Uniform Flow of Water in Alluvial Channels.

Abstract

The flow of water in canals and rivers in alluvial beds is analysed, and it is shown that the uniform flow of water in alluvial channels is of two types: (1) where bed material is not inm ovement and (2) where bedm aterial is in movement. It is shown that for (1) friction varies directly as velocity and Chezy's formula can be written as V=cRS. For (2) friction varies as the square of velocity and Chezy's formula retains its old form V= Cd/RSc; and C are constants for the particular type of bed material and are dependent on the coefficient of friction found by Froude from his experiments. The formulae V= cRS and V= Cd/RS are shown to be dimensionally correct. A formula for silt transportation iasr rived at tof ind out what maximum silt charge can be carried at a velocity. This formula is also shown to be dimensionally correct. The Froude coefficient of friction is correlated with diameter of bed material so that the values of c and C can be obtained from the average weighted mean diameter of bed material in millimeters. It is also suggested that a channel is stable when the velocity required to overcome friction equals the velocity required to transport suspended silt. The word silt used in the paper refers to inorganic matter carried by water either as bed load or in suspension.