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HYDRAULICS.

Hydraulics (from two Greek words, hudor, water, and aulos, a pipe) properly treats of the flow of water through pipes; but it is usual in hydraulics to treat of the motion of liquids generally-of the flow of water in rivers and canals, of its waves, and of the resistance experienced by bodies in moving through it. Other liquids obey the same laws as water

If a vessel be filled with water, and holes made in it at different distances from the surface of the liquid, as shown in Fig. 1, the water will gush out of these holes with different velocities; the velocity of the escaping liquid at B is greater than at A, and at C greater than at B. The following law holds when water escapes from an orifice its velocity is the same as that which a body would acquire in falling through a space equal to the height of the surface of the water above the centre of the orifice. Thus the velocity of the water escaping at A is the same as that of a body having fallen from D to A; its velocity from B is the same as that of a body having fallen from D to B, and so on.

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FIG. 1.

We can show the truth of this law by an experiment. Fill a vessel with water to the height A (Fig. 2), having an orifice, E, opening upwards. If the principle hold, the jet should rise to A, the height of the surface of the water in the vessel; for we know from what we learnt on falling bodies, that if the particles of water be projected from B with

B

FIG. 2

a velocity equal to that which a body would acquire in falling from A to B, they will rise to A. Well, on making the experiment, the reader will find that the jet falls a little short of A, but nothing more than can be accounted for by the friction of the water against the sides of the tube, the obstruction of bends, and the resistance of the air: but for these the jet would rise to A, and thus completely verify the principle. By a proper arrangement a jet of 9 in. may be got from a column of water 10 in. high. On this principle artificial fountains are constructed.

We learnt from an experiment on Atwood's machine that a body in falling freely from a state of rest through a space of 16 ft. acquires a velocity of 32 ft. per second; therefore if A B be 16 ft., the velocity of the water escaping from B will be 32 ft. per second; if A B be 4 ft., the velocity will be 16 ft. per second; and if A B be I ft., the velocity will be 8 ft. per second. From this it is seen that the velocity varies as the square root of the height of the surface of the water above the orifice. The rule for finding the velocity in any case is to take the square root of the height of the surface above the centre of the orifice, and multiply the result by 8.

If you fill a vessel, A (Fig. 3), with water, and allow it to discharge itself from an orifice in the bottom, the velocity of the escaping liquid will continually

diminish as the depth of water in the vessel becomes less. If the vessel were kept full by pouring in water at the top, then, of course, the velocity would continue the same. The following is an instructive experiment on this point

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Fill the vessel, A, with water, and allow it to quite empty itself from an orifice in the bottom; say it takes five minutes to do so. Fill the vessel again and allow it to run for five minutes, but this time keep it constantly full by pouring in water at the top: it will be found to discharge twice the full of the vessel during these five minutes.

This experiment exactly agrees with what we learnt on falling bodies: that when a body falls under the influence of gravity, the space that it describes in any time is only half as much as it would have been had the velocity all through the descent been the same as it is at the end of the time.

In performing the last experiment we must have noticed that the section of the escaping liquid becomes less after leaving the orifice. This arises from the particles of water crossing and interfering with one another on rushing in from all directions towards the orifice. This narrow part, C, shown in the figure, is called the vena contracta, or" contracted vein;" the narrowest part is at a distance from the orifice equal to about half its diameter, the diameter of that part being about two-thirds that of the orifice.

Since we can find the velocity with which water escapes from an aperture in a vessel, it would occur to our readers that we should be able to tell the quantity of water that would be discharged by an orifice in a given time. And so we can. Suppose the orifice to be I square inch, and that the water escapes with a velocity of 12 ft. per second, that is, 144 in. per second, then will 144 cubic inches of water flow out every second, that is, 8,640 cubic inches, or rather more than 31 gallons, per minute. But it is found in practice, or on making the experiment, that the actual flow from an orifice is only about twothirds of the quantity thus calculated. The diminution arises from the same cause as the contracted vein.

If, instead of allowing the water to flow from a mere hole in a thin bottom, a short pipe is used of a length equal to twice the diameter of the orifice, the discharge is increased: such a pipe increases the flow from being two-thirds of the calculated amount to be four-fifths of that amount, and if the pipe be made funnel-shaped at both ends, the discharge will still be increased. The reason why a short pipe increases the flow seems to be that the sides of the pipe attract the particles of water, thus widening the column, and causing a partial vacuum, which acts as a suckage on the water in the vessel. When water spouts from

an orifice in the side of a vessel, it follows the same law as a projectile, and describes what is called a parabola; for it is acted on by two forces-the forces of projection and gravity. To find the horizontal range, we describe a semicircle (S E X) on the depth, as in Fig. 4; from the centre of any orifice we draw a horizontal line to meet the circumference: twice the length of this line is the horizontal range from that orifice. Since B E, drawn from the middle point of the depth, is the longest of these lines that can be drawn, it follows that the water will spout farthest from that point; from orifices A and c, equally distant from the middle point, the horizontal range will be the same as is seen in the figure.

The surface of water at rest is always horizontal, meaning by this that every part of its surface is equally distant from the earth's centre. This is usually expressed by saying that water always tends to find its own level. Thus, if two vessels, A and B, be connected at the bottom, as in Fig. 5, when water is poured into one it will rise to the same height in both, however different the vessels be in size or shape.

