Numerous deterministic and probabilistic techniques have been utilized extensively to examine the velocity distributions for open channel flows under the various flow and channel characteristics. It is generally known that traditional approaches such as logarithmic velocity laws and power laws furnish vertical velocity profiles for the wide channels (width-to-depth ratio > 5) only. Also, the accuracy of the traditional methods is highly parameter dependent which, in turn, is evaluated using empirical or semi-empirical relationships only. Owing to the limitations of the conventional approaches, the entropy concept is formulated probabilistically and applies to all aspect ratios (width-to-depth ratio). The prominent entropy types explored to date are Shannon entropy, Tsallis entropy, and Renyi entropy. Recently, Fractional entropy has been demonstrated to study the velocity distributions for the open channel flows. Laboratory measurements have been used to demonstrate the applicability and correctness of all the techniques in adverse channel bed slope conditions (Singh & Khosa, 2022). The measurements comprise the velocity data at the different adverse slope values. Finally, a rigorous comparative analysis for the estimated velocity profiles using the four generally used velocity laws and four entropy-based velocity distributions have been conducted, which showed that the information entropy-based methods are far better than the traditional techniques.
Flow measurement is critical in hydraulic engineering for developing and managing water resources. The mean flow velocity and cross-sectional flow area at the measurement location are two major metrics required for discharge estimation. River bathymetric surveys or advanced technologies such as the Acoustic Doppler Current Profiler (ADCP) might be used to determine the cross-sectional area. The mean flow velocity can be measured using different techniques depending on whether the measurements are taken from a distance (non-contact) or a contact method (traditional approach). Non-contact velocity measuring techniques are becoming increasingly common in recent years since they are less time-consuming and easier to utilize while dealing with heavy flows and inclement weather. One such modern approach is the entropy-based concepts (such as Shannon entropy, Tsallis entropy and Renyi entropy) used to calculate the discharge from non-contact observations, yielding superior results to classic approaches such as the velocity area method. Entropy-based velocity distribution depends on the crucial parameter called entropy parameter (a function of the ratio of the mean and maximum velocity), which is linked to the channel and flow characteristics. Its value is surmised to be constant for a particular river reach. Due to this fact, the entropy-based approach was used in this study to evaluate the discharge in case of the adverse bed slope condition that may arise due to several reasons, and one among them is the excessive mining in the particular river reach. This study collected the experimental velocity data for the mild, horizontal and adverse bed slope conditions from a rectangular flume fitted with a mechanical apparatus to change the bed slope. Results concluded that the mild and horizontal slope conditions depicted only a slight variation in entropy parameter value, i.e., almost constant. The same was adopted for finding the mean velocity for the adverse bed slope condition to calculate the discharge. Furthermore, the discharge error analysis presented a substantial justification for the utilized single constant value of the entropy parameter for the whole cross-section, and the same can be employed for future explorations on the same channel stretch.