If a hollow sphere, a, Fig. [173], be pierced with a number of small holes at various points, and a cylinder, b, provided with a piston, c, fitted into it, when the apparatus is filled with water, and the piston is pushed inwards, the water will spout out of all the orifices equally, and not exclusively from that which is opposite to the piston and in the direction of its pressure. The jets of water so produced would not, as a matter of fact, all pursue straight paths radiating from the centre of the sphere, because gravity would act upon them; and all, except those which issued vertically, would take curved forms. But when proper allowance is made for this circumstance, each jet is seen to be projected with equal force in the direction of a radius of the sphere. This experiment proves that when pressure is applied to any part of a liquid, that pressure is transmitted in all directions equally. Thus the pressure of the piston—which, in the apparatus represented in the figure, is applied in the direction of the axis of the cylinder only—is carried throughout the whole mass of the liquid, and shows itself by its effect in urging the water out of the orifices in the sphere in all directions; and since the force with which the water rushes out is the same at every jet, it is plain that the water must press equally against each unit of area of the inside surface of the hollow sphere, without regard to the position of the unit.
If we suppose the piston to have an area of one square inch, and to be pushed inwards with a force of 10 lbs., it cannot be doubted that the square inch of the inner surface of sphere immediately opposite the cylinder will receive also the pressure of 10 lbs.; and since the pressures throughout the interior of the hollow globe are equal, every square inch of its area will also be pressed outwards with a force equal to 10 lbs. Hence, if the total area of the interior be 100 square inches, the whole pressure produced will amount to a hundred times 10 lbs.
Fig. 164.—Pascal’s Principle.
Fig. 165.—Collar of Hydraulic Cylinder.
That water or any other liquid would behave in the manner just described might be deduced from a property of liquids which is sufficiently obvious, namely, the freedom with which their particles move or slide upon each other. The equal transmission of pressure in all directions through liquids was first clearly expressed by the celebrated Pascal, and it is therefore known as “Pascal’s principle.” He said that “if a closed vessel filled with water has two openings, one of which is a hundred times as large as the other; and if each opening be provided with an exactly-fitting piston, a man pushing in the small piston could balance the efforts of a hundred men pushing in the other, and he could overcome the force of ninety-nine.” Pascal’s principle—which is that of the hydraulic press—may be illustrated by Fig. [164], in which two tubes of unequal areas, a and b, communicate with each, and are supposed to be filled with a liquid—water, for example, which will, of course, stand at the same level in both branches. Let us now imagine that pistons exactly fitting the tubes, and yet quite free to move, are placed upon the columns of liquid—the larger of which, b, we shall suppose to have five times the diameter, and therefore twenty-five times the sectional area, of the smaller one. A pressure of 1 lb. applied to the smaller piston would, in such a case, produce an upward pressure on the larger piston of 25 lbs.; and in order to keep the piston at rest, we should have to place a weight of 25 lbs. upon it. Here then a certain force appears to produce a much larger one, and the extent to which the latter may be increased is limited only by the means of increasing the area of the piston. Practically, however, we should not by any such arrangement be able to prove that there is exactly the same proportion between the total pressures as between the areas, for the pistons could not be made to fit with sufficient closeness without at the same time giving rise to so much friction as to render exact comparisons impossible. We may, however, still imagine a theoretical perfection in our apparatus, and see what further consequences may be deduced, remembering always that the actual results obtained in practice would differ from these only by reason of interfering causes, which can be taken into account when required. We have supposed hitherto that the pressures of the pistons exactly balance each other. Now, so long as the system thus remains in equilibrium no work is done; but if the smallest additional weight were placed upon either piston, that one would descend and the other would be pushed up. As we have supposed the apparatus to act without friction, so we shall also neglect the effects due to difference in the levels of the columns of liquid when the pistons are moved; and further, in order to fix our ideas, let us imagine the smaller tube to have a section of 1 square inch in area, and the larger one of 25 square inches. Now, if the weight of the piston, a, be increased by the smallest fraction of a grain, it will descend. When it has descended a distance of 25 in., then 25 cubic inches of water must have passed into b, and, to make room for this quantity of liquid, the piston with the weight of 25 lbs. upon it must have risen accordingly. But since the area of the larger tube is 25 in., a rise of 1 in. will exactly suffice for this; so that a weight of 1 lb. descending through a space of 25 in., raises a weight of 25 lbs. through a space of 1 in. This is an illustration of a principle holding good in all machines, which is sometimes vaguely expressed by saying that what is gained in power is lost in time. In this case we have the piston, b, moving through the space of 1 in. in the same time that the piston a moves through 25 in.; and therefore the velocity of the latter is twenty-five times greater than that of the former, but the time is the same. It would be more precise to say, that what is gained in force is lost in space; or, that no machine, whatever may be its nature or construction, is of itself capable of doing work. The “mechanical powers,” as they are called, can do but the work done upon them, and their use is only to change the relative amounts of the two factors, the product of which measures the work, namely, space and force. Pascal himself, in connection with the passage quoted above, clearly points out that in the new mechanical power suggested by him in the hydraulic press, “the same rule is met with as in the old ones—such as the lever, wheel and axle, screw, &c.