Box Culvert Headwater by Outlet Control (HDS-5)

Headwater for a rectangular BOX culvert under OUTLET control, where the barrel and the tailwater set the head.

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Details, formula, and sources

This is the box case; circular barrels are separate. Same FHWA HDS-5 (FHWA-HIF-12-026) full-flow energy equation HW = H + ho - So L, with the total head loss H = [1 + Ke + 29 n^2 L / R^(4/3)] V^2/2g stacking the exit loss (the 1), the entrance loss Ke (the HDS-5 box table value), and the Manning friction loss (the 29 is 2g/1.486^2 in US-customary units), but with box geometry: A = span x rise, the full-flow wetted perimeter P = 2(span + rise) so R = A/P (not D/4), and the rectangular closed-form critical depth dc = (Q^2/(g B^2))^(1/3) (B = span); D is the box RISE. The outlet head ho is the greater of the tailwater and (dc + D)/2. A 6 x 4 ft box (n 0.012), 120 ft on a 0.5% slope with 30-75 deg wingwall flares (Ke 0.4) passing 150 cfs against a 3 ft tailwater heads up 3.83 ft; an 8 x 5 ft box with 45 deg bevels (Ke 0.2) at 300 cfs heads up 4.96 ft. The ACTUAL design headwater is the GREATER of this and the box inlet-control value; if HW lands below the box crown the full-flow form is only approximate. HW is measured above the inlet invert. Rectangular boxes flowing full (arch/pipe-arch and partly-full backwater are separate). Public-domain FHWA reference; the HDS-5 nomographs carry about +/-10%, and the engineer of record and the DOT drainage manual govern.

Full-flow outlet control (box): H = [1 + Ke + 29 n^2 L / R^(4/3)] V^2/2g; HW = H + ho - So L. A = span x rise, P = 2(span + rise), R = A/P, V = Q/A; ho = max(TW, (dc + D)/2), dc = (Q^2/(g B^2))^(1/3), D = rise. The 29 = 2g/1.486^2 (US-customary). HW is measured above the inlet invert.

FHWA HDS-5, Hydraulic Design of Highway Culverts, 3rd ed. (FHWA-HIF-12-026, 2012), Chapter 3 full-flow outlet-control energy equation and the Table box entrance-loss coefficients Ke, by name; the friction constant 29 = 2g/1.486^2 and the rectangular critical depth dc = (Q^2/(g B^2))^(1/3) are verified in the compute.

HDS-5 is a public-domain FHWA publication (FHWA-HIF-12-026); the outlet-control energy equation and the box Ke entrance-loss values are reproduced from it. Span, rise, discharge, length, slope, Manning n, tailwater, 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, length_ft, slope, manning_n, tw_ft, config, hw_ft, head_loss_ft, friction_coeff, v_fps, dc_ft, ho_ft, barrel_area_ft2

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