A New Energy-Based Rating Algorithm for Controlled Submerged Flow at Gated Spillways

We propose a rating formula for controlled-submerged (CS) spillway flow of the form Fr_G = α [(H-h)/G]^0.5 where Fr_G=gate Froude number = Q/ [A_G (gG)^0.5], G=gate opening, H=headwater stage, and h=water stage just downstream of the gate, derived from energy balance between an upstream station and a station right after the gate. We validate our formulation with experimental data sets for submerged sluice gate flow in rectangular channels which yielded α ≈ 0.85±0.01& 0.91±0.08, respectively. We then apply it to data collected in the field at a prototype gated spillway of trapezoidal sill. This data comprises discharge measurements by acoustic Doppler current profiler (ADCP), and gate openings and head and tailwater stages monitored at the site near real-time by a SCADA system. Since h is not typically monitored in the field, we estimated the h values in the set of calibration data {Q, H, h, G} by applying continuity and momentum principles between the tailwater station where the stages are monitored and the gate (~ 215 ft apart).The parameter α and respective standard error estimated with the field data was α= 0.924±0.02. In our proposed formulation, the parameter α accounts for the upstream well location, size of the vena contracta, sill geometry, and nonlinear hydrodynamics of the rapidly varying flow near the gate. An advantage of the rating formulation we propose is that it yields estimates of discharge with lower uncertainty limits than those estimated with a rating of the form y_c/G=a [(H-T)/G]^b, [y_c=critical depth and T= water stage downstream of well] since H-T includes nonlinearities of the energy dissipation process between the gate and the tailwater well.