Discussion of “Unsteady Stage-Discharge Relationships for Sharp-Crested Weirs” by Firouz Ghasemzadeh, Salah Kouchakzadeh, and Gilles Belaud

I would like to thank the authors for writing this interesting article dealing with unsteady stage-discharge relationships for sharp-crested weirs. The operation of triangular and rectangular sharp-crested weirs in unsteady flow conditions was experimentally investigated. Results indicated the presence of looped rating curves, with transposition of the rising and falling limbs compared to that commonly observed in stream gauge ratings. The authors found that the deviation between steady and unsteady flow rates in the looped rating curves depends on the weir type and the hydrograph gradient (i.e., the temporal depth variation), especially when the latter changes rapidly. Finally, they proposed calibrated relationships, where two empirical coefficients account for the so-called hydrograph equivalent slope defined as the geometric mean of the absolute slope value of the water head above the weir crest, between the rising and the falling limb, which incorporates the effect of flow unsteadiness. For a circular sharp-crested orifice at the bottom of a tank, the unsteady stage-discharge relationship, only differing in the exponent x of the water level, h, above the crested orifice (x ¼ 1=2 for circular holes, x ¼ 3=2 for rectangular weirs, x ¼ 5=2 for triangular weirs), was recently derived (Baiamonte 2020a, b). The only objective of this discussion is to show that the deviation between steady and unsteady flow rates in the looped rating curves could be analytically derived without calibration. As a consequence, the effect of the average hydrograph gradient found by the authors can be analytically determined for both the rising and the falling limbs. The analysis is performed for dimensionless groups, which makes the results more general and more useful for their ability to contract, or make more succinct, the functional form of physical relationships.