Fig. 78.

Fig. 78 represents a common coffee-pot, supposed to be filled up to the dotted line a, with a decoction of coffee, or any other liquid. The coffee, we know, stands exactly at the same height both in the body of the pot, and in its spout. Therefore the small quantity in the spout balances the large quantity in the pot, or presses with the same force downwards, as that in the body of the pot presses upwards. This is obviously true, otherwise, the large quantity would sink below the dotted line, while that in the spout would rise above it, and run over.

Fig. 79.

a

b

The same principle is more strikingly illustrated by fig. 79.

Suppose the cistern a to be capable of holding one hundred gallons, and into its bottom there be fitted the tube b, bent as seen in the figure, and capable of containing one gallon. The tops of the cistern and tube being open, pour water into the tube at c, and it will rise up through the perpendicular bend into the cistern, and if the process be continued, the cistern will be filled by pouring water into the tube. Now it is plain that the gallon of water in the tube, presses against the hundred gallons in the cistern with a force equal to the pressure of the hundred gallons, otherwise that in the tube would be forced upwards higher than that in the cistern, whereas we find that the surfaces of both stand exactly at the same height.

From these experiments we learn, "that the pressure of a fluid is not in proportion to its quantity, but to its height, and that a large quantity of water in an open vessel, presses downwards no more than a small quantity of the same height."

In this respect, the size or shape of a vessel is of no consequence, for if a number of vessels differing entirely from each other in figure, position, and capacity, have a communica. tion made between them, and one be filled with water, the sur

How does the experiment with the coffee pot shew that a small quantity of liquid will balance a large one? Explain fig. 79, and shew how the pressure in the tube is equal to the pressure in the cistern. What conclusion, or general truth, is to be drawn from these experiments ? What difference does the shape or size of a vessel make in respect to the pressure of a fluid on its bottom?

face of the fluid in all will be at exactly the same elevation. If therefore, the water stands at an equal height in ail, the pressure in one must be just equal to that in another, and so equal to that in all the others.

Fig. 80.

To make this obvious, suppose a number of vessels, of different shapes and sizes, as represented by fig. 80, to have a communication between them by means of a small tube passing from one to the other. If now, one of these vessels be filled with water, or if water be poured into the tube a, all the other vessels will be filled at the same instant up to the line b, c. Therefore the pressure of the water in a, balances that in 1, 2, 3, &c., while the pressure in each of these vessels is equal to that in the other, and so an equilibrium is produced throughout the whole series.

If an ounce of water be poured into the tube a, it will produce a pressure on the contents of all the other vessels, equal to the pressure of all the others on the tube; for, it will force the water into all the other vessels to rise upwards to an equal height with that in the tube itself. Hence we must calculate, that the pressure in each vessel is not only equal to that in any of the others, but also that the pressure in any one, is equal to that in all the others.

From this we learn, that the shape or size of a vessel has no influence on the pressure of its liquid contents, but that the pressure of water is as its height, whether the quantity be great or small. We learn also, that in no case will a quantity of liquid, however large, force another quantity however small, above the level of its own surface.

Explain fig. 80, and shew how the equilibrium is produced. Suppose an ounce of water be poured into the tube a, what will be its effect on the contents of the other vessels ? What conclusion is to be drawn from pouring the ounce of water into the tube a ?

This is proved by experiment; for if, from a pond situated on a mountain, water be conveyed in an inch tube to the valley an hundred feet below, the water will rise just a hundred feet in the tube; that is, exactly to the level of the surface of the pond. Thus the water in the pond, and that in the tube press equally against each other, and produce an exact equilibrium. Thus far we have considered the fluid as acting only in vessels with open mouths, and therefore at liberty to seek its balance, or equilibrium by its own gravity. Its pressure, we have seen, is in proportion to its height, and not its bulk.

Now by other experiments it is ascertained that the pressure of a liquid is in proportion to its height, and its area at the base.

Fig. 81.

