Estimation of Mean Velocity in Natural Channels Based on Chiu’s Velocity Distribution Equation

The applicability of the linear relationship between the mean and the maximum flow velocities, based on the entropy concept, was investigated using data collected during a period of 20 years for four gauged river sections in the upper Tiber River basin in Central Italy. The value of the entropy parameter M of this relationship for the four gauged sections was found to be constant and is equal to 2.13. The same value can be surmised for other river sections located within the river reach investigated. For each site, the error in estimating the cross-sectional mean velocity from the observed maximum velocity was analyzed and was found to be normally distributed. The mean value of the percentage error was very close to zero and did not exceed 0.001, while the maximum value of the standard deviation was about 0.06. A simple method for estimating the velocity profiles at a river section is proposed. The method, based on the velocity distribution equation derived by Chiu using the probabilistic formulation and entropy maximization, is capable of determining the velocity profiles with reasonable accuracy, even near the side walls. Furthermore, because it is difficult to measure velocity at too many points in the flow area during high floods, a practical approach for estimating the cross-sectional mean velocity was also developed. This approach is based on the assumption that the mean velocity along each sampled vertical has a parabolic shape, easily derivable by three simple constraints. Seven flood events observed at gauged sections were used to test it, and the estimated cross-sectional mean velocity was found quite accurate also for new river sites where the parameter M is unknown.