Comparative Analysis of Analytical and Empirical Methods for Estimating the Longitudinal Dispersion Coefficient in Open-Channel Flows

The accurate estimation of the longitudinal dispersion coefficient is crucial for predicting solute transport in natural water bodies.In this study, an analytical (integral) method based on first principles is compared with Fischer's widely used empirical approach, which is implemented in hydraulic modeling software such as the Hydrologic Engineering Center-River Analysis System (HEC-RAS).The primary objective is to evaluate the accuracy, applicability, and limitations of both methods under varying hydraulic conditions.A key advantage of the analytical approach is its ability to estimate the dispersion coefficient using velocity data alone, eliminating the need for high-cost tracer experiments that rely on solute concentration measurements.The determination index suggests an acceptable level of agreement between the two methods; however, the empirical approach systematically overestimates dispersion coefficients.Furthermore, a clear inverse relationship is observed between the slope of the channel and the magnitude of the dispersion coefficient, which is attributed to the increasing influence of shear velocity on the diffusion process.As slope values increase, solute separation time decreases, and concentration gradients become steeper.Conversely, at lower slopes, solute dispersion occurs over a broader time frame, resulting in lower concentration peaks.These findings indicate that while Fischer's method provides a robust empirical framework, it should be supplemented with field measurements to improve reliability.In contrast, the analytical method offers a more theoretically grounded alternative that may enhance predictive accuracy in solute transport modeling.The implications of these results extend to water quality management, contaminant transport studies, and hydraulic engineering applications, where the selection of an appropriate dispersion estimation method significantly influences predictive outcomes.