Sharp-crested weir
Rectangular with or without end contractions, V-notch and Cipolletti, by the Rehbock and Francis equations, with Villemonte's reduction for a submerged crest.
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Each solves for the discharge or for the level that passes it, and says so when the answer runs into the limits of its method.
Rectangular with or without end contractions, V-notch and Cipolletti, by the Rehbock and Francis equations, with Villemonte's reduction for a submerged crest.
Critical flow over the crest on the total head, with the approach velocity found by iteration and a check against the modular limit.
Pier and abutment contractions, and a discharge coefficient that follows the head away from the design head.
Circular or rectangular, discharging freely or drowned by the tailwater.
Free flow by energy, submerged flow by Henderson's energy and momentum solution. Solve for the discharge, the opening or the upstream depth, with the thrust on the gate.
Headwater in inlet and in outlet control after FHWA HDS-5, for concrete pipes, corrugated metal pipes and box culverts, with the performance curve.
The hydraulic jump from either depth: sequent depth, length, energy dissipated, and the USBR basin that suits it.
The results are for preliminary design and checking. The coefficients are typical values: confirm them for the structure at hand, and have the design reviewed by a qualified engineer.