Culvert Flow Rough Calculator
Gives a rough inlet-control capacity for a circular culvert by treating it as a submerged orifice, Q = Cd·A·√(2·g·H). A quick sanity-check for drainage designers and site engineers sizing pipe and box culverts before a full hydraulic analysis.
Enter Values
Before you rely on this: First-pass guide only. Verify safety-critical or regulated work against the relevant standards, your project requirements and a qualified professional.
How to use this calculator
- Enter the culvert diameter D in metres; the tool computes the barrel area A = π·D²/4.
- Enter the headwater depth H (m) above the culvert invert/centre.
- Optionally change the discharge coefficient Cd (default 0.6) and read the discharge Q in m³/s and L/s.
How it works
When the inlet of a culvert is submerged, it behaves like an orifice: the discharge is driven by the head of water above it. Q = Cd·A·√(2·g·H), where A = π·D²/4 is the pipe cross-section, g = 9.81 m/s² and H is the headwater depth above the invert. Cd (about 0.5–0.6, default 0.6) accounts for contraction and entrance losses.
This is deliberately simple. Real culverts may be inlet- or outlet-controlled, and the governing capacity is the lower of the two. Barrel slope, length, roughness, entrance type and tailwater level all matter, which is why design work uses HDS-5 / HY-8 or the AUSTROADS method rather than a single orifice equation.
Worked example
600 mm pipe, 1.2 m head. With D = 0.6 m, H = 1.2 m and Cd = 0.6: A = π × 0.6² / 4 = 0.2827 m²; Q = 0.6 × 0.2827 × √(2 × 9.81 × 1.2) = 0.6 × 0.2827 × 4.852 = 0.823 m³/s, about 823 L/s.
Common mistakes
- Treating the orifice result as the design capacity — the true capacity is the lower of inlet and outlet control, which this tool does not check.
- Measuring H from the wrong datum; it is the headwater depth above the culvert invert/centre, not the ground surface or the pipe crown.
- Ignoring tailwater, barrel slope, length and roughness, all of which can reduce the real discharge below this estimate.
Frequently asked questions
What does this calculator actually model?
A submerged circular culvert behaving as an orifice under a headwater depth H. It is a rough inlet-control estimate, not a full culvert hydraulic analysis.
What value of Cd should I use?
Around 0.5–0.6 for a sharp-edged submerged inlet; 0.6 is a common default. A well-rounded, efficient entrance sits at the higher end.
What is inlet versus outlet control?
Inlet control means the entrance limits flow (governed by headwater and inlet geometry); outlet control means the barrel and tailwater limit flow. The real capacity is the lower of the two.
Where is H measured from?
H is the depth of water (headwater) above the culvert invert/centre. Using the ground surface or pipe crown will give the wrong head.
What should I use for design?
Use FHWA HDS-5 with HY-8, or the AUSTROADS culvert design method, which handle inlet/outlet control, slope, roughness and tailwater.
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