Estimating the cross-sectional mean velocity in natural channels by the entropy approach

The applicability of the linear relationship between the mean flow velocity and the maximum flow velocity, based on the entropy concept (Chiu, 1991), is investigated using the data collected during 20 years in three gauged river sections in the upper Tiber River basin in Central Italy. The error in estimating the cross-sectional mean velocity from the observed maximum velocity is analyzed and is found to be normally distributed. The mean value of the error is very close to zero and it does not exceed 0.013 ms-1, while the maximum value of the standard deviation is about 0.07 ms-1. Furthermore, since it is difficult to measure velocity at too many points in the flow cross-sectional area during high floods, a simple method is proposed for constructing the velocity profiles at a river section. The method is based on a velocity distribution law derived by Chiu (1988) using the principle of maximum entropy for wide open-channels. It is assumed that the mean and maximum velocities within different portions of the flow section have a parabolic shape which is easily derived by three simple constraints. Comparing the reconstructed velocity profiles with velocity points measured along verticals, the method was found capable of estimating with a reasonable accuracy the shape of the observed velocity profiles of high flood events simply by knowing the flow area and the maximum velocity of the cross-section along with the dimensionless entropy parameter.