| Steep rocky hillsides | ·70 | to | ·90 |
| Ordinary hills | ·50 | ” | 75 |
| Undulating country | ·40 | ” | ·50 |
| Flat country | ·30 | ” | ·35 |
The figures can be increased when the surface is specially hard or frozen, and decreased when it is soft, sandy, covered with woods or vegetation, or cultivated.
Whether or not the above procedure is necessary in its entirety depends chiefly on the size of the proposed work and on the degree of inconvenience likely to arise from any wrong estimation of the discharge.
In designing syphons to carry torrents across the Upper Jhelum Canal in the Punjab, the discharge from a catchment area of ·79 square miles was found to be about 4000 cubic feet per second. This is at the rate of about 5000 cubic feet per second per square mile, and is equivalent to a run-off of 7·8 inches in an hour. The catchment area was among low hills, not far from the Himalayas, and the declivities of the rills were very steep. The superintending engineer, Mr R. E. Purves, states[18] that the discharge observations were reliable, and that falls of rain of an inch in ten minutes occur not infrequently, even though the fall in twenty-four hours might not exceed 2 or 3 inches. In order to account for the discharge in the case under consideration, it would at first seem to be necessary to assume not only that a fall at the rate of 7·8 inches per hour had occurred, but that the whole of it had run off. It is not, however, necessary to assume quite so much. The ground being saturated, the rain falling in a period of five minutes might be reaching the discharge site with little loss. A suddenly increased fall at the rate of 6 inches per hour might then occur, and the water travelling more quickly and with hardly any loss, would overtake that already passing the site. This case seems to show that for a very small catchment area the whole of the fall, and more, must be allowed for.
The Chief Engineer of the Punjab did not accept the above figures.[19] He remarked that observations taken under great difficulties as to time and place are liable to error, and he considered that an allowance of rainfall at the rate of 4·8 inches per hour—a rate which had been observed elsewhere—and a run-off of ·75 of the fall would be sufficient. He accepted a discharge of 2000 cubic feet per second for catchment areas of less than 5 square miles, assuming the run-off to be ·75 of the fall, but afterwards increased the figure to 2400 cubic feet per second. The chief engineer did not overlook the fact that in the designs for the drainage aqueducts a free-board of 5 feet had been allowed, and perhaps this led to an acceptance of an estimated discharge less than would otherwise have been accepted. It does not seem to be at all certain that the figure put forward by Mr Purves was far wrong. When the original project estimate for the Upper Jhelum Canal was framed, the irrigation engineers had had no experience of small and steep catchments, and no one had suspected that the discharge per square mile would be anything like the above. The sums of money provided for works for the passages of torrents had to be increased in ratios varying from 2·5 to 1 to 6 to 1.
The following statement shows the figures for other small catchment areas in the neighbourhood of the Upper Jhelum Canal:—
| Catchment Area. | Discharge per square mile. | Run-off. |
|---|---|---|
| Sq. miles. | Cub. ft. per sec. | Inches. |
| .79 | 5000 | 7·8 |
| 1·47 | 3825 | 5·82 |
| 2·96 | 2214 | 3·46 |
In the south-east of New South Wales flood discharges of 135 and 84 cubic feet per second have been found for catchment areas of ·91 and 2·5 square miles respectively in broken country.
3. Rivers.—It is possible to apply the methods of the preceding article to large catchment areas, but the results would be quite unreliable. If the calculations were made so as to err on the side of safety, the resulting discharges would often be enormous. The following table shows some figures based on actual flood discharges. None of the localities have excessive rainfalls, though most are liable to occasional very heavy falls. In mountainous districts in the North of England and in Scotland the flood discharges per square mile of catchment area have been found to vary from 64 to 320 cubic feet per second.
| Reference Number. | Country. | Locality. | Catchment Area. | Flood Discharge per sq. mile of Catchment Area. | Remarks. |
|---|---|---|---|---|---|
| Sq. miles | Cub. ft. | ||||
| 1 | India. | Upper Jhelum. | 5 to 10 | 1613 | |
| 2 | ” | Nagpur. | 6·6 | 480 | |
| 3 | South Africa. | Near Cape Town. | 34·5 | 78 | |
| 4 | ” | Near Port Elizabeth. | 35 | 640 | Estimated. |
| 5 | New South Wales. | South-East District. | 49 | 37 | |
| 6 | India. | Upper Jhelum. | 56 | 1000 | |
| 7 | ” | ” | 174 | 550 | |
| 8 | New South Wales. | South-East District. | 418 | 11·2 | |
| 9 | India. | Kali Nadi Stream. | 2593 | 51 or more | Estimated roughly. |