406 WATEK-SUPPLY formula Q = 62.15 A (i R - E), where Q is the daily supply in gallons, A is the catchment area in acres, R is the average annual rainfall and E the loss from evaporation, both in inches. 1 The storage capacity must be regulated by the number of consecutive days, in time of drought, that the supply might have to be drawn from the reservoir without its receiving any accession of water. This period has been variously estimated at from 70 to 300 days according to the locality ; for, owing to the smaller fluctua tions in the rainfall and in the periods of drought in very rainy districts, and the less amount of evaporation, a much smaller storage suffices for very wet districts than for very dry ones. Storage Reservoirs. Where no natural lake is available for a reservoir, an artificial lake may be formed by con structing a dam across a narrow gorge of a mountainous valley, thereby impounding, in the winter, the stream draining the valley, and storing up a supply for the following summer. To prevent an escape of the water thus impounded, the reservoir must be formed on an impervious stratum, and all cracks and fissures closed, or the bed and banks must be rendered watertight by a surface layer of impervious material. Occasionally the configuration of the ground and the amount of storage re quired render it neces sary to form a series of impounding reservoirs at different levels along a valley, thereby in creasing the number, but keeping down the height of the dams. For instance, in supplying Manchester from the Long- dendale valley, six large reservoirs, having a total area of 497 acres, and a capacity of 4160 million gallons, were formed in steps by dams from 70 to 100 feet high (see AQUEDUCT, vol. ii. p. 224). RESERVOIR DAMS. The capacity of a reservoir depends upon the form and levels of the valley in which it is situated, and the height of the dam retaining it. As, however, the extent of the water surface is considerably increased by raising the water-level, an additional height of dam adds largely to the capacity of a reservoir. Thus Thirlmere, with an existing maximum depth of 108 feet, will have its area increased from 350 to 800 acres by raising the barrier at its outlet 50 feet. Accordingly, dams of considerable height are sometimes erected : as, for instance, the Entwistle embankment of the Bolton waterworks, retaining a reservoir 120 feet deep, the Villar dam, for the supply of Madrid, founded 158^ feet below the water-level of its reservoir (fig. 7), and the Furens dam, near St Etienne, with a height of 164 feet at the water-level (fig. 5) ; whilst the Gileppe dam, near Verviers, was made 147f feet high (fig. 6) in preference to four dams of 95 feet. A reservoir dam is constructed either with earthwork in an embankment sloped on each side, and with a water tight puddle or concrete trench along the centre, or of masonry. Earthwork embankments have, till within the last three or four years, been exclusively adopted in Great Britain ; whilst masonry dams have been long ago con structed in Spain, and more recently introduced into France. Earthen Embankments. In moist climates, and for moderate heights, embankments of earth are adopted with advantage for reservoir dams, more especially when ample materials can be readily obtained, either by excavations in the reservoir, thus enlarging its capacity, or elsewhere 1 Theory and Practice of Hydro- Mechanics, lust. C. E., p. 44. near at hand, and where a rock foundation is not easily attainable. All loose material must be removed from the site of the dam ; and the puddle trench in the centre must be carried down to a solid impervious bed (fig. 3). The embankment must be brought up in thin layers carefully so Scale to Figs.3 & 4. 100 FEET, FIG. 3. Nethcrtrees Reservoir Embankment, Paisley. punned or rolled, the most retentive materials being placed near the middle, and the looser materials towards the outside. The inner slope, facing the reservoir, is usually made 3 to 1, and pitched on the surface to protect it from the wash of the waves. The outer slope is formed to the angle of stability of the material employed, generally 2 to 1 ; and occasionally berms are introduced, diminish ing the liability to slips (fig. 4). The best puddled clay is used for the central trench ; but the remainder of the embankment should not be composed exclusively of clay, ^f^^P|^^^^^f^^W^|iF FIG. 4. Gladhouse Reservoir Embankment, Edinburgh. as stiff clay under the influence of the weather, especially on the exposed outer slope, tends to slip. An earthen dam possesses ample stability if it is perfectly solid ; but it may fail from the infiltration of water through it, owing to faulty construction, or from settlement, leading to its overtopping by the water in the reservoir. Masonry Dams. In hot dry countries, an earthen embankment is liable to crack and become somewhat dis integrated ; and high embankments, owing to their flat side slopes, require a very large amount of material. Accordingly, in Spain, masonry dams have been adopted; and they are preferable to earthen dams when the height exceeds about 80 feet, and where a rock foundation can be secured. The Spanish masonry dam of Puentes (Lorca), 164 feet high, was indeed built upon piles; but it was eventually undermined, and settled ; and the outburst of the water from the reservoir on its failure in 1802 caused the loss of 608 lives. Besides a solid rock founda tion, the conditions of stability of a masonry dam are that the maximum pressure shall not exceed the limit that the masonry can sustain without injury, and that the lines of resultant pressures, with the reservoir empty and full, shall not anywhere pass outside the middle third of the section of the dam, so as to prevent the possibility of tension at the faces. With the reservoir empty, the pres sures on the dam are merely those due to its weight ; and the line of resultant pressures is the locus of the points of intersection of the verticals from the centres of gravities of the several portions of the dam above a series of horizontal lines, with the base lines of those portions (figs. 5 and 8). With the reservoir full, the water exerts a horizontal thrust against the inner face of the dam, equal to the weight of a column of water having the depth of the water resting against the dam, and acting at the centre of pressure, which is at two-thirds of the depth down from the water-level. The line of resultant pressures, in this case, is the locus of the points obtained by the intersection
of the resultant lines of the pressures of the masonry and