The head needed at a bifurcation in order to get the supply into a branch or distributary is always small unless the velocity is high. For a velocity of 3 feet per second the head required is only about ·16 ft., for 2 ft. per second ·1 ft.
On an Inundation Canal which has no weir across the river, the mean supply downstream of the regulator (which is built a few miles down the canal lest it should be damaged by the shifting of the river) is, as has been mentioned, about half the full supply. The command in such canals is not generally very good. A distributary can often obtain only mean supply and it should be designed so as to command the country when it is carrying mean supply. A detailed description of Inundation Canals in Northern India, is given in _Punjab Rivers and Works_.
Let M, F, m, f, be the mean and full supply discharges at the heads of a canal and of an average distributary on it and let the number of distributaries be n. It has been seen (Chap. I. Art. 6.) that M = ·8F about. Let k be the proportion of the supply lost by absorption in canal and branches. Then n m = (1 - k) M = ·8 (1 - k) F. If the distributaries all run with full supplies--at the time of greatest demand--for 4 days out of 5, then,
Since k depends on the wetted area, it is not likely to be so great for F as for M, but the above gives a general idea of the ratio of the full kharif discharge to the mean kharif discharge. On a large canal the circumstances of the distributaries will not all be similar. Some will run full for a greater proportion of their time than others. They can be divided into groups and the ratio of the full to the mean supply calculated for each group. The mean supply is, as above stated, obtained from the area to be irrigated, and the duty as estimated at the distributary head.
At one time a system was introduced of making distributaries of large size with the idea of running them for short periods. One reason given for abandoning this arrangement, was that there was a tendency to run such a distributary for too long. This reason is not very intelligible. It would be applicable to any distributary which was not intended to be run without cessation. The result would be that some other distributary would be kept short of water and this would imply extremely bad management. The chief reason against such a distributary is the greater cost of its construction. It would effect a saving of water. The ratio of the discharge to the wetted area would be high, though this would be to some extent neutralized by the greater frequency of closures, since, when water is admitted to a dry channel, the absorption is at first great. There would also be some difficulty in the distribution of the water because of the short period for which it would remain open. It will be seen (Chapter III. Art. 5), that it is desirable to open and close always at the same hour of the day. An ordinary distributary might run for 11 days out of 14. One of double the size could not conveniently be run for 5¹⁄₂ days. A distributary can always be enlarged if necessary, but if made too large it is extremely difficult to make it smaller.