PART III. SECTION I.-HYDROSTATICS, OR THE PHENOMENA OF LIQUID PRESSURE. ANALYSIS OF THE SECTION. The particles of a fluid, being freely movable among one another, offer no resistance to separation, and hence their properties differ in many important points from those of solids. Fluids are of two classes; first, those practically incompressible, called Liquids; and, second, those compressible to any extent, called Gases. The first class is the subject of this section. The particles of a liquid (or any fluid) being equally movable in every direction, cannot be affected with pressure at any part, without this pressure being instantly felt at every portion of the liquid; so that a plug or piston forced inwards on a square inch of the surface of a liquid filling a vessel with a force of a pound, instantly produces a pressure of a pound on each square inch of any surface pressed by the liquid, or on every square inch of the surface of any body immersed in the liquid. The pressure on any immersed surface arising from the weight of a liquid, depends wholly on the extent of the surface and on the vertical depth, and not on the quantity of surrounding liquid. Thus the pressure on the base or bottom of a vessel may be either equal to, greater than, or less than the weight of its liquid contents—a fact which is usually called the hydrostatic paradox. The open or free surface of a liquid is horizontal: and when various pipes or vessels communicate with each other, water or any other liquid will rise to the same level in all. A body wholly or partially immersed in a liquid (or fluid) is buoyed up with force equal to the weight of the displaced liquid, and will therefore sink or swim according as its own weight is greater or less than this. The relation between the weight of any body and that of the water it displaces, is the estimate of its SPECIFIC GRAVITY compared with water, as a standard. "Fluid." 293. The very same matter may, as has been already explained, exist in the form of a solid, a liquid, or a gas. A 166 The Liquid Condition of any Mass. pound of ice, a pound of water, and a pound of steam differ In the ice they are comparatively near, and are as it were spitted or glued together by cohesion; in the water, the repulsion of heat seems almost to balance this attraction, and to leave the particles at liberty to flow or glide about among each other almost without friction; and in the steam this heat-repulsion altogether overcomes the attraction, the particles are separated to a great distance, and, as we have reason to suppose, are in incessant commotion. A body in either the liquid or the gaseous state is called a fluid, from this mobility or flow among its particles. Owing to the common feature of fluidity, there are certain properties belonging alike to liquids and to gases ; but, on the other hand, so important are the differences, that the phenomena of the two conditions of matter must be treated separately. There are thus two distinct branches relating to Fluids, namely, (i.) Hydrostatics and Hydraulics, which treat of the phenomena of liquid pressure and of liquid motion respectively. (ii.) Pneumatics which treats of the phenomena of air and gases. "Liquids incompressible." 294. In a liquid the particles are so near together that it is only by very great force that they can be pressed closer; and indeed, until improved means of experiment were recently contrived, liquids were accounted absolutely incompressible. Nor need we wonder that their compressibility escaped detection so long, for a pressure of 3500 lbs., or about 1 ton, on a column of water a square inch in section would reduce its bulk only by a hundredth part; and on a similar column of mercury, it would take 13 times as much to effect this degree of compression. "Fundamental principle of Liquids.” 295. As the particles of a liquid are equally ready to move in every direction, a pressure upon any one portion of the liquid must be equally resisted at all points, in order that the liquid may remain at rest. Thus if we were, by means of a pressure of 100 lbs., to force into a cask filled with liquid a plug having a surface of a square inch, every square inch of surface of the cask must be able to stand this pressure Fundamental Principle of Liquid Pressure. 167 of 100 lbs., otherwise the vessel will burst. And if the cask were three feet in girth, an iron hoop an inch broad running round it must, if the cask depends on its binding, be able to resist a force of 3600 lbs. trying to pull it asunder. 296. In like manner, if a close vessel, B (fig. 72), fitted with a narrow tube, a c, be filled with water, and if then, by means of a movable plug or piston in the tube, the water be pressed with a force of one pound, the az acting on one, B Fig. 72. we should equally affect all. Hence a piston of double area would be twice as much affected as the smaller one; and one of ten times the area, such as d, would be pressed upwards with a force of ten pounds. Through the medium of a confined fluid, a force of one pound may in this way become a bursting force of ten, or a hundred, or a thousand pounds, according to the size of the vessel, or may be used as a mechanical power to increase the intensity of a force to any degree. It will be explained below that the hydrostatic press is merely a large plug or piston as here described, forced up against the substance to be pressed, by the action of a smaller piston in another barrel. The pressure of one pound may be applied by pouring in a pound of water in the tube, a c, and the same results will obviously be produced on the plugs in b and d; and if, in the other tubes also, water were substituted for the pistons, it is evident that, to effect a balance in all, it would require to stand as high in every one as in the tube, a c, producing thus the same level in all, whatever their size. "Hydrostatic Paradox." 