Try a Common Scenario
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Size a vegetated (grass-lined) swale for stormwater conveyance. Enter your design flow and channel geometry to get the normal depth, mean velocity, hydraulic radius, Froude number and capacity from Manning’s equation, with an automatic check against the permissible velocity for the grass lining you select.
Swale capacity is Manning flow through a shaped, vegetated channel
Enter design flow Q, bottom width b, side slope z, longitudinal slope S, and vegetation. The calculator iterates on Manning’s n and normal depth y until Q = (k/n)AR2/3S1/2, then checks mean velocity against a vegetation-specific erosion limit. US customary and SI units are both supported; a swale may also be called a grassed waterway, open drain, roadside ditch, or V-ditch.
Calculate Vegetated Swale Hydraulics
For educational purposes only. Not a substitute for professional engineering judgment.
Vegetated Swale Design Overview
Vegetated swales convey stormwater while providing filtration and infiltration. Design uses Manning's equation with variable roughness coefficients that depend on flow depth, velocity, and grass retardance.
- Normal Depth - Uniform flow depth for design flow
- Velocity Check - Must be below permissible velocity for erosion control
- Froude Number - Flow regime indicator (subcritical preferred)
- Residence Time - Contact time for water quality treatment
Vegetation Retardance Classes
| Vegetation Type | Class | Height Range |
|---|---|---|
| Bermuda Grass | C | 6-12 inches |
| Buffalo Grass | C | 3-6 inches |
| Kentucky Bluegrass | C | 4-10 inches |
| Tall Fescue | B | 8-18 inches |
| Native Grass Mix | B | 12-24 inches |
| Unmowed/Dense Grass | A | > 24 inches |
| Short Mowed Grass | D | 2-4 inches |
Source: Chow (1959) Open-Channel Hydraulics, Table 5-6
Manning's n Values by Retardance Class
| Class | Low VR | Medium VR | High VR | Description |
|---|---|---|---|---|
| A | 0.50 | 0.25 | 0.150 | Very high retardance - dense, tall vegetation |
| B | 0.35 | 0.15 | 0.080 | High retardance - tall grass (18-24 in) |
| C | 0.25 | 0.10 | 0.050 | Moderate retardance - medium grass (6-12 in) |
| D | 0.15 | 0.06 | 0.035 | Low retardance - short grass (2-6 in) |
| E | 0.08 | 0.04 | 0.025 | Very low retardance - very short grass |
VR = Velocity x Hydraulic Radius. Source: HEC-22 Table 7-6
Permissible Velocities (ft/s)
| Retardance Class | Slope 0-5% | Slope 5-10% | Slope > 10% |
|---|---|---|---|
| Class A | 8.0 | 7.0 | 6.0 |
| Class B | 7.0 | 6.0 | 5.0 |
| Class C | 6.0 | 5.0 | 4.0 |
| Class D | 5.0 | 4.0 | 3.0 |
| Class E | 4.0 | 3.0 | 2.5 |
For erosion-resistant soils. Source: HEC-22 Table 7-5
Interactive model
Interactive 3D swale hydraulics
Change flow, bottom width, side slope, channel grade, and roughness to see normal depth, wetted width, velocity, and erosion risk respond.
Open full model (opens in a new tab)Worked trapezoidal-swale sizing example
For Q = 5 cfs, a 2 ft bottom, 4H:1V side slopes, a 2% longitudinal grade, and established Kentucky bluegrass, the same iterative engine used above gives:
- Normal depth, y
- 1.166 ft
- Top width, T
- 11.33 ft
- Mean velocity
- 0.64 ft/s
- Froude number
- 0.14
A preliminary 20% depth allowance adds 0.23 ft above the computed water surface. That is an illustration, not a universal freeboard criterion; confirm the total section depth, overflow route, and permissible velocity with the governing drainage manual and site grading plan.
How the swale calculation works
A vegetated swale carries flow as steady, uniform open-channel flow, so its capacity is governed by Manning’s equation:
Q = (k / n) · A · R2/3 · S1/2
where the geometry of a trapezoidal channel of bottom width b, side slope z (H:V) and flow depth y is:
- Flow area: A = (b + z·y) · y
- Wetted perimeter: P = b + 2y√(1 + z2)
- Hydraulic radius: R = A / P
- Top width: T = b + 2·z·y
- Mean velocity: V = (k / n) · R2/3 · S1/2
- Froude number: Fr = V / √(g · Dh), with hydraulic depth Dh = A / T
Variable definitions:
- Q — design (peak) flow rate, cfs or m³/s
- k — unit conversion constant: 1.486 for US customary units, 1.0 for SI
- n — Manning’s roughness coefficient (varies with vegetation retardance and the VR product)
- S — longitudinal channel slope, ft/ft or m/m
- g — gravitational acceleration, 32.2 ft/s² (9.81 m/s²)
Because grass bends over as flow increases, n is not constant. The calculator selects a retardance class (A–E) for the vegetation, then iterates Manning’s n against the VR product (velocity × hydraulic radius) until the normal depth converges. It then computes the Froude number to classify the flow regime (subcritical Fr < 0.95, critical 0.95–1.05, supercritical > 1.05) and compares the velocity to the permissible limit for erosion control.
Conveyance swale versus bioswale
This calculator sizes the hydraulic conveyance section under steady, uniform flow. It can evaluate a vegetated or dirt-lined swale, but it does not credit infiltration, pollutant removal, check dams, engineered soil media, or an underdrain.
For a water-quality bioswale, first confirm the conveyance and erosion checks here, then evaluate storage