A HYDRAULIC PRESS This picture was taken when the press was making a huge hollow forging of steel 52 inches inside diameter, as reaction chambers for the cracking of gasoline. (Courtesy of the Bethlehem Steel Company) Brilliant French mathematician, physicist, and philosopher. He enunciated the law of transmission of pressure by liquids, showed that the force of a liquid against the bottom of an open vessel is independent of the shape of the vessel, and verified the theory of Torricelli by having a barometer carried to the top of a mountain and the fall of the mercury column noted 8. A swimming tank 50 ft. square is filled with water to a depth of 5 ft. Find the force of the water on the bottom; on a side. 9. Find the total force against the gate of a lock if its width is 60 ft. and the depth of the water 20 ft. Will it have to be made stronger if it holds back a lake than if it holds back a small pond? 10. A U-tube having a cross section of 1 sq. cm. is filled to a certain level with mercury (density 13.6 g. per cubic centimeter). Then 20 cc. of water are poured into one side. What is now the difference in level between the top of the water on one side and the top of the mercury on the other? (1) B FIG. 12. Illustration of hydrostatic paradox 11. If the areas of the surfaces AB in Fig. 12, (1) and (2), are the same, and if water is poured into each vessel at D till it stands at the same height above AB, how will the downward force on AB in Fig. 12 (2) compare with that in Fig. 12 (1)? Test your answer, if possible, by making AB a piece of cardboard and pouring water in at D, in each case, until the cardboard is forced off. PASCAL'S LAW 22. Transmission of pressure by liquids. From the fact that pressure within a free liquid depends simply upon the depth and density of the liquid, it is possible to deduce a very surprising conclusion, which was first stated by the famous French scientist, mathematician, and philosopher Pascal (see opposite page). Let us imagine a vessel of the shape shown in Fig. 13 (1) to be filled with water up to the level ab. For simplicity let the upper portion be assumed to be 1 square centimeter in cross section. Since the density of water is 1, the force with which it presses against any square centimeter of the interior surface which is h centimeters beneath the level ab is h grams. Now let 1 gram of water (that is, 1 cubic centimeter) be poured into the tube. If a given square centimeter of surface was before h centimeters beneath the level of the water in the tube, it is now h + 1 centimeters beneath this level. Therefore the new pressure which the water exerts against it is h + 1 grams; that is, applying 1 gram of force to the square centimeter of surface ab b has added 1 gram to the force exerted by the liquid against each square centimeter of the interior of the vessel. Obviously it can make no difference whether the pressure which was applied to the surface ab was due to a weight of water, or to a piston carrying a D load, as in Fig. 13 (2), or to any other cause whatever. We therefore arrive at Pascal's conclusion, namely, that pressure applied anywhere to a body of confined liquid is transmitted undiminished to every portion of the surface of the containing vessel. (1) (2) FIG. 13. Proof of Pascal's law 1 kg a 1000 kg B FIG. 14. Multiplication of force by transmission of pressure 23. Multiplication of force by the transmission of pressure by liquids. Pascal himself pointed out that with the aid of the principle stated above we ought to be able to transform a very small force into one of unlimited magnitude. Thus, if the area of the cylinder ab (Fig. 14) is 1 square centimeter, and that of the cylinder AB is 1000 square centimeters, a force of 1 kilogram applied to ab would be transmitted by the liquid so as to act with a force of 1 kilogram on each square centimeter of the surface AB. Hence the total upward force exerted against the piston AB by the 1 kilogram applied at ab would be 1000 kilograms. Pascal's own words are as follows: "A vessel full of water is a new principle in mechanics, and a new machine for the multiplication of force to any required extent, since one man will by this means be able to move any given weight." 24. The hydraulic press. The experimental proof of the correctness of the conclusions of the preceding paragraph is furnished by the hydraulic press, an instrument now in common use for subjecting to enormous pressures paper, cotton, etc. and for punching holes through iron plates, testing the strength of iron beams, extracting oil from seeds, making dies, embossing metal, braking automobiles, etc. Hy draulic presses of great power have been designed for use in steel works to replace huge steam hammers (see opposite page 16). Compressions of 14,000 tons or more are thus obtained. Much cold steel, as well as hot, is now pressed instead of hammered. When the small piston p of the press shown in Fig. 15 is raised, water from the cistern Centers the piston chamber K FIG. 15. Diagram of a hydraulic press through the valve v. As soon as the downstroke begins, the valve v closes, the valve v' opens, and the pressure applied on the piston p is transmitted through the tube K to the large reservoir, where it acts on the large cylinder P. The force exerted upon P is as many times that applied to p as the area of P is times the area of p. 25. No gain in the product of force times distance. It should be noticed that while the force acting on AB (Fig. 14) is 1000 times as great as the force acting on ab, the distance through which the piston AB is pushed up in a given time is but of the distance through which the piston ab moves down. For forcing ab down a distance of 1 centimeter crowds but 1 cubic centimeter of water over into the large cylinder, |