170

Liquid Pressure varies only with Depth.

mission; and (2) on the incompressibility of liquids, for if the space, eƒ, were filled with air or any compressible fluid, a serious loss of Energy would arise, as will be at once perceived.

301. Liquids have weight; consequently the particles below the surface have to bear the weight of those that are above them: also this pressure, being occasioned by the weight acting vertically downwards, is in proportion simply to the VERTICAL DEPTH, and is not dependent on the quantity of surrounding liquid, or on the shape or size of the containing vessel.

In an upright column or tube of water, it is evident that the weight of water pressing on the bottom, a (fig. 76), is doubled when the tube is filled up from 6 to c, tripled when up to d, and so on. The liquid is supposed to be incompressible; so that the weight of each mass of water-column, of the same height, will be the same and will remain unchanged by the addition of more water above.

Fig. 76.

VA

We have much greater difficulty in conceiving how the pressure on the bottom may be different from the weight of the liquid; which happens when the vessel is shaped irregularly, as in the adjoining cuts (fig. 77). In the first, the vessel widens out towards the mouth; now a little consideration shows that whatever liquid there is more than the vertical column, A a, standing on A, is prevented from falling, that is, has its pressure supported, by the sides A B and A C, of the vessel, and balances the column, A a, on all sides round about. So that in reality A has to support only the upright column, A a.

Fig. 77.

In the other case, where the vessel tapers at the mouth, let us suppose the bottom, D E, divided into a number of portions of the same size as the mouth, F, and that there are eight of these portions. It is an immediate consequence of the principle of equal pressure in all directions, that the weight of a small liquid mass half-an-inch thick at the top, will be transmitted undiminished to each of the eight portions of the base, and will produce the same pressure there as eight of these masses spread over the bottom. So, again, if we consider a half-inch layer of the liquid lower down, say twice as large as F, it is evident in like manner that its pressure on the whole

Experimental Proof of this Law.

171

base will be the same as four layers like itself laid on the base, that is, the same as eight of the upper little layers.

Thus we see that each horizontal layer of the same thickness, no matter where it lies in the liquid, produces the same pressure, and a pressure depending only on its thickness and the size of the base. Hence the resulting effect of the whole is to produce a pressure depending only on the size of the base and the vertical height of liquid; that is, it is the same as the pressure of an upright column of the same vertical height.

Paradoxical as it may at first appear, then, the bottom in this case will suffer a pressure greater than that of the liquid contents of the vessel.

"Experimental proof of the law-Pressure as vertical depth."

302. By putting different heights of liquid into an upright tube, of which the bottom is closed by a flap having a spring or lever to support it, we find that for a double, triple, &c. height of column the lever must be loaded with double, triple, &c. weights, indicating double, triple, &c. pressing force.

Suppose vessels differing from each other in form and capacity, as sketched at a, b, and c (fig. 78), but all having flat bottoms, of exactly the same area. By having the bottoms movable, and held to their places by weights or springs capable of indicating the pressure borne, we find that if fluid be poured into all to the same level or perpendicular height, as represented here by the dotted lines, al

a

Fig. 78.

though the quantity be very different in each, the pressure on the bottom will be the same in all. Or by letting the three vessels all communicate with the same vessel of water below them, we infer the equality of pressures from the fact that the water is supported in all at the same level.

303. The following are farther illustrations of the pressure increasing with the depth:

A tube two feet long and a square inch in section, holds nearly a pound of water; hence the pressure of water at any depth, whether on the side of a vessel, or on its bottom, or on any body immersed,

172

Familiar Illustrations of this Law.

is only a little less than one pound on the square inch for every two feet of depth-a general truth well worth keeping in memory.

A bubble set at liberty far below the surface of water, is small at first, owing to the compression, and gradually enlarges as it rises. The effects of liquid pressure at great depths are most strikingly exhibited at sea.

If a strong square glass bottle, empty, and firmly corked, be sunk in water, its sides are generally crushed inwards before it reaches a depth of ten fathoms.

A water-tight wooden chamber, if similarly let down with a man in it, would quickly allow him to be drowned by the water bursting in upon him; as once actually happened to an ignorant projector. When a ship founders in shallow water, the wreck on breaking to pieces generally comes to the surface, or floats, and is cast upon the beach; but when the ship sinks in deep water, the great pressure forces water into the pores of the wood, and renders it so heavy that no part can ever rise again to reveal her fate. Thus it is that a whaling-boat drawn down to a great depth by a whale, never reappears on the surface.

A diver in deep water suffers much from the compression of his chest, as the elastic air within yields under the strong pressure. This limits the depth to which ordinary divers can safely go.

It is not known whether there is a limit to the pressure which fishes can bear with impunity, but they abound chiefly in the shallower waters on coasts, or on banks in the midst of the occan, such as the banks of Newfoundland, the Dogger-bank, or the bank of Lagullas, off the Cape of Good Hope. At the abyssal ocean depths which are now being explored, the same animal life could not exist unprotected from the enormous liquid pressure as exists in the superficial layer. Hence the tiny creatures brought up in deep-sea soundings, from depths of 500 to 700 fathoms, are enclosed in calcareous shells, whose thickness increases with the depth at which their home may have been situated.

One way of proving the compressibility of water under enormous pressure, is to sink a vessel, prepared for the purpose, in the deep sea. The vessel has a small round opening, into which, instead of a cork, a sliding rod has been closely fitted. Thus, when it is sunk, the pressure will push the rod inwards, in a degree proportioned to the yielding of the water within; and a stiff-sliding ring on the rod, or other contrivance, may be used to indicate how far the rod had been driven inwards, or the degree of compression at the

Pressure in all Directions Exemplified.

173

greatest depth. In this way it has been found that water compressed by 1000 fathoms of water over it, or a force of 3,000 lbs. to the square inch, loses about one-hundredth of its bulk (Art. 294).

304. The following are proofs of the pressure produced by gravity in a free liquid operating equally in all directions.

A bottle-cork at the bottom of the sea would not be flattened as if it were pressed unequally, or only above and below, but would he reduced in all its dimensions, so as to look like a phial-cork.

By means of a valve or flap, so contrived as to tell the force required to keep it shut, we find that water tends to escape just as powerfully through an opening in the side of a vessel as through an opening in the bottom, with the same height of water over each. Equal openings in the side of a vessel must be closed with forces exactly proportioned to the heights of liquid above them.

In an open square-sided vessel full of water, the whole pressure on any upright side is just half of that on an equal extent of horizontal bottom. For, the centre of the side being just half as deep as the bottom, the pressure there is only half that at any part of the bottom; and on points above the level of the centre, is just as much less than half, as, at corresponding distances below, it is more than half. So it amounts to an exact half on the whole.

Considering that the pressure on every point below the central level is greater than on every point above it, we see why, in order to support a sluice or flood-gate by a single stay on the outside, the point at which the support has to be applied is below the central level. Calculation and experiment discover that this point, called the centre of pressure, is at one-third from the bottom. The knowledge of such facts furnishes rules for the construction of large vessels to hold liquids, and of canal and other embankments.

The pressure on the upright side of a deep narrow vessel is just as great as on the same extent of side of a wide vessel, having the same depth of fluid: because it depends merely on the extent of surface acted upon, and the depth of liquid.

Hence a flood-gate which shuts out the ocean, as in docks opening to the sea, bears no more pressure than if it formed the side of a vessel so narrow that a few hogsheads of water would fill it.

A deep crevice in a rock, if filled by rain, may cause the rock to split or be torn asunder.

Extensive walls or faces of masonry, intended to confine banks of sand or earth, if left without low openings for water to escape from

174 A Liquid Surface at Rest is Horizontal. behind them, may be burst after rain, unless they have the strength of flood-gates of the same size. Ignorance of this danger has led to some extraordinary catastrophes.

Other examples of liquid pressure being exerted in all directions, and proportioned always to the depth, are: the swelling and bursting of leaden pipes when filled from a very elevated source; the tearing up of the coverings of subterranean drains or watercourses, when, during a flood, any accident chokes them near their lower openings; the violence with which water escapes by an opening near the bottom of any deep vessel, or enters by an opening or leak near the keel of a deep-floating ship; the great strength required in the lower hoops and securities of those enormous porter-vats which contain sometimes thousands of barrels of liquid.

sure.

305. Some persons have a difficulty in conceiving that within a liquid there is an upward as well as a downward and a lateral presBut if the particles below at every point of a liquid had not an upward tendency equal to the weight or downward pressure of the fluid over them, they could not support that column, but would move away, which they do not. Their tendency upwards is owing to the surrounding pressure from which they are trying to escape. If a glass tube, open at both ends, and having a sliding plug or piston in it near one end, be plunged into water with the plugged end down, the water presses the plug up; and, by having a spiral spring inside the tube for the plug to compress, we may show that the pressure is always proportioned to the depth. On removing the plug, a column of water is pushed into the tube from below, and supported there at the level of the liquid around, by this upward

pressure.

"Level surface of a liquid."

306. That the surface of a liquid which is at rest must be level, follows from the perfect mobility of the particles among each other, and from their being equally attracted towards the centre of the earth.

The particles forming the surface may be regarded as the tops of so many columns of particles, supported by a uniform resistance or pressure below; for no particle below can be at rest unless urged equally in all directions, and therefore all the particles, at any one level, which, by equally urging one another, keep themselves at rest, must be bearing the weight of equal columns. Thus a higher column, however produced, must sink