The several figures above need no explanation to the attentive reader.
FLOW OF WATER UNDER PRESSURE.
Under this head three general cases are to be considered: 1, that of liquids issuing from orifices; 2, their flow through tubes, or in streams; and, 3, the effects of the momentum and impact of liquids. The principles governing the action of the two last will be introduced, 2, under that portion of the work relating to “piping,” and, 3, under the sections pertaining to the jet pump. Throughout the different portions of the book will the three cases be still further elucidated.
Now, as to the laws governing the escape of liquids under pressure through an opening, it may be understood that when the liquid escapes from a vessel, owing to the excess of the internal pressure, the volume which escapes depends on the section of the orifice and the velocity with which the liquid molecules move at the moment of their escape from it.
This velocity depends upon the density of the liquid, the excess of pressure at the opening, and the friction of the liquid, both at the opening and against the walls. When the aperture is made in a very thin wall of a large vessel, so as to remove, as much as possible, the causes tending to modify the motion of the escaping fluid, the laws of the escape are comprised in the following theorem, discovered by Torricelli, in 1643, as a consequence of the law of the fall of bodies discovered by Galileo: “Liquid molecules, flowing from an orifice, have the same velocity, as if they fell freely in vacuo from a height equal to the vertical distance from the surface to the center of the orifice.”
Deductions from the above:—1, the velocity depends on the depth of the orifice from the surface, and is independent of the density of the liquid. Water and mercury in vacuo would fall from the same height in the same time; and so escaping from an orifice at the same depth, below the surface, would pass out with equal velocity; but mercury, being 13·5 times as heavy as water, the pressure exerted at the aperture of a vessel filled with mercury, will be 13·5 times as great as the pressure exerted at the aperture of a vessel filled with water; 2, the velocity of liquids is as the square roots of the depths of the orifices below the surfaces of the liquids.
Note.—Torricelli discovered, in the early part of the 17th century, the remarkable fact that a fluid issues from a small orifice with the same velocity (friction and atmospheric resistance excluded) which it would have acquired in falling through the depth from its surface. This was one of a long series of discoveries leading toward the now almost exact science of hydro-mechanics.
Thus stating, the velocity of a liquid escaping from an orifice one foot below the surface to be one; from a similar orifice four feet below the surface, it will be two, and at nine feet three, at sixteen feet four, and so on.