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

The tendency of the figures in column 5 of the table is to decrease as the catchment area increases. This tendency has long been known, and attempts have been made to found on it formulæ for calculating flood discharges. One such formula is Q = c M^¾ where Q is the flood discharge in cubic feet per second and M is the area of the catchment in square miles. The formula is roughly correct, c being a constant for catchment areas of not dissimilar characters and with rainfalls not differing much. But for other cases there is no knowing how c may vary, and this renders the formula practically useless. The author of another such formula quotes cases Nos. 5 and 8 in the above table, and the two cases mentioned at the end of Art. 2 as agreeing fairly well with the result of his formula. The tendency just mentioned is due to the fact that every river is composed of tributaries which have their own small catchment areas but are, when measured to the general outlet or point where the discharge is under consideration, of very different lengths, to the improbability of heavy rainfall occurring over all these small areas at such times as to cause the different flood waves to arrive simultaneously at the outlet, and to the facts that in the case of the longer tributaries the flood waves flatten out (Hydraulics, Chap. IX., Arts. 3 and 4) so as to arrive more gradually, and that, unless rain is also falling all along their courses, these longer tributaries undergo losses from evaporation and absorption. But occasionally it happens that the various flood waves do arrive at the outlet more or less simultaneously, and that the rainfall continues so long and is so widely distributed—though not necessarily of the same intensity as that which caused the flood—that the flood waves do not flatten out and that losses in the channels do not occur. Floods can thus vary to an extraordinary degree in severity, and formulæ are quite useless. This is why floods occur surpassing all previous records, as, for instance, the recent floods in Paris. However severe a flood may be, it can never be said that the maximum has, even probably, been attained unless it can be shown that the rainfall has been so heavy, so long continued, and so distributed that anything worse is not likely to occur.

The best method of estimating the flood discharge of a large perennial stream is to ascertain, by local inquiry, the height to which it is known to have risen, and to take cross-sections of the channel and calculate the discharge ([Chap. III., Arts. 4] and [5]). In designing works, allowance can be made for a flood exceeding any known before. This method applies also to a case in which a river is formed by the junction of two or more large tributaries. It is possible that the tributaries have not, within the memory of man, been in high flood simultaneously. If so, the chances of this occurring are no greater and no less than if the stream was composed merely of a number of small affluents. Remarks regarding intermittent streams are given in [Chap. III., Art. 7].

Since an acre contains 43,560 square feet, and a twelfth of this is 3630, it follows that a fall of 4 inches of rain, of which 1 inch runs off, in an hour, gives a discharge of 3630 cubic feet per hour, or about 1 cubic foot per second. This is 640 cubic feet per second for a square mile. The figures in column 5 of the above table show that the run-off was, in the cases quoted, generally far less than 1 inch. In case No. 4 it was 1 inch, and in case No. 2 it was ¾ inch.

In the case of the Kali Nadi (No. 9 in the table) an aqueduct to carry the Lower Ganges Canal over the stream was being designed. The flood discharge, estimated from the supposed flood-level and cross-section of the stream was (Min. Proc. Inst. C.E., vol. xcv.) 26,352 cubic feet per second. The discharge, estimated by assuming a fall of 6 inches of rain in twenty-four hours over the catchment area—then believed to be 3025 square miles—and a run-off of ·25 of the fall, was 114,950 cubic feet per second. This figure was rejected on the ground that the rainfall would not be continuous over so large an area as 3025 square miles. An allowance of 7 cubic feet per second per square mile was made and, a fresh survey having shown that the catchment area was only 2593 square miles, a discharge of 18,000 cubic feet per second was allowed for. The aqueduct was built, about the year 1875, with five arched spans of 35 feet each, the total area of the waterway being about 3000 square feet. The length of the piers and abutments was 212 feet, the width of the canal carried over the aqueduct being 192 feet. In 1884 the aqueduct was partly destroyed by a flood whose discharge was about 44,000 cubic feet per second. In July 1885 it was wholly destroyed by a flood whose discharge was estimated at 132,475 cubic feet per second, but was probably more. The discharge must have been more than 51 cubic feet per second per square mile. The aqueduct was rebuilt with a waterway of about 15,000 square feet. Below the aqueduct there was a bridge which had been standing for a hundred years. Its waterway was only 1146 square feet. It was not much damaged by the flood of 1884, but much of the water passed round it, breaking through the embanked roadway or pouring over it. It is understood that the bridge was destroyed by the flood of 1885.

This case shows the necessity for making every possible allowance in calculating flood discharges for important works. The smallness of the discharge, as calculated from the cross-section of the stream, was probably owing to its being dry when the survey was made, so that the velocity could not be observed, but it is probable that such a discharge as wrecked the aqueduct had never before passed down the stream.

4. Prediction of Floods.—At any place high up on the course of a stream, the occurrence of a flood can often be predicted when rain storms—often accompanied in the tropics by lightning—can be seen to be occurring towards the sources of the stream. For any station lower down the stream and for precise information in any case, the readings of gauges higher up the stream can be telegraphed. If the station is at a great distance from the gauge and if there is railway communication, the readings can be sent by post.

In order to be able to predict the time of the arrival of a flood at the lower station the reading of a gauge there, and also of that at the upper station, should be taken at frequent intervals. In the case of large rivers and distances of hundreds of miles, the interval may be six or even twelve hours, but in other cases it should be much less. If the readings are plotted, as in [fig. 56], oblique lines can be drawn to connect the saliences and depressions, and the time taken by each change can thus be readily seen. When the upper part of the stream is formed by two or more important tributaries there should be a gauge in each.

As to what constitutes a flood, the gauge diagram of a river ([fig. 56]) is generally such that a line can be sketched as shown dotted. The rises above this line are floods. The maximum flood discharge of a Northern Indian river is estimated roughly as being 100 times the low-water discharge. Leslie’s rule for floods in the British Isles is that if all the daily discharges of a stream during the year are ranged in order of magnitude, the discharges of the upper quarter are considered to be floods.

Fig. 56.