RATIONAL FORMULA FOR PEAK RUN -OFF FROM CATCHMENT AND THEORIES FOR THE ASSESSMENT, IN RELATIONSHIP TO THE RAINFALL AND NATURE OF THE CATCHMENT.

From the old times to recent years, hydrological studies have been made and theories set forth which comprehend the effects of the characteristics of the catchment on run run off. In this connection attempts have also been made to establish the relationships between rainfall and the run off under various circumstances. Some elementary account of the rationale of these theories is given as depending upon the following major factors (1) Rainfall:-- Intensity, distribution in time and space and duration (2) Nature of the catchment:-- Area, shape, slope, permeability of the soil and vegetable cover and the initial state of wetness. As for as the relationship between intensity and spread of storm is concerned, it has so far deliberately eschewed any mention of the spread of the storm. Rainfall recording stations are points in the space and therefore the intensities recorded there are point intensities. Imagin of an area round a recording station, the intensity will be highest at the center and will gradually diminish as we go farther away from the centre, till at the fringes of the area covered by the storm, intensity will be zero. The larger the area considered the smaller will be the mean intensity. It is therefore logical to say that the mean intensity is some inverse function of the size of the area. In hydrological theories it is assumed that the spread of the storm is equal to the area of the catchment, therefore the area is to be taken to be the same as the area of the catchment however the effects of this assumption may lead to the errors which, on analysis have been found to about twelve percent. In conclusion the use of the empirical formula should be avoided. They are primitive and are safe only in the hands of the expert. The average designer who cannot rely so much in his intuition and the judgement should go by the rational procedure outlined above as based on the data for the rational treatment. Indeed for a terse treatment, the factors involved are complicated and recourse need be taken to such treatment only when very important structures are involved and the accurate data can be collected however in the case of small bridges the simple formula given may serve the purpose for calculating the peak run -off.