A relationship expressed solely in terms of the Froude number (Fr) shows a high correlation between observed and estimated values when experimental conditions are similar or when the weir width is small and the overflow discharge is limited; however, the correlation decreases as the experimental conditions differ or the overflow discharge increases.
When comparing, for each condition, the discharges calculated using existing discharge-coefficient equations with those measured by the load cell, the Borghei (1999) equation, which includes geometric parameters (weir width ratio and depth ratio), provides consistent results across all experimental conditions.
The De Marchi (1934) equation, which forms the basis of many empirical formulas in previous studies and does not explicitly include the bed slope of the main channel, shows slight discrepancies between measured and calculated values, suggesting that one or more parameters in the gradually varied flow function (specific energy, flow depth, weir height) may have high sensitivity.
When determining the discharge coefficient to accurately predict overflow discharge over a side weir, a formula expressed only in terms of the upstream Froude number, or one that places excessive weight on it, is likely to have limited applicability under diverse conditions.
In future work, an empirical equation that incorporates the bed slope of the main channel, S₀, will be examined in order to derive the necessary functional form for an accurate discharge-coefficient formula