Culvert Headwater by Inlet Control (HDS-5)

Inlet control is the case where the inlet (its size, shape, and edge), NOT the barrel length or the outlet, sets the headwater. FHWA HDS-5 (FHWA-HIF-12-026) Appendix A gives two regimes for a circular barrel: unsubmerged at low flow (weir-like) HW/D = Hc/D + K[Q/(A sqrt D)]^M + Ks S, with the specific head at critical depth Hc found by iterating the circular-segment geometry; submerged at high flow (orifice-like) HW/D = c[Q/(A sqrt D)]^2 + Y + Ks S; the two blend across flow factors 3.5 to 4.0. Ks = -0.5 (mitered +0.7) is the slope term, and K, M, c, Y are the Table A.1 constants for concrete pipe (square/groove/projecting) and corrugated metal (headwall/mitered/projecting). A 36 in concrete pipe, square edge with headwall, passing 30 cfs on a 1% slope heads up 2.67 ft (HW/D 0.89, unsubmerged); the same pipe as CMP projecting at 60 cfs is submerged at 5.59 ft. The ACTUAL headwater is the GREATER of inlet and outlet control - outlet control (barrel friction, tailwater) is a separate check. A design aid; the HDS-5 nomographs carry about +/-10%, and the engineer of record and the DOT drainage manual govern.

Inlet control HW/D (circular barrel): unsubmerged Form 1 HW/D = Hc/D + K[Q/(A sqrt D)]^M + Ks S; submerged HW/D = c[Q/(A sqrt D)]^2 + Y + Ks S; Ks = -0.5 (mitered +0.7). Barrel A = pi D^2/4; critical depth from g A^3 = Q^2 T on the circular segment, Hc = dc + Vc^2/2g. HW = (HW/D) D.

FHWA HDS-5, Hydraulic Design of Highway Culverts, 3rd ed. (FHWA-HIF-12-026, 2012), Appendix A equations A.1 and A.3 and the Table A.1 constants for circular concrete and corrugated-metal pipe, by name; the equation assembly and slope term verified against the HDS-5 Appendix A worked values, and the circular critical-depth solve against the Froude = 1 definition.

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

Estimate. AHJ and licensed professional govern.

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

• Unsubmerged Form 1 HW/D = Hc/D + K[Q/(A sqrt D)]^M + Ks S; Hc from the circular critical depthHDS-5 Eq A.1, Table A.1
• Submerged HW/D = c[Q/(A sqrt D)]^2 + Y + Ks S, above flow factor ~4.0HDS-5 Eq A.3, Table A.1
• Slope / scope Ks = -0.5 (mitered +0.7); circular barrels only; inlet control only (outlet control is a separate check)HDS-5 Appendix A