—which is, that the distance is increased in proportion to the force; for it is evident that as one of the openings is a hundred times larger than the other, if the man who pushes the small piston drives it forward 1 in., he will drive backward the large piston one-hundredth part of that length only.” Though the hydraulic press was thus distinctly proposed as a machine by Pascal, a certain difficulty prevented the suggestion from becoming of any practical utility. It was found impossible, by any ordinary plan of packing, to make the piston fit without allowing the water to escape when the pressure became considerable. This difficulty was overcome by Bramah, who, about the end of last century, contrived a simple and elegant plan of packing the piston, and first made the hydraulic press an efficient and useful machine. Fig. [166] is a view of an ordinary hydraulic press, in which a is a very strong iron cylinder, represented in the figure with a part broken off, in order to show that inside of it is an iron piston or ram, b, which works up and down through a water-tight collar; and in this part is the invention by which Bramah overcame the difficulties that had previously been met with in making the hydraulic press of practical use. Bramah’s contrivance is shown by the section of the cylinder, Fig. [165], where the interior of the neck is seen to have a groove surrounding it, into which fits a ring of leather bent into a shape resembling an inverted U. The ring is cut out of a flat piece of stout leather, well oiled and bent into the required shape. The effect of the pressure of the water is to force the leather more tightly against the ram, and as the pressure becomes greater, the tighter is the fit of the collar, so that no water escapes even with very great pressures. To the ram, b, Fig. [166], a strong iron table, c, is attached, and on this are placed the articles to be compressed. Four wrought iron columns, d d d d, support another strong plate, e, and maintain it in a position to resist the upward pressure of the goods when the ram rises, and they are squeezed between the two tables. The interior of the large cylinder communicates by means of the pipe, f f, with the suction and force-pump, g, in which a small plunger, o, works water-tight. Suppose that the cylinders and tubes are quite filled with water, and that the ram and piston are in the positions represented in the figure. When the piston of the pump, g, is raised, the space below it is instantly filled with water, which enters from the reservoir, h, through the valve, i, the valve k being closed by the pressure above it, so that no water can find its way back from the pipe, f, into the small cylinder. When the piston has completed its ascent, the interior of the small cylinder is therefore completely filled with water from the reservoir; and when the piston is pushed down, the valve, i, instantly closes, and all egress of the liquid in that direction being prevented, the greater pressure in g forces open the valve, k, and the water flows along the tube, f, into the large cylinder. The pressure exerted by the plunger in the small cylinder, being transmitted according to the principles already explained, produces on each portion of the area of the large plunger equal to that of the smaller an exactly equal pressure. In the smaller hydraulic presses the plunger of the forcing-pump is worked by a lever, as represented in the figure at n; so that with a given amount of force applied by the hand to the end of the lever, the pressure exerted by the press will depend upon the proportion of the sectional area of b to that of o, and also upon the proportion of the length m n, to the length m l. To fix our ideas, let us suppose that the distance from m of the point n where the hand is applied is ten times the distance m l, and that the sectional area of b is a hundred times that of o. If a force of 60 lbs. be applied at n, this will produce a downward pressure at m equal to 60 × 10, and then the pressure transmitted to the ram of the great cylinder will be 60 × 10 × 100 = 60,000 lbs. The apparatus is provided with a safety-valve at p, which is loaded with a weight; so that when the pressure exceeds a desired amount, the valve opens and the water escapes. There is also an arrangement at q for allowing the water to flow out when it is desired to relieve the pressure, and the water is then forced out by the large plunger, which slowly descends to occupy its place. The body of the cylinder is placed beneath the floor in such presses as that represented in Fig. [166], in order to afford ready access to the table on which the articles to be compressed are placed.
Fig. 166.—Hydraulic Press.
The force which may, by a machine of this kind, be brought to bear upon substances submitted to its action, is limited only by the power of the materials of the press to resist the strains put upon them. If water be continually forced into the cylinder of such a machine, then, whatever may be the resistance offered to the ascent of the plunger, it must yield, or otherwise some part of the machine itself must yield, either by rupture of the hydraulic cylinder, or by the bursting of the connecting-pipe or the forcing-pump. This result is certain, for the water refuses to be compressed, at least to any noticeable degree, and therefore, by making the area of the plunger of the force-pump sufficiently small, there is no limit to the pressure per square inch which can be produced in the hydraulic cylinder; or, to speak more correctly, the limit is reached only when the pressure in the hydraulic cylinder is equal to the cohesive strength of the material (cast or wrought iron) of which it is formed. It has been found that when the internal pressure per square inch exceeds the cohesive or tensile strength of a rod of the metal 1 in. square (see page [207]), no increase in the thickness of the metal will enable the cylinder to resist the pressure. Professor Rankine has given the following formula for calculating the external radius, R, of a hollow cylinder of which the internal radius is r, the pressure per square inch which it is desired should be applied before the cylinder would yield being indicated by p, while f represents the tensile strength of the materials: