Calculate mean outlet velocity and the maximum local scour-hole geometry predicted for a cohesionless receiving bed by FHWA HEC-14 Equation 5.1. The calculation uses published, dimension-specific coefficients—not a velocity-ratio heuristic.
Outlet design workflow
- Establish the design discharge, tailwater, and barrel condition with the culvert outlet-control calculator.
- Use this page to calculate velocity and HEC-14 Chapter 5 scour geometry for cohesionless soil.
- Review field evidence and long-term channel degradation; Equation 5.1 does not include degradation.
- Design qualifying circular-culvert riprap with the HEC-14 outlet-protection calculator, or use the broader riprap tool.
HEC-14 Equation 5.1
This calculator predicts depth, width, length, and volume of a culvert-outlet scour hole in cohesionless soil. It uses the full-flow hydraulic radius, grain-size gradation σ, peak-flow duration, culvert slope, and invert height above the bed.
Applicability
Equation 5.1 is not a cohesive-soil or riprap-sizing method. Review long-term channel degradation and field conditions separately. Use the dedicated outlet-protection calculator for HEC-14 Chapter 10 riprap design.
Ready to Calculate
Enter outlet geometry, flow, and cohesionless-soil parameters to calculate velocity and scour geometry.
For educational purposes only. Not a substitute for professional engineering judgment.
Interactive model
Interactive HEC-14 outlet-scour visualization
Explore the published Equation 5.1 inputs and see how full-flow hydraulic radius, discharge, material gradation, duration, slope, and outlet drop affect cohesionless-soil scour geometry.
Open full model (opens in a new tab)How the calculation works
Outlet velocity comes from continuity. Scour geometry follows FHWA HEC-14 (2006), Chapter 5, Equation 5.1 and Tables 5.1–5.3.
Outlet velocity
V = Q / A
A is the actual flow area at the entered outlet depth.
Full-flow hydraulic radius
Rc = Afull / Pfull
HEC-14 explicitly uses the full-flow value even when outlet velocity uses a partial-flow area.
Cohesionless-soil scour geometry
[hs/Rc, Ws/Rc, Ls/Rc, Vs/Rc3] = CsCh(α/σ1/3) [Q/(√g Rc2.5)]β(t/316)θ
σ = √(D84/D16), t is minutes, Cs is the slope correction, and Ch is the outlet-drop correction. Maximum depth occurs about 0.4Ls downstream.
HEC-14 Table 5.1 coefficients
| Scour output | α | β | θ |
|---|---|---|---|
| Depth hs | 2.27 | 0.39 | 0.06 |
| Width Ws | 6.94 | 0.53 | 0.08 |
| Length Ls | 17.10 | 0.47 | 0.10 |
| Volume Vs | 127.08 | 1.24 | 0.18 |
HEC-14 recommends 30 minutes when peak-flow duration is unknown and states that the published time exponents are not applicable during the first 30 minutes.
Frequently asked questions
How is outlet velocity calculated?
Mean outlet velocity is V = Q/A, using the design discharge and the flow area at the entered outlet depth. The calculator uses circular-segment geometry for a partly full pipe and the selected open-section geometry for other outlet shapes.
How does HEC-14 Equation 5.1 estimate outlet scour?
For cohesionless soils, HEC-14 Equation 5.1 relates scour depth, width, length, and volume to full-flow hydraulic radius Rc, discharge, material gradation σ = √(D84/D16), peak-flow duration in minutes, culvert slope, and the outlet-invert height above the bed. Each scour dimension has its own published α, β, and θ coefficients and slope/drop correction factors.
Does tailwater change the Equation 5.1 result?
HEC-14 reports that maximum scour geometry occurs at tailwater depths below about half the culvert height, but Equation 5.1 does not provide a continuous tailwater correction. This calculator therefore uses tailwater as an applicability warning, not as an invented multiplier.
Does this calculator size outlet riprap?
No. HEC-14 Chapter 10 riprap sizing is a separate method with discharge, culvert size, tailwater, and applicability limits. Use the linked outlet-protection calculator for a qualifying circular culvert. Cohesive-soil scour also requires separate HEC-14 Equations 5.2–5.4 and laboratory soil properties.
Standards & related tools
FHWA HEC-14
Official manual containing Equation 5.1 and Tables 5.1–5.3.
Culvert Outlet Control
Solve HDS-5 headwater, tailwater, losses, and barrel outlet conditions.
HEC-14 Riprap Apron
Apply the separate Chapter 10 riprap method for qualifying circular culverts.
Riprap Sizing by Application
Check channel, bridge, culvert, wave, overtopping, and filter stone designs.
What This Solves
Calculates mean outlet velocity and FHWA HEC-14 Equation 5.1 scour-hole depth, width, length, and volume for a cohesionless receiving bed.
Best Used When
- You know the actual flow depth needed for a continuity-based outlet velocity
- You have a cohesionless-bed gradation from D84 and D16
- You need Chapter 5 local-scour geometry before selecting an energy-dissipation strategy
Do NOT Use When
- You need to design a riprap apron or outlet protection pad — Use Outlet Protection Calculator
- You need to design a stilling basin or energy dissipation structure — Use Energy Dissipator Calculator
Key Assumptions
- Outlet velocity is calculated from pipe flow area and discharge using continuity
- Scour geometry uses HEC-14 Equation 5.1 with full-flow hydraulic radius
- The receiving-bed soil is cohesionless and gradation sigma equals sqrt(D84/D16)
- Peak-flow duration is at least 30 minutes
- Tailwater is applicability context only because Equation 5.1 has no continuous tailwater correction
- Long-term downstream channel degradation is evaluated separately
Input Quality Notes
Use the actual outlet flow depth for velocity, sieve-analysis D84/D16 for sigma, and a defensible peak duration. HEC-14 reports maximum geometry below about 0.5 culvert-height tailwater; use the tailwater input to flag applicability, not to adjust Equation 5.1.
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Last verified: August 2026