It is important to observe that in speaking of the transmission of pressure to the sides of the containing vessel, these pressures must always be supposed to be perpendicular to the sides.
Equilibrium or state of rest of superposed liquids. In order that there should be equilibrium when several heterogeneous liquids are superposed in the same vessel, each of them must satisfy the conditions necessary for a single liquid, and further there will be a stable state of rest only when the liquids are arranged in the order of their decreasing densities from the bottom upwards.
The last condition is experimentally demonstrated by means of the phial of four elements. This consists of a long narrow bottle containing mercury, water, colored red, saturated with carbonate of potash, alcohol, and petroleum. When the phial is shaken the liquids mix, but when it is allowed to rest they separate; the mercury sinks to the bottom, then comes the water, then the alcohol, and then the petroleum. This is the order of the decreasing densities of the bodies. The water is saturated with carbonate of potash to prevent its mixing with the alcohol.
This separation of the liquids is due to the same cause as that which enables solid bodies to float on the surface of a liquid of greater density than their own. It is also on this account that fresh water, at the mouths of rivers, floats for a long time on the denser salt water of the sea; and it is for the same reason that cream, which is lighter than milk, rises to the surface.
The pressure upon any particle of a fluid of uniform density is proportioned to its depth below the surface.
Fig. 89.
Example 1. Let the column of fluid ABCD Fig. (1) be perpendicular to the horizon. Take any points, x and y, at different depths, and conceive the column to be divided into a number of equal spaces by horizontal planes. Then, since the density of the fluid is uniform throughout, the pressure upon x and y, respectively, must be in proportion to the number of equal spaces above them, and consequently in proportion to their depths.
Example 2. Let the column be of the same perpendicular height as before, but inclined as is Fig. (2); then its quantity, and of course its weight, is increased in the same ratio as its length exceeds its height; but since the column is partly supported by the plane, like any other heavy body, the force of gravity acting upon it is diminished on this account in the same ratio as its length exceeds its height; therefore as much as the pressure on the base would be augmented by the increased length of the column, just so much it is lessened by the action of the inclined plane; and the pressure on any part of Cc will be, as before, proportioned to its perpendicular depth; and the pressure of the inclined column ACac will be the same as that of the perpendicular column ABCD.
Fluids rise to the same level in the opposite arms of a recurved tube.