297. The fact that the weight of one pound of water, or any other force of one pound similarly applied, may thus be made to produce a pressure of hundreds or of thousands of pounds, has been called the "hydrostatic paradox ;" yet there is in reality nothing more paradoxical in it, than that one pound at the long end of a 168 The Hydrostatic Paradox. lever should balance ten pounds at the short end. Like the me chanical powers, described in the last section, it is but a means of causing different intensities of force to balance each other, by applying them to parts of an apparatus moving with different velocities. Here the tube, a, being ten times smaller than the tube, e, the piston in a must descend ten inches to raise the greater piston in e one inch; so that, as was explained in the case of the other mechanical powers, there is no increase of force here, but only a translation of a small force moving through a great space, into a great force moving through a correspondingly small space. Moreover it is to be noticed that, since liquids are practically incompressible and free from friction, there is much less waste of Energy in the transmission of power by their agency. We have in the hydrostatic lever, as we may call this, a much nearer approach to absolute rigidity and perfect freedom of motion than in the solid lever moving about a fulcrum. “Illustrations of Liquid Pressure." 298. This law of fluid pressure is very strikingly illustrated by the bursting of a strong cask with the weight or action a of a few ounces of water. Suppose a cask, a (fig. 73), filled with water, to have a long narrow tube, bc, screwed tightly into its top. The tube can contain only a few ounces of water; yet these few ounces in the tube may suffice to burst the cask. In explanation, it is unnecessary to say more than that if the tube have an area of a fortieth of an inch, and contain when filled, half a pound of water, that water would produce a pressure of half a pound upon every fortieth of an inch all over the interior of the cask, or of nearly 2000 lbs. on every square foot,—a pressure greater than any ordinary cask can bear. 299. A similar effect is seen in the toy called the hydrostatic bellows. This consists of (fig. 74) two wooden discs, d, c, (connected as in a common bellows by flexible sides of leather), and a long small tube, Fig. 73. a b, by which water can be poured to enter the body of the apparatus. If the tube, a b, holds an ounce of water, and has itself only one-thousandth of the area of the top of the bellows, an ounce of water in it will balance the weight of a thousand ounces on the top of the bellows at d. If mercury were substituted in this The Hydrostatic Bellows.-Bramal's Press. 169 a machine for water, the pressure of a column of the same height would support just thirteen and a half times as much, because mercury is so many times heavier. A man standing on the bellows might raise himself by blowing into the tube with his mouth, if the difference between the diameters of the tube and the bellows were sufficiently great; though of course, in accordance with the general principle of Energy, the space through which he would raise himself would be correspondingly small. 300. A remarkable illustration of liquid pressure is seen in the Hydrostatic or Hydraulic Press, perfected by Bramah in the end of the last century. The annexed cut (fig. 75) will give an idea of it. Compared with the bellows, it exhibits с Fig. 74. merely a strong forcing pump, e, in the figure, instead of the lofty tube; and a large barrel, a b, with its piston, cƒ, instead of the leather and boards. The pump is d Fig. 75. worked by the handle, d, and drives water along the horizontal tube into the space, f, under the large solid piston, c, which last, with its spreading top, is urged against the object to be compressed. If the small pump have only one-thousandth of the area of the large barrel, and if a man, by means of its lever-handle, d, press its piston down with a force of a hundred pounds, the piston of the great barrel will rise with the force of a hundred thousand pounds. Scarcely any resistance could withstand the power of such a press; with it the hand of a child might break a strong iron bar. It is used to condense bulky yielding substances, as cotton or hay, for sea voyages, to raise great weights, to uproot trees, to test the strength of cables, to launch vessels, to insert the axles into railway carriage wheels, to force the oil out of seeds, and for numerous other purposes. The efficiency of the hydraulic press as a mechanical power depends (1) on the perfect mobility of fluid particles, which furnishes the means of increasing the intensity of force without practical loss by friction in the course of its trans |