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driven 10 ft. into the clay, and sheeting of 3-in. planks is fixed to the piles by-in. bolts. On the lee side this sheeting is supported by 9-in. by 6-in. struts. The groins are generally 100 yds. in length and 200 yds. apart, and cost about £5 per yard-run. The bank of shingle that is formed by these groins makes a complete protection to the shore, which had become very dangerous, owing to the constant removal of shingle. Groins should not be

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built above high-water level of spring tides, or they will only cause excessive wave action and erosion.

"Various efforts have been made in East Anglia to deal with coast erosion in some definite united way, but up to the present in vain. Each locality acts on its own devices, but the erosion is yearly becoming so serious that it is hoped the Board of Trade may see its way to bring the matter before Parliament, and create some 'Coast Guarding' commission in a true sense of the word."

Figs. 506D and 506E give further details.

CHAPTER XXII.

HYDRAULICS.

THE term Hydraulics is the name given to that branch of study which affects the engineer's practice concerning the behaviour of liquids. It includes hydrostatics, the behaviour of water in a state of rest, and hydromechanics, water in motion. It is very important that every engineer should most thoroughly understand this branch of his studies; and with the excellent literature, both British and foreign, now published, he should find no difficulty in obtaining that knowledge. The only thing which may puzzle him is to decide which is the best of the many excellent treatises. Of course the present chapter does not intend to be an exhaustive treatment of the subject, but more a practical guide to the more everyday problems of the flow of water, and as an introduction to the remaining chapters of the book, which all more or less concern the flow of water.

A fluid is a body which offers no permanent resistance to change of shape. This is important.

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The most important law in hydraulics is that of Pascal, which states that "fluids transmit pressure equally in all directions, and any increase of pressure at one point of a liquid is at once transmitted to every other point." Take fig. 507, a vessel having pistons held by light springs, and assumed to be quite devoid of friction. Say one of them is 1 sq. in. in sectional area, and it has a load of 10 lbs. on it. All the others will at once be subject to a pressure of 10 lbs. per sq. in. if they are on the same level. If not, of course the extra weight of the water will make a difference. Now everyone knows that water finds its own level. This is because pressures at two points in the same horizontal plane are equal. Upon this law depends the phenomena of suction, which is really balancing the air pressure. For instance, take the ordinary mercurial barometer in which the mercury will stand to a certain height, about 30 in., due to atmospheric pressure.

Again, a body when immersed in a liquid is buoyed up by a pressure equal to the weight of the liquid displaced by the body. This is the principle of Archimedes. It is for this reason that we can obtain the volume and density of a body by weighing in air and water (see Testing Road Stones).

A gas differs from a liquid in the lesser extension of its particles, and a gas is very compressible, and liquids practically incompressible. That is the difference between them. Gases also have very little weight, but the common idea that they have none is quite erroneous. For instance, the barometer will fall, according to its height above sea-level, approximately 1 in. for every 1000 ft. Now when water is at rest it comes to a level surface. This is called the free surface. As we go down below it, so the pressure exerted by

the potential energy of the liquid gets greater. It is called the head, and is the actual pressure in excess of that of the atmosphere. Now if water has a head of 1 foot, the corresponding pressure which it will exert is 434 lb. per sq. in. For comparison, 1 in. of mercury exerts a pressure of 491 lb. per sq. in.

Now when we measure down from the free surface, a distance the weight of water per cubic foot 62.5 lbs. Then p square foot

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= wh

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=

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h and w

pressure per

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total pressure on that surface.

This, of course, applies to level surfaces, and in horizontal surfaces the centre of pressure or point where the pressure is concentrated coincides with the centre of gravity. When the surface is vertical or sloping the conditions become changed. We consider the pressure as a uniformly varying stress, 鳳

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and its intensity at any given point varies as the distance of that point from the water surface, always measured in a line with the plane of the surface under consideration. Then consider fig. 508. A plane surface is immersed in water. It is inclined at an angle 0 to the horizontal. Take any strip dxx= distance from C of G of this strip to the surface. w=62 lbs. for water.

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Then obviously the intensity of pressure (the mean over the whole surface)

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and the distance of centre of pressure from this surface

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(277)

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For the reasons stated respecting the resistance of a liquid to change of shape, we find that in any fluid the internal stress will be normal; on the other hand, in a solid body it may be normal, oblique, or shearing. Before going to the more practical and everyday side of the problem we must first investigate the theory of Hydraulics. The first point is the principle of continuity of flow. That is to say, if v = velocity in any tube, a = a sectional area, then Q the quantity of fluid passed

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Now we have already spoken of head in reference to water. have water under a given pressure, and it be allowed to flow quite unrestrained, it will do so with considerable velocity according to the "head." If we know the head we can calculate this velocity. Let h head and v=

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velocity in

FIG. 509.

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FIG. 510.

ft. per second, g = 32·2 and is a formula for the effect of gravity upon falling bodies (vide text-books on Mechanics). Then

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2g

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this quantity being known as the velocity head. These equations give us

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the unrestrained flow from such orifices, which is purely theoretical. Various coefficients of contraction, discharge velocity, etc., have to be considered, and they are exactly what we are going to consider; but at the same time the reader should bear in mind that upon the relations between head and velocity all problems relating to the flow of water depend.

Now probably the most important practical hydraulic calculation an engineer will have to make is that of gauging the flow of small streams for water supply and power purposes. Take any rectangular channel, as in fig. 509; in the centre we shall have decidedly more velocity than at the sides. Say the flow at the centre was 5 ft. per second. Then at the sides we may reasonably expect a flow of 3 ft. per second, and at intermediate points 4 ft., etc., as shown on the diagram. Now take the mill lade in fig. 510, in which, by means of a current meter, we have found the several velocities as tabulated below in feet per minute, the letters in the diagram referring to corresponding letters and figures in the table. The areas between the contours must then be obtained preferably by a planimeter.

Then we want to find the simplest way of calculating the mean velocities

between two contours.

To do so add the velocities of two contours and divide by 2. For instance, say the velocity at A was 280 ft. per minute and at B 270. The mean velocity between the two contours will therefore be 270+280 ÷ 2 = 275 ft., and the quantity flowing in this section will be 275 × * 12.413412.75 cub. ft. per minute. The mean velocity between B and C is 265 ft., and the corresponding quantity flowing will be 9757.3 cub. ft. per minute. Therefore the total quantity flowing will be found by calculating the velocity and quantity between each two contours, and adding together the quantities thus found.

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This is the manner in which streams and rivers of considerable quantity are measured, and where a gauge would be inconvenient.

The current meters which are used, of course, vary in form. Some register on dials which are an integral part of the gauges, others have means of electrical contact with the surface. Of the former type, the Moore, Revy, and Woltman meters are examples, and of the latter, Harlacter's and Deacon's. It is most essential that they be very exactly calibrated by experiment, and equations and coefficients not relied upon.

Frequent observations are necessary at different points, both vertically and horizontally. At the same time the variations of water surface-level must be very carefully noted. We can then plot the discharge rates at various levels. These diagrams are useful to the engineer who has automatic float gauges. Of course accumulations of weeds will impede the use of current meters. Submerged floats have then to be resorted to. Quite the simplest and most effective form is the rod float, made out of a rod of wood. They have a cork at the top and a lead weight at the bottom; they should be in length equal to from 90-94 of the average depth of the stream in question. In all cases, however, the cross section of the stream must be very accurately obtained by sounding and levelling. The sounding, of course, has to be done from a boat. This may be kept in position by a line from the shore where there is no traffic on the stream, or if this is impracticable, by taking observations to three points on the shore by means of a theodolite, and plotting the angles so found on paper, from which, if the points are also plotted in their exact positions on the paper, the boat's position at any observation can be found. The current meters would be, if possible, suspended from a bridge. If not, two poles with a strong steel wire joining them would be resorted to. Along this wire, by means of an accurately made winch, the meter could be made to travel to any position. A counter on the winch would give the distance out on the stream the gauge was. Regarding the velocity, it must not be supposed that it will be constant at all depths any more than at all points on a horizontal section.

* 12.4 = the sectional area in square feet of the stream at this section.

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