What This Solves
Calculates the discharge velocity at pipe and culvert outlets to assess erosion potential, scour depth, and the need for outlet protection.
Best Used When
- You need to determine if outlet velocity exceeds permissible limits for the downstream channel
- You want to estimate scour hole dimensions at a pipe outlet
- You are evaluating whether outlet protection or energy dissipation is needed
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 depth estimates use FHWA HEC-14 empirical relationships
- Tailwater conditions affect the effective outlet velocity
- The pipe outlet is unsubmerged or the degree of submergence is known
- No significant entrance or exit losses beyond standard coefficients
Input Quality Notes
Accurate pipe flow depth at the outlet is needed. For partial flow, use normal depth calculations. Tailwater depth affects both velocity and scour — use field data or downstream channel analysis.
Estimate the velocity at a culvert or pipe outlet and the resulting scour potential. Enter the design discharge, outlet geometry and downstream bed material to get the outlet velocity, Froude number, estimated scour-hole dimensions and a recommended riprap size, using FHWA HEC-14 energy-dissipator methodology.
Bed Material Critical Velocities
| Material | Vc (ft/s) |
|---|---|
| Fine sand (0.06-0.25mm) | 0.5-1.0 |
| Medium sand (0.25-0.5mm) | 1.0-1.5 |
| Coarse sand (0.5-2mm) | 1.5-2.5 |
| Fine gravel (2-6mm) | 2.5-4.0 |
| Coarse gravel (6-60mm) | 4.0-7.0 |
| Cobbles (60-250mm) | 7.0-12.0 |
| Clay/silt (cohesive) | 2.0-5.0 |
| Cohesive soil (mixed) | 3.0-6.0 |
Scour Potential Classification
Ready to Calculate
Enter outlet geometry and flow parameters to calculate velocity and scour potential.
For educational purposes only. Not a substitute for professional engineering judgment.
How outlet velocity and scour are calculated
The analysis follows FHWA HEC-14 (Hydraulic Design of Energy Dissipators for Culverts and Channels) and HDS-5 (Hydraulic Design of Highway Culverts). The outlet velocity is found by continuity, then compared with the critical velocity of the bed material to gauge scour and protection requirements.
Outlet velocity (continuity)
V = Q / A
Q = design discharge, A = flow area at the outlet for the chosen shape and flow depth.
Velocity head
hv = V² / (2g)
g = 32.2 ft/s² (9.81 m/s²). Velocity head is the kinetic energy available at the outlet.
Froude number (flow regime)
Fr = V / √(g · Dh)
Dh = hydraulic depth (area ÷ top width). Fr > 1 is supercritical (fast, shallow); Fr < 1 is subcritical.
Critical velocity of bed material
Vc = K · √((SG − 1) · g · d₅₀)
Simplified Shields criterion with K = 1.2 and specific gravity SG = 2.65; d₅₀ = median bed-particle size.
Equilibrium scour depth
ds = 0.42 · D · (V/Vc)1.5 · t0.67
D = diameter (or outlet depth), t = flow duration (hours). Scour hole: Ls = 2.5(ds + D), Ws = 1.5(ds + W).
Riprap sizing
d₅₀ = 0.2 · D · Fr4/3
HEC-14 outlet riprap relation, applied with a practical minimum stone size of about 3 in (0.25 ft) when protection is required.
Scour potential is classified from the velocity ratio V/Vc: below 0.8 is low, 0.8–1.2 moderate, 1.2–2.0 high and above 2.0 severe. The recommended protection level (none, minimal, moderate or extensive) is set from that classification together with the absolute outlet velocity.
Maximum permissible velocities by outlet/channel lining
Indicative non-erosive velocity limits used to screen whether an outlet discharges onto a stable surface. If the calculated outlet velocity exceeds the limit for the receiving surface, scour protection or an energy dissipator is generally required.
| Receiving surface / lining | Max permissible velocity (ft/s) | Max permissible velocity (m/s) |
|---|---|---|
| Bare / erodible soil | ~2.0 | ~0.6 |
| Established grass / turf | ~6.0 | ~1.8 |
| Riprap (graded stone) | ~12.0 | ~3.7 |
| Concrete | ~20.0 | ~6.1 |
Values are screening guides for maximum permissible (non-erosive) velocity. The calculator above also reports the critical velocity of the specific bed material you select, which is a more precise basis for the scour check.
Frequently asked questions
How is outlet velocity calculated?
Outlet velocity is the continuity velocity V = Q / A, where Q is the design discharge and A is the cross-sectional flow area at the outlet. For a partially full circular pipe the flow area is computed from the geometry of the wetted segment; for box, trapezoidal and triangular outlets it is found from the width, depth and (for box/trapezoidal) height. This calculator follows the FHWA HEC-14 and HDS-5 approach: it solves for the flow area for the chosen shape and depth, then divides the discharge by that area to get the mean outlet velocity.
What outlet velocity is too high?
There is no single universal limit — it depends on what the flow discharges onto. As a guide for unlined channels, bare erodible soil tolerates roughly 2 ft/s, established grass about 6 ft/s, riprap up to about 12 ft/s, and concrete up to about 20 ft/s. The calculator goes further by comparing the outlet velocity to the critical (incipient-motion) velocity of the downstream bed material and classifying scour potential as low, moderate, high or severe, which is more reliable than a single velocity threshold.
How is scour depth at the outlet estimated?
The tool uses a simplified HEC-14 equilibrium relationship: scour depth d_s = 0.42 · D · (V/Vc)^1.5 · t^0.67, where D is the pipe diameter (or outlet flow depth for non-circular shapes), V/Vc is the ratio of outlet velocity to the bed-material critical velocity, and t is the flow duration in hours. Scour is only predicted when V/Vc exceeds about 0.5. The scour hole length is estimated as L_s = 2.5(d_s + D) and width as W_s = 1.5(d_s + W). These are planning-level estimates, not a substitute for a site-specific scour study.
When do I need riprap or an energy dissipator at the outlet?
Protection is recommended when the outlet velocity exceeds the critical velocity of the bed material (scour potential moderate or higher) or when the absolute velocity is high (above roughly 5 ft/s on erodible material). When protection is required, the calculator sizes the riprap from the Froude number using the HEC-14 form d50 = 0.2 · D · Fr^(4/3), with a practical minimum stone size of about 0.25 ft (3 in). Very high Froude numbers or velocities above about 15 ft/s typically call for a structural energy dissipator (impact basin, baffled apron or stilling basin) rather than riprap alone.
Standards & related tools
FHWA HEC-14 (energy dissipators)
Hydraulic Design of Energy Dissipators for Culverts and Channels — the source methodology.
Manning's Pipe Calculator
Find the discharge and velocity inside the pipe before it reaches the outlet.
Manning's n Reference
Roughness coefficients for common pipe and channel materials.
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Last verified: February 2026