We see from the above demonstration why it is that a dam is built in the form represented in Fig. 76. We see, also, why in the monstrous vats in some of the English breweries (some of them holding many thousand barrels) the hoops and other securities at the lower part of them require to be made of very great strength. It is manifest, also, that if a sluice-gate is to be kept shut by a single support, this must be applied at one third of the distance from the bottom, there being as much pressure, as seen by Fig. 75, on the lower third as on the upper two thirds of the gate.
123. Lateral Pressure in Fluids.—The pressure of a liquid on the side of a vessel, of which I have spoken above, is a lateral pressure, and it is caused by the downward pressure of gravitation in the liquid. But how? The particles of a fluid are freely movable among each other, and therefore are ready to escape from pressure in any direction. The particles at a, Fig. 75, pressed upon by the column of particles extending above them to the surface, are ready to escape laterally, and would do so if there were an opening made in the vessel at that point. But if the vessel contained a block of ice, fitting it as accurately as the body of water, there would be no escape at the opening, because the particles of the solid are so held together that the downward pressure of the earth's attraction occasions no lateral pressure.
Fig. 77.
Fig. 78.
The manner in which the downward pressure of the earth's attraction causes lateral pressure may be made clear by Figs. 77 and 78. We will suppose that the particles of solids and liquids are alike round, and that a solid differs from a liquid only in having its particles firmly united by attraction. Let a, b, and c, in Fig. 77, represent three particles of a solid. As they are united firmly they will have a united pressure from the centre of gravity directly toward the centre of the earth, as represented by the arrow. Let now d, e, and f, Fig. 78, represent three particles of water. These being but very slightly coherent, will make each an independent pressure toward the earth's centre, as indicated by the arrows. It is plain that d tends to separate e and f, and will do so if they are left free to move in a lateral direction. For example, if e be at the side of a vessel, and an opening be made there, the downward pressure of d will give e a lateral movement, forcing it out of the opening.
124. Another View.—To return to Fig. 75, observe that the lateral pressure at any point in the side of a vessel, as a, is occasioned wholly by the downward pressure of a vertical column of particles extending from that point to the surface. The neighboring columns of particles have nothing to do with it. The same thing is true in regard to any other point either in the line A B or another line drawn on the side of the vessel. It is therefore true of the whole side, that the pressure upon it is occasioned alone by the columns of particles that are in close proximity to the side, and not at all by the other columns of particles in the vessel. The number of these columns, therefore, in the vessel, or, in other words, the breadth of the body of water in it, makes no difference with the pressure on its side. For this reason two flood-gates so little apart that a few hogsheads or even pails of water fill up the space between them, are as much pressed upon as they would be if a lake or an ocean of water lay between them. It has been objected to the project of digging a ship canal between the Red Sea and the Mediterranean, that as the water in the former is twenty feet higher than in the latter, it would burst through the flood-gates with such force as to produce most disastrous results. But according to the principle which I have illustrated, there would be no more danger of this than there would be if two ponds were united by a canal, in one of which the water is twenty feet higher than in the other.
Fig. 79.