River and Canal Engineering, the characteristics of open flowing streams, and the principles and methods to be followed in dealing with them.

by E. S. Bellasis

A masonry dam may act as its own waste weir, the flood water flowing over the crest and down the rear slope; but in cases where heavy floods are liable to occur it is usual to provide a separate waste weir by cutting away the side of the gorge either close to the dam or at some other place.

While a dam is in course of construction arrangements must be made to deal with flood water. Generally the construction of some part of the dam has to be deferred to let the water pass. In the case of a masonry dam it does not much matter what part is thus deferred provided the usual procedure of stepping the work back is followed. In the case of an earthen dam it is best to defer a portion, not in the lowest ground where the dam is highest, but to one side of it, thus allowing the highest part of the dam to be brought up continuously. Temporary embankments and weirs can be constructed to cause the water to traverse the desired route without doing damage. Stepping of the earthwork should be avoided as far as possible. If it has to be adopted, the steps should be small. Sometimes the flood water is conveyed away by means of a “by-wash,” by an entirely different route.

Fig. 57.

In Indian reservoirs the discharge over the waste weir may at times be great. The waste weir is sometimes in the position shown in [fig. 57], a e being the weir. In such a case a special hydraulic problem arises. In a case where a stream whose velocity is V issues from a reservoir or takes off at right angles from a larger stream there is (Hydraulics, Chap. II., Arts. 19 and 20) a fall in the water of about V²/2g. The same thing occurs downstream of a weir, at least when there is a clear fall which is vertical or nearly so, so that the water after falling has no horizontal velocity. The water has to be started afresh on its course. In the case represented by the figure, the width of the channel is often restricted because of high ground beyond f, and the velocity in the channel may be very high. Suppose the channel below e f to be of brickwork with vertical sides, and to have a 20-foot bed, a slope of 1 in 500, and a depth of water of 10 feet. The velocity may be 15 feet per second, and V²/2g is 3·49 feet. If the water has a clear fall over the weir at e, allowance must be made for a depth of water of 13·49 feet, not 10 feet, in the channel at e. Ordinarily the length a e will be much greater, relatively to e f, than shown in the figure. Suppose that a e is 300 feet and that the slope of the floor of the channel is carried on at 1 in 500 from e f up to a, b, c, and d, following in each case the lines marked on the figure which represent the directions of flow. The length f a will be about 310 feet, and the floor level at a will be about ·62 feet higher than at e f. The water-levels below the weir will be in each case 13·49 feet above the floor. This should be allowed for in the design. It is true that the stream on first starting into horizontal motion below the weir moves more or less at right angles to it, and has thus a large sectional area and a low velocity; but it very soon has to turn parallel to the weir and acquire the full velocity of 15 feet per second, and there must be the requisite extra head to give this velocity. If the weir is drowned, the water on passing over it may have a high horizontal velocity, but it will be at right angles to the axis of the channel, and its effect will be wasted in eddies.

2. Capacity of Reservoirs.—A reservoir depends for its supply on the yield of a particular valley or valleys which form its catchment area, and the capacity of the reservoir or reservoirs can be altered by altering the height or number of the dams. The need for a reservoir is entirely owing to the inequality in the distribution of the rainfall. If the rain fell in equal quantities week by week, the daily fluctuations could probably be equalised by the service reservoirs. The impounding reservoir could be quite small. Actually, a reservoir is needed to “equalise” the flow—that is, to give a steady flow for an intermittent one. The smaller the reservoir, the sooner it will go dry in a drought and the sooner it will overflow in wet weather and cause waste of the water. In other words, the larger the reservoir the better it will fulfil its function of equalising the flow and the greater the degree to which the catchment area will be utilised.

Fig. 58.

In the British Isles the distribution of the rainfall which is most trying for a reservoir, occurs when the rain is heavy during the winter and very light in summer. Fig. 58 shows a diagram for a reservoir in the driest year, when the rainfall is ([Chap. II., Art. 1]) ·63 of the mean annual fall. The distribution of the fall is supposed to be unfavourable as just described. The lower part of the figure shows the water-level at the end of each month, the reservoir being supposed to have vertical sides so that the quantity of water in it is proportional to the depth of water. The upper part of the figure shows the water impounded (available fall multiplied by area of catchment) in full lines, and the consumption in a dotted line. The distance between the two lines in any month is the same as the rise or fall of the reservoir in that month. There is supposed to be no overflow, and the total consumption of water in the year is equal to the quantity impounded in the year, so that the levels of the reservoir water surface on 1st January and 31st December, as shown by the horizontal lines A, B at the left and right of the figure, are the same. Deacon, who has investigated the subject, has found (Ency. Brit., Tenth Edition, vol. 33, “Water Supply”) that, in order to satisfy the above conditions, the capacity of the reservoir must be 30 per cent. of the water impounded during the year, or about 110 days’ consumption. On 1st January the reservoir must be about two-thirds full. At the end of February it is ready to overflow. At the end of August it is just becoming dry. The daily consumption is supposed to be steady throughout the year.

As an instance, suppose the catchment area to be 1000 acres, the mean annual fall 60 inches, with a loss from evaporation and absorption of 14 inches. The available rainfall of the year is (see last column of table below) 23·8 inches, or 1·983̇ feet. The water impounded and consumed during the year is 1000 × 43,560 × 1·983̇ × 6·25 = 539,962,000 gallons. The reservoir capacity must be 3/10ths of this, or 161,988,600 gallons. This is represented by the height C E. If the mean available rainfall in January and February is 6·3 inches, or ·525 feet, the water impounded during those months is 1000 × 43,560 × ·525 × 6·25 = 143,931,000 gallons, and the consumption is 539,962,000/6 = 89,993,667 gallons. The difference, 53,937,333 gallons, represents the addition A C, to the reservoir. Similarly, the light summer rainfall causes the depletion A E, and the heavy rainfall in the last four months of the year the addition E B. If the height of the reservoir above A B were less than A C, there would be overflow at the end of February; and if the depth below A B were less than A E, the reservoir would go dry before the drought ended. If the capacity of the reservoir were increased either at the top or bottom, the cost would be increased and nothing would be gained. It is not meant that the highest and lowest levels of any reservoir designed as above would always, in the driest year, exactly correspond with the points of overflow and going dry, but they would do so nearly. Deacon states that such a reservoir would fail only once in fifty years, and then only for a short time.