by the distance through which it acts equals the weight multiplied by the distance through which it moves, since, if 1 pound on the piston a represents the force P, the equivalent weight W on b may be obtained from the equation WX PX 10, whence W = 40 P 40 pounds. FIG. 24 = = BUOYANT EFFECTS OF WATER 34. In Fig. 25 is shown a 6-inch cube entirely submerged in water. The lateral pressures are equal and in opposite directions. The upward pressure acting on the lower surface of the cube is 6 x 6 x 21 x .03617; the downward pressure acting on the top of the cube is 6 x 6 x 15 x .03617; and the difference is 6 x 6 x 6 x .03617, which equals the volume of the cube in cubic inches times the weight of 1 cubic inch of water. That is, the upward pressure exceeds the downward pressure by the weight of a volume of water equal to the volume of the body. FIG. 25 This excess of upward pressure over the downward pressure acts against gravity; that is, the water presses the body upwards with a greater force than it presses it downwards; consequently, if a body is immersed in a fluid, it will lose in weight an amount equal to the weight of the fluid it displaces. This is called the principle of Archimedes, because it was first stated by him. This principle may be experimentally demonstrated with the beam scales, as shown in Fig. 26. From one scale pan suspend a hollow cylinder of metal, and below that a solid cylinder a of the same size as the hollow part of the upper cylinder. Put weights in the other scale pan until they exactly balance the two cylinders. If a is immersed in water, the scale pan containing the weights will descend, showing that a has lost some of its weight. water, and the volume of water that can be poured into will equal that displaced by a. The scale pan that contains the weights will gradually rise until t is filled, when the scales again balance. If a body is lighter than the liquid in which it is immersed, the upward pressure will cause it to rise and project partly out of the liquid, until the weight of the body and the weight of FIG. 26 Now, fill t with the liquid displaced are equal. If the immersed body is heavier than the liquid, the downward pressure plus the weight of the body will be greater than the upward pressure, and the body will fall downwards until it touches bottom or meets an obstruction. If the weights of equal volumes of the liquid and the body are equal, the body will remain stationary and will be in equilibrium in any position or depth beneath the surface of the liquid. 35. An interesting experiment in confirmation of the foregoing facts may be performed as follows: Drop an egg into a glass jar filled with fresh water. The mean density of the egg being a little greater than that of the water, it will 4 fall to the bottom of the jar. Now, dissolve salt in the water, stirring it so as to mix the fresh and salt water. The salt water will presently become denser than the egg and the egg will rise. Now, if fresh water is poured in until the egg and water have the same density, the egg will remain stationary in any position that it may be placed below the surface of the water. 36. The principle of Archimedes gives a very easy and accurate method of finding the volume of an irregularly shaped body. Thus, subtract its weight in water from its weight in air and divide by .03617; the quotient will be the volume in cubic inches; or divide by 62.5 and the quotient will be the volume in cubic feet. If the specific gravity of the body is known, its cubical contents can be found by dividing its weight by its specific gravity, and then dividing again by either .03617 or 62.5. EXAMPLE.-A certain body has a specific gravity of 4.38 and weighs 76 pounds; how many cubic inches are there in the body? 76 SOLUTION. = 479.72 cu. in. Ans. 4.38 .03617 37. GRAVITATION Every body in the universe exerts on every other body a certain attractive force that tends to draw the two bodies together; this attractive force is called gravitation. If a body is held in the hand, a downward pull is felt, and if released, the body will fall to the ground. This pull is commonly called weight, but it really is the attraction between the earth and the body. 38. Specific Gravity. The ratio between the weight of a body and the weight of a like volume of water is called its specific gravity. The formula for the specific gravity of a liquid is therefore as follows: specific gravity= actual weight of a liquid weight of an equal volume of water The actual weight of a liquid can be found when its volume and its specific gravity are known since the actual |