Effect of Channel Bed Slope on Shannon Entropy-Based Velocity Distribution in Open Channel Flow

Streamflow measurement is essential in hydraulic engineering to develop and manage water resources and ensure they are managed correctly and adequately. Two primary parameters for discharge measurements in natural rivers, namely, the mean flow velocity and cross-sectional flow area at the measurement site, are requisites. The cross-sectional area of the section could be measured using river bathymetric surveys or by using advanced and modern methods such as Acoustic Doppler Current Profiler (ADCP). For mean velocity, numerous ways and tools are available depending on the fact, whether the measurements are taken from a distance (non-contact) or using a contact method (traditional approach). Nowadays, non-contact velocity measurement approaches are becoming more popular as they are less time-consuming and user‑friendly to deal with high flows and rough weather. In contrast, the entropy-based concepts (such as Shannon entropy, Tsallis entropy and Renyi entropy) are utilized to obtain the discharge from the non-contact measurements, which gives better results than the traditional approaches such as the velocity area method. Entropy-based velocity distribution depends on the crucial parameter called entropy parameter (a function of the mean and maximum velocity), which is linked to the channel characteristics such as channel roughness and bed slope. Due to a lack of concrete evidence regarding its variation with the channel characteristics, the entropy parameter was surmised as constant. In this study, the experimental velocity data was collected from a rectangular flume fitted with a mechanical apparatus to change the bed slope. The obtained velocity data was employed to comment on the actual variation of the Shannon entropy parameter for the one such channel characteristic, i.e., channel bed slope. The velocity data analysis depict only a slight variation in entropy parameter. In addition, the discharge error analysis provided a substantial justification for using a unique constant value of the entropy parameter for the whole cross-section can be utilized instead of individual values for each channel bed slope condition.