Culvert Headwater by Outlet Control (HDS-5)

Culvert headwater under OUTLET control, where the barrel and the tailwater set the head.

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Details, formula, and sources

Outlet control is the case where the barrel itself (its length, roughness, and the tailwater), NOT the inlet edge, sets the headwater. For a circular barrel flowing full, FHWA HDS-5 (FHWA-HIF-12-026) gives the 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 table value for the inlet type), and the full-flow Manning friction loss (the 29 is 2g/1.486^2 in US-customary units); V = Q/A and R = D/4 are full-barrel values. The outlet head ho is the greater of the tailwater and (dc + D)/2, dc being the circular critical depth. A 36 in concrete pipe (n 0.012), 100 ft long on a 1% slope with a square-edge headwall (Ke 0.5) passing 50 cfs against a 2 ft tailwater heads up 3.29 ft; the same barrel as corrugated metal (n 0.024, projecting Ke 0.9) quadruples the friction and heads up to 5.03 ft. The ACTUAL design headwater is the GREATER of this and the inlet-control value; if HW lands below the barrel crown the full-flow form is only approximate. HW is measured above the inlet invert. Circular barrels only (box/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: H = [1 + Ke + 29 n^2 L / R^(4/3)] V^2/2g; HW = H + ho - So L. A = pi D^2/4, R = D/4, V = Q/A; ho = max(TW, (dc + D)/2), dc the circular critical depth from g A^3 = Q^2 T. 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 / Appendix A full-flow outlet-control energy equation and the Table entrance-loss coefficients Ke, by name; the friction constant 29 = 2g/1.486^2 and the critical-depth solve (Froude = 1) are verified in the compute.

HDS-5 is a public-domain FHWA publication (FHWA-HIF-12-026); the outlet-control energy equation and the Ke entrance-loss values are reproduced from it. Diameter, 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: diameter_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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