Suppose a vessel ten feet high, and two feet in diameter, such as is represented at a, fig. 81, to be filled with water; there would be a certain amount of pressure, say at c, near the bottom. Let d represent another vessel, of the same diameter at the bottom, but only a foot high, and closed at the top. Now if a small tube, say the fourth of an inch in diameter, be inserted into the cover of the vessel d, and this tube be carried to the height of the vessel a, and then the vessel and tube be filled with water, the pressure on the bottoms and sides of both vessels will be equal, and jets of water starting from d, and c, will have exactly the same force.

d

This might at first seem improbable, but to convince ourselves of its truth, we have only to consider that any impression made on one portion of the confined fluid in the vessel d, is instantly communicated to the whole mass. Therefore the water in the tube b presses with the same force on every other portion of the water in d, as it does on that small portion over which it stands.

This principle is illustrated in a very striking manner by

What is the reason that a large quantity of water will not force a small quantity above its own level? Is the force of water in proportion to its height, or its quantity? How is a small quantity of water shown to press equal to a large quantity by fig. 81? Explain the reason why the pressure is as great at d, as at c.

the experiment, which has often been made, of bursting the strongest wine cask with a few ounces of water.

Fig. 82.

Suppose a, fig. 82, to be a strong cask already filled with water, and suppose the tube b thirty feet high, to be screwed, water tight, into its head. When water is poured into the tube, so as to fill it gradually, the cask will show increas ing signs of pressure, by emitting the water through the pores of the wood, and between the joints and finally as the tube is filled, the cask will burst asunder.

The same apparatus will serve to illustrate the upward pressure of water; for if a small stopcock be fitted to the upper head, on turning this, when the tube is filled, a jet of water will spout up with a force, and to a height that will astona ish all who never before saw such an experi

ment.

In theory, the water will spout to the same height with that which gives the pressure, but in practice, it is found to fall short, in the following proportions:

If the tube be twenty feet high, and the orifice for the jet half an inch in diameter, the water will spout nearly nineteen feet. If the tube be fifty feet high, the jet will rise upwards of forty feet; and if an hundred feet, it will rise above eighty feet. It is understood in every case, that the tubes are to be kept full of water.

The height of these jets shew the astonishing effects that a small quantity of fluid produces when pressing from a perpendicular elevation.

An instrument called the hydrostatic bellows, also shows, in a striking manner, the great force of a small quantity of water, pressing in a perpendicular direction.

This instrument consists of two boards, connected together with strong leather, in the manner of the common bellows. It is then furnished with a tube a, fig. 83, which communi. cates between the two boards. A person standing on the upper board, may raise himself up by pouring water into the tube. If the tube holds an ounce of water, and has an area

How is the same principle illustrated by fig. 82? How is the upward pressure of water illustrated by the same apparatus? Under the pressure of a column of water twenty feet high, what will be the height of the jet? Under a pressure of a hundred feet, how high will it rise?

h

Fig. 83.

d

Fig. 84.

equal to a thousandth part of the area of the top of the bellows, one ounce of water in the tube will balance a thousand ounces placed on the bellows.

This property of water was applied by Mr. Bramah to the construction of his hydraulic press. But instead of a high tube of water, which in most cases could not be readily obtained, he substituted a strong forcing pump, and instead of the leather bellows, a metallic pump barrel, and piston.

This arrangement will be understood by fig. 84, where the pump barrel, a, b, is represented as divided lengthwise, in order to shew the inside. The piston ć, is fitted so accurately to the barrel, as to work up and down water tight; both barrel and piston being made of iron. The thing to be broken, or pressed, is laid on the flat surface i, there

being above this, a strong frame to meet the pressure, not shown in the figure. The small forcing pump, of which dis the piston, and h the lever by which it is worked, is also made

of iron.

Now suppose the space between the small piston and the large one, at w, to be filled with water, then, on forcing down the small piston, d, there will be a pressure against the large piston, c, the whole force of which will be in proportion as the aperture in which c works, is greater than that in which d works. If the piston d is half an inch in diameter, and the piston c, one foot in diameter, then the pressure on c will be 576 times greater than that on d. Therefore, if we suppose the pressure of the small piston to be one ton, the large piston

What is the hydrostatic bellows? What property of water is this instrument designed to show? Explain fig. 84. Where is the piston? Which is the pump barrel, in which it works? In the hydrostatic press, what is the proportion between the pressure given by the small piston, and the force exerted on the large one?