128. Experiments.—Some very neat experiments can be tried, showing that the upward pressure varies with the depth. Take a large glass tube, A B C D, Fig. 82, and let there be fitted to one end a circular plate of brass, which may be held there by a string, F. Thus arranged, plunge it quite deep into water, and you will find that you will not need to hold on to the string, for the brass disk will be held tight to the tube by the upward pressure of the water. Now draw up the tube slowly, and at length the disk will fall from the end of the tube. Why? Because the end of the tube has come to a point where the upward pressure of the water is less than the downward pressure of the disk. To have this experiment succeed, the end of the tube where the disk is applied must be very even and smooth. Another experiment may be tried in this way. Tie to one end of a glass tube a piece of thin India-rubber or bladder, and fill the tube partly with water. The India-rubber will of course bulge out or be convex from the weight of the water. Press the closed end down a little way in a vessel of water, so that the level in the tube shall be above the level in the vessel. The India-rubber is still somewhat convex, because, as the upward pressure upon it is in proportion to its distance from the surface of the water outside of the tube, it is not as great as the pressure downward of the higher water in the tube. Push the tube now so far down that the level in the tube is the same with that in the vessel. The India-rubber is now flat, because the downward and upward pressures upon it are equal, just as would be the case with a stratum of water in place of it. But press the tube lower down, and the India-rubber bulges upward into the tube, because the upward pressure is now greater than the downward.
129. Great Effects from Small Quantities of a Fluid.—You are now prepared to understand the explanation of some very striking phenomena in the pressure of liquids. If you take a perfectly tight cask, and, filling it with water, screw into its top a long tube, by pouring water into the tube you can burst the cask. To understand this you must bear in mind two facts—that the fluid in the cask is not compressible, and that its particles move freely among each other. Any pressure, therefore, exerted upon it is felt through the whole of it equally. "If the tube," says Dr. Arnot, "have an area of a fortieth of an inch, and contain when filled half a pound of water, this produces a pressure of half a pound upon every fortieth of an inch all over the interior of the cask; which is more than a common cask can bear." Suppose a small reservoir of water exists in the side of a mountain wholly closed up, and that water from a height above finds its way to it by a crevice, it may by its pressure even burst open the side of the mountain. And it matters not how large or small the crevice may be, for pressure in a liquid is only as the height. If the reservoir be ten yards square and an inch deep, and the fissure leading to it be but an inch in diameter and two hundred feet in height, it is calculated that the pressure of the water in the fissure would be equal in force to the weight of 5000 tons.
Fig. 83.
130. Explanation.—The manner in which these effects are produced may be made clear by Fig. 83. Let A be a close vessel filled with water, and let a tube, b, be made fast in it, with a movable plug or piston at c. If the surface of the water be pressed upon by this piston with the force of a pound, as the water is incompressible and its particles are freely movable among each other, the pressure will be extended equally through all the water, and every portion of the vessel of equal extent with the tube's opening at c will be pressed upon with the force of a pound. If another tube, d, of the same size were inserted with a piston, i, the force of a pound applied to the piston c would push upward the piston i with the same force. And if there were several pistons of the same size, by pushing upon one with the force of a pound they would all be pressed upward with exactly this force. Farther, if e be a tube five times as large as b, its piston, n, will be forced upward with a pressure of five pounds by the downward pressure of a pound upon c. Suppose now that a pound of water were substituted for the piston c, the other pistons would be pressed upward as before. And if all the pistons be removed, the pound of water in b will press the water up the tube d with the force of a pound, and up the tube e with the force of five pounds.
Fig. 84.
To make this still more clear I will present it in a little different form. Let B, Fig. 84, be a close vessel with two tubes, one of which is five times as large as the other. If sufficient water be poured into the vessel to occupy a part of the tubes, it will stand at the same height in both tubes, as indicated. If there be a pound of water, then, in the tube c, there will be five pounds in a. Now if the five pounds of water in a made any more pressure on the whole body of water in B than the pound of water in c does, it would press up the water in c to a greater height. But this is impossible, as has been shown in § 118. Observe that the five pounds of pressure in a is spread over five times the area or extent of surface that the pound's pressure in c is. If the tube c have an area of an inch square, the water in it will exert a pressure of a pound on every square inch in the vessel. The water in a exerts a pressure of five pounds; but it must be remembered that it does not press with this force on every square inch, but on every space of five square inches, and that therefore its pressure on every inch is the same as that in the tube c.
131. Hydrostatic Paradox.—You see in the phenomena and explanations given above that a small quantity of a fluid can, under certain circumstances, exert an enormous pressure. This fact has been called the Hydrostatic Paradox. It does seem, at first view, incredible or paradoxical, when one asserts that a few ounces of water can be made to raise weights of hundreds or even thousands of pounds. But the explanations which I have given show you that there is no unexplainable mystery in the fact. The cause of it is the same as that which gives a level surface to liquids; viz., the force of gravitation acting upon a substance whose particles are freely movable among each other.