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This property of liquids often enables a town to be supplied with water from a hill at a distance, though a valley and uneven grounds lie between; for water, when confined in a pipe, will rise to the same height as its source. Fig. 6 shows water conducted by a pipe from a lake (S) on a hill, through a valley, to a house situate on a rising ground. This property of liquids was not unknown to the ancients, for Pliny distinctly says that "water ascends in a pipe to the height of its source." However, they did not avail themselves of the property, probably from want of the material and means of construct ing the necessary apparatus. Their mode of conducting water from one place to another was by open channels called aqueducts, either cut in the level ground, or supported on arches when necessary: such structures cost great labour and expense.

When water is thus conveyed through pipes of any considerable length, the friction against the sides is so great, that in practice it is found necessary to allow them one-third or one-fourth more diameter than would be necessary to convey the same quantity of water if there were no friction. A pipe 30 ft. long and 13 in. in bore, only delivers half the quantity of water that it ought to do, theoretically considered. A great gain in the flow is secured by increasing the capacity of the tube; thus a tube 2 in. in diameter would deliver five times as

"Aqua in plumbo subit altitudinem extortûs sui."-Plin., Nat. Hist., 31, vi. 31.

much water as a tube I in. in diameter, although its section is only four times as great.

The quicker the flow of water through a pipe the less it presses against the sides; this explains why water-pipes often burst when choked or stopped in any way. If water in flowing through a pipe met with no retardation, but had the velocity due to the height of its source, then it would exert no lateral pressure, so that if a hole were made in the pipe, no water would spout out; and if the pipe be short, so that the velocity of the water is greater than if no pipe were used, there is then not only no outward pressure against the sides of the pipe, but the opposite, namely, a pressure exerted in an inward direction. This is readily illustrated by the following experiment. In an orifice near

FIG. 7.

the bottom of a vessel (Fig. 7) insert a cylindrical pipe of a length equal to three or four times the diameter of the orifice; in the upper side of this pipe insert a small bent tube, which dips into a vessel underneath filled with water, as shown in the figure. Now, when the water is allowed to flow from the pipe, A, liquid will rise in the tube, CB; and if this be not too long, the vessel, D, will be exhausted of its water, which will rise in the tube, C B, and flow out at A. The experiment is made clearer by colouring the water in the vessel, D.

Venturi, availing himself of this principle, employed the lateral draught of a mill-race near Modena to drain a marsh situated at a lower level. It is also employed in the circulating system of animals: a current of blood passing along one vessel may assist in emptying a lateral branch, or two currents entering a large trunk at the same part may drain a small one lying between them. In rivers, the friction of water against solids is readily observed. The velocity of the water is least at the bottom of the current, where the friction is greatest; for the same reason the velocity at the sides is less than in the middle of the stream. The water in rapid motion in the middle draws the water at the sides after it, and this causes the river to be somewhat raised in the centre. The velocity of a stream may be practically determined by throwing into it pieces of turnip or other body of the same specific weight as water, and noting the mean time required to pass through a known distance.

When the velocity of the stream is known, the number of cubic feet of water that it discharges per minute is at once found by multiplying the sectional area of the stream expressed in square feet by its velocity in feet per minute. When a pebble is dropped into a still piece of water, a series of small waves is transmitted from the point of disturbance in widening circles; the size of these continually diminishes, and the motion is finally overcome from the imperfect mobility and friction of the fluid. It is merely motion that is transmitted from one part of the liquid to another, and not water that is carried onwards. We may satisfy ourselves of the truth of this by dropping a cork on the surface of water through which waves are passing; the cork will be seen merely to move up and down, and not to advance with the waves. These undulations can be well observed by dropping a glass bead into a basin of mercury.

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Water offers considerable resistance to bodies moving through it, but the amount depends much on the shape of the body. The surfaces ought to be oblique to the direction of the motion; thus, when a cylinder is moved through water end foremost, if the end be terminated in a hemisphere the resistance is only one-half of what it would be if the end were a plane perpendicular to the axis; and if the termination be an equilateral cone, the resistance is re duced to one-fourth. When the speed of a body moving through water is doubled, the resistance is made four times as great, for the body has to displace twice the number of particles, and also to displace them with twice the velocity; if the speed be made three times as great, then the resistance becomes nine times as great, and so on. A good deal of resistance is due to a vacuum being formed in the water behind the moving body, thus causing it to be subjected to a hydrostatic force in front pressing backwards. The sooner and more easily this is filled up, the more is the force in front counteracted; hence, the bow and the stern of a ship being unchanged, the longer the body is, within certain limits, the less is the resistance.

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We now come to speak of water as a motive power. Here is a tube (Fig. 8) filled with water and suspended by a string. Let us fix our attention on any two points, C and D, on opposite sides of the tube. The pressure of the column of water, A B, is transmitted equally to C and D; thus these points experience equal pressures, but opposite in direction. Now make a hole at C, so that the water may be free to gush out: the tube at once moves in the opposite direction! Why? Simply pecause the pressure has been removed from the point C and continues at D, hence the motion.

On this principle is founded Barker's Mill. The following experiment beautifully illustrates its mode of action: into the end of a large tube, A B, a cork is inserted; to this is fitted two small tubes, C and D, bent as in the figure. When the whole is suspended from the ceiling and water poured into the large tube, a rapid rotatory motion commences. For, as was shown above, the current escaping from C gives the tube a tendency to move in the opposite direc

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