Box Culvert Headwater by Inlet Control (HDS-5)

Headwater for a rectangular BOX culvert under INLET control, where the entrance sets the head.

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Details, formula, and sources

Same FHWA HDS-5 (FHWA-HIF-12-026) Appendix A equations with the Table A.1 concrete-box constants. Two inlet families: WINGWALL FLARES (Chart 8, Form 1) carry the specific head at critical depth HW/D = Hc/D + K[Q/(A sqrt D)]^M + Ks S -- and a rectangular section has a closed-form critical depth dc = (Q^2/(g B^2))^(1/3) with Hc = 1.5 dc, so no iteration; 90-degree HEADWALLS with chamfers or bevels (Chart 10, Form 2) drop the Hc term, HW/D = K[Q/(A sqrt D)]^M + Ks S. Above a flow factor of about 4 both go submerged (orifice-like) HW/D = c[Q/(A sqrt D)]^2 + Y + Ks S, blended across 3.5-4.0. D is the box RISE (interior height), A = span x rise, Ks = -0.5. A 6 x 4 ft box with 30-75 degree wingwall flares passing 150 cfs on a 1% slope heads up 4.34 ft (HW/D 1.08); a 8 x 5 ft box with 45-degree bevels at 300 cfs heads up 5.54 ft. Beveled and flared edges (lower K) always beat a square headwall. The ACTUAL headwater is the GREATER of inlet and outlet control -- outlet control is a separate check. Public-domain FHWA reference; the HDS-5 nomographs carry about +/-10%, and the engineer of record and the DOT drainage manual govern.

Box inlet control HW/D: unsubmerged Form 1 (wingwall flares) HW/D = Hc/D + K[Q/(A sqrt D)]^M + Ks S; Form 2 (headwalls) HW/D = K[Q/(A sqrt D)]^M + Ks S; submerged HW/D = c[Q/(A sqrt D)]^2 + Y + Ks S; Ks = -0.5. D = rise, A = span x rise; rectangular critical depth dc = (Q^2/(g B^2))^(1/3), Hc = 1.5 dc. HW = (HW/D) D.

FHWA HDS-5, Hydraulic Design of Highway Culverts, 3rd ed. (FHWA-HIF-12-026, 2012), Appendix A equations A.1/A.2/A.3 and the Table A.1 concrete-box constants (Chart 8 wingwall flares Form 1; Chart 10 headwall chamfers/bevels Form 2), by name; the equation assembly verified against the HDS-5 Appendix A worked values and the rectangular critical depth against its closed form Hc = 1.5 dc.

HDS-5 is a public-domain FHWA publication (FHWA-HIF-12-026); the inlet-control equations and the Table A.1 box constants are reproduced from it. Span, rise, discharge, slope, and the inlet configuration are the user's inputs.

Estimate. AHJ and licensed professional govern.

Field names used by the API: span_in, rise_in, flow_cfs, slope, config, hw_ft, hw_over_d, dc_ft, hc_ft, barrel_area_ft2

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