121. Pressure due to the Weight of Liquids. If a cylindrical vessel is filled with a heavy liquid, its weight produces a pressure upon the walls of the vessel. If we suppose the liquid divided into horizontal layers of equal thickness, it is plain that the second layer from the top supports a pressure equal to the weight of the first, the third layer supports a pressure equal to the weight of the second and first, and so on to the bottom. Hence, the pressure upon any layer is proportional to its depth below the upper surface, and is equal to the weight of the column of fluid above it.

In consequence of the Principle of PASCAL, this pressure is transmitted laterally, and acts against the sides of the vessel with an equal intensity. Hence, every part of the surface is pressed with a force equal to the weight of a column of liquid whose base is the surface pressed, and whose height is equal to the distance from that surface to the upper level of the fluid.

122. The Pressure on the Bottom of a Vessel, arising from the weight of a liquid, is entirely independent of the shape of the vessel, as well as of the quantity of liquid which it contains. It depends only on the size of the sur

face pressed, and its distance below the upper surface of the liquid.

This principle may be demonstrated by means of an apparatus shown in Fig. 80. The apparatus consists of a tube, o, firmly attached to the cover of a glass vessel, P. By means of a screw joint, different-shaped vessels, A, B, C, may be attached to the upper end of the tube. A disk, i, of ground glass is held in contact with the lower end of the tube by a string, which is secured at its upper extremity to an arm of a balance.

The vessel A is screwed on, and filled with water until the downward pressure exactly counterpoises a given weight in the scale-pan, M, when the upper surface of the water is marked by a sliding bead, n. The other vessels, B and C, are successively screwed on, and filled with water up to the level, n; if any more water is poured into either, the downward pressure overcomes the weight, M, and the water escapes into the vessel, P.

This principle of pressure on the bottom of vessels is sometimes called the Hydrostatic Paradox. It is so called, because the same pressure may be obtained by using very different quantities of the same liquid.

123. Hydrostatic Bellows. A good illustration of the principle that the pressure exerted by a column of water depends upon its height and not its amount is seen in a form of apparatus called the hydrostatic bellows. It consists (Fig. 81) of two boards connected by leather, in which a tube, A, is inserted.

000

E

Fig. 81.

When water is poured into the tube a pressure is exerted upon the upper board C, which will lift a weight as many times greater than the weight of the water in the tube, as the area of the board is greater than the area of a cross-section of the tube. By placing another tube upon A, we can increase the pressure and lifting power.

124. Lateral Pressures. Reaction Wheel. The fact that liquids exert lateral pressures upon the walls of vessels is demonstrated by means of the reaction wheel.

This wheel is shown in Fig. 82; it consists of a vertical cylindrical tube, C, turning freely in a ring, n, near its upper extremity, and resting upon a pivot at its lower extremity. Just above the pivot the tube terminates in a cubical box, from the faces of which project four tubes, having their ends curved, as represented in the figure. Water is supplied from a cistern through the funnel, D.

When the water is admitted, it flows down the tube, C, and escaping through the curved tubes at the bottom, the wheel is turned in the direction indicated by the arrowhead.

The reason of this will be plain from a consideration of the small figure, a b, which is a plan of two of the tubes. The weight of the water causes a pressure upon A, which, were a closed, would be exactly counterbalanced by the pressure upon it; but a being open, the pressure upon

A is not counterbalanced, but

B

D

n

C

Fig. 82.

acts from a towards A, producing rotary motion. The pressures in all of the tubes conspire to produce rotation in the same direction.

125. Pressure Upwards. That liquids exert a pressure upwards is demonstrated by means of the apparatus shown in Fig. 83.

It consists of a tube of glass, with a movable disk, a, ground so as to fit the bottom of the tube. The disk being held closely against

the tube by a string, b, the whole is plunged into a vessel of water. In this state the disk, though heavier than the water, does not fall

Fig. 83.

to the bottom, showing that it is held in place by an upward pressure. If water now be poured into the tube in a gentle stream, the disk will adhere till the latter is filled to the level of the fluid on the outside. This shows that the upward pressure is equal to the weight of a column of water whose base is that of the tube, and whose altitude is its distance below the upper surface of the fluid.'

The upward pressure of fluids is called their Buoyant Effort.

in

It is

consequence of their buoyant effort that fluids sustain lighter bodies on

their surfaces. The same principle causes fluids to buoy up bodies of all kinds, diminishing the weight of heavy ones, and causing light

Fig. 84.

ones to float.

126. Pascal's Experiment.— The following experiment was made by PASCAL, in 1647. He fitted into the upper head of a strong cask a tube of small diameter and about thirtyfour feet in length, as shown in Fig. 84. The cask being filled with water, he succeeded in bursting it by pouring a comparatively small quantity of water into the tube. In this case the pressure exerted laterally was the same as though the tube had been throughout of the same diameter as the cask, or even greater.

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127. Hydraulic Press. The principle of equal pressures has been applied in the construction of a press, by

means of which a single man may exert an enormous power. This press is shown in perspective in Fig. 85, and in section in Fig. 86, the letters in both figures corresponding to the same parts.

The press consists of two cylinders, A and B, of unequal diainIn the cylinder B is a solid piston, C, which rises as the

eters.

water is forced into B, and thus forces up a platform, K. The cylinder A forms the barrel of a pump, by means of which water is raised from a reservoir, P, and forced into the cylinder B. This pump is worked by a lever, O, attached to a solid piston, a. the piston a is raised, a vacuum is formed behind it, which is filled by water from the reservoir, P, which enters by opening the valve S. When the piston is depressed, the valve S closes, the

When