About Culvert Sizing Calculator
The culvert sizing calculator estimates the hydraulic capacity of a single culvert barrel under the two control conditions described in FHWA HDS-5 (Hydraulic Design of Highway Culverts). A culvert is governed by inlet control when the inlet geometry limits flow, and by outlet control when barrel friction and the tailwater limit flow; the design capacity is the smaller of the two.
Enter the culvert shape and size (circular diameter or box span and rise), the barrel length, Manning's roughness n, the entrance loss coefficient ke, the outlet head difference H = HW - TW, and the headwater depth HW. The tool computes the outlet-control full-barrel discharge, the inlet-control orifice discharge, the governing capacity, and the resulting barrel velocity.
How It Works
- Choose a circular or box culvert and enter its dimensions and barrel length L.
- Enter Manning's n for the barrel, the entrance loss coefficient ke, the outlet head H = HW - TW, and the headwater depth HW above the invert.
- The calculator computes outlet-control capacity from the full-barrel energy balance Q = A*sqrt(2gH / (1 + ke + 2g n^2 L / R^(4/3))) and inlet-control capacity from the submerged-orifice form Q = Cd*A*sqrt(2g*HW).
- It reports both capacities, identifies the governing (smaller) one and its control type, and gives the barrel velocity at that flow.
Worked Example
A circular concrete culvert has diameter D = 1.0 m, length L = 20 m, Manning's n = 0.012, entrance loss ke = 0.5, head H = 1.5 m, and headwater HW = 1.5 m. The barrel area A = pi*D^2/4 = 0.785 m^2 and hydraulic radius R = D/4 = 0.25 m. Outlet control gives Q = 0.785 * sqrt(2*9.81*1.5 / (1 + 0.5 + 2*9.81*0.012^2*20 / 0.25^(4/3))) = 3.13 m^3/s. Inlet control (Cd = 0.6) gives Q = 0.6 * 0.785 * sqrt(2*9.81*1.5) = 2.56 m^3/s. The smaller value, 2.56 m^3/s, governs, so the culvert is under inlet control with a barrel velocity of 3.26 m/s.
Formulas
- Outlet control (full barrel, Manning friction)
Q = A * sqrt( 2g * H / (1 + ke + (2g * n^2 * L) / R^(4/3)) )- Inlet control (submerged orifice)
Q = Cd * A * sqrt( 2g * HW )- Barrel geometry (full)
Circular: A = pi*D^2/4, R = D/4 | Box: A = w*h, R = w*h / (2(w+h))- Governing capacity and velocity
Q_design = min(Q_inlet, Q_outlet), V = Q_design / A
Standards & References
- FHWA HDS-5: Hydraulic Design of Highway Culverts
- Manning's equation for barrel friction loss
- Orifice equation for submerged inlet control
Frequently Asked Questions
What is the difference between inlet and outlet control?
Under inlet control the culvert entrance geometry limits the flow and the barrel is not the constraint, so capacity depends mainly on headwater and inlet shape. Under outlet control the barrel friction and tailwater limit flow. The actual capacity is the smaller of the two, and HDS-5 requires checking both.
What entrance loss coefficient ke should I use?
Typical ke values are about 0.2 for a smooth, tapered or bevelled inlet, 0.5 for a square-edged inlet in a headwall, and 0.7 to 0.9 for a projecting or mitred pipe. Use the value matching your inlet detail from HDS-5 Table 12.
Does this tool perform a full HDS-5 nomograph analysis?
No. It uses simplified full-flow outlet-control and submerged-orifice inlet-control equations to give a quick capacity estimate and identify the governing control. For final design use the FHWA HDS-5 inlet-control regression equations and the full energy-grade-line outlet-control procedure.
Why does the barrel velocity matter?
High barrel and outlet velocities can cause scour and erosion at the culvert outlet. The tool reports the velocity at the governing capacity so you can check it against allowable limits and decide whether outlet protection or energy dissipation is needed.