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### Science for Kids - Archimedes Principle. Water-Pressure and Water-Works

Archimedes (287-212 B. C.) was the greatest of the ancient mathematicians. He lived in Syracuse on the island of Sicily. The king of Syracuse in Archimedes' time once ordered of a goldsmith a crown of pure gold. It was delivered to him. It looked like pure gold and it had the proper weight. Still the king had reason to suspect that the goldsmith had cheated by melting up silver along with the gold. He asked Archimedes to discover a method of proving the fraud. A modern chemist could have solved the problem in a minute, but chemistry in those days was unknown. So the mathematician put his wits to work. He was sorely puzzled. One day, while in the public bath, he noticed that the part of his body under the water was much lighter (more buoyant) than the part above it. He got to thinking about this. Suddenly he jumped from the bath like a crazy man (so the story goes), rushed into the street without waiting to dress, and ran home shouting "Eureka! Eureka!" which means "I have found it."

Now what had occurred to Archimedes was this: He knew that gold and silver are different as to their buoyancy in water, or, as we say now, as to the specific gravity. So taking a weight of gold equal to the weight of the crown, and comparing it with the crown as to buoyancy, he could prove whether the crown was pure gold or not.

By means of Archimedes' principle we may also compute the volume of solid objects of any shape. Weigh the object in air, and then weigh it under water. The difference in the two weights represents the weight of the water displaced. Suppose this difference be ten grams. We know that ten grams of water by weight is ten cubic centimeters of water by volume. We also know that the volume of water displaced is identical with the volume of the object submerged. Therefore, the volume of the object is ten cubic centimeters. In other words, the difference in grams between the weight of an object in air and its weight in water is equal to the volume of that object in cubic centimeters.

Fig. 1
Water-Pressure. The pressure of a liquid is exerted equally in every direction against the sides and bottom of whatever contains it. Suppose there is a tank of water at the top of a house, with a pipe leading down from it and branching off to different rooms. Now if you turn on the water at a tap directly below the tank, will it run out with any greater force than from a tap located many feet further away from the tank on the same side? You know that it will not. This illustrates the principle above-stated.

It is possible to take advantage of this principle in various kinds of work. Since liquids thus transmit equal pressure in every direction against the walls of their containers, it is possible to use water as a means for multiplying the area of pressure. Thus in the hydraulic press ( Fig. 1 ) a downward pressure exerted at the narrower tube will be equally exerted by the top surface of the wider end, as well as by all the other contained

Fig. 2
surfaces. If for example there is a six-pound pressure down on the larger surface, there will be a pressure on the narrower end as many pounds as the top area of the larger end is contained in the top area of the narrower end. This is what is meant by multiplying the pressure. If the larger top surface is ten times larger than the smaller one, the pressure exerted on the smaller top surface will be ten pounds. Thus we have a multiplication of pressure, but this must not be confused with multiplication of work. If the smaller piston is pushed down one inch, will the larger piston rise one inch ? Certainly not. For one thing, there would not be enough water to fill such an addition to the space. The larger piston will rise only in proportion to the difference between its area and the area of the smaller one. If it be ten times as large as ab, and ab be forced down one inch, then AB will be forced up one-tenth of an inch. The pressure on the larger top surface is ten times as great as the pressure on the top smaller one, but it works through only one-tenth of the distance, thus fulfilling the law of conservation of energy. You have heard of the law of the indestructibility of matter. You know that matter may be changed, but it cannot be produced or destroyed. So energy or work can be changed; the area over which it operates can be multiplied. But the work done cannot be multiplied. Energy like matter can be changed in form, as from electricity to light, but, like matter, it can neither be produced nor destroyed. However wonderful a machine may be, the amount of work it does is never greater than the amount of energy it takes to make it work. The work taken out cannot be greater than the work put in. Water-pressure is used in the operation of elevators ( Fig. 2 ). Water is forced into the cylinder and produces a pull on the cable. The elevator goes up. The operator stops the car by closing the valve that shuts off the water from the water-mam. He lowers it by opening a valve that permits the water in the cylinder to run off into the sewer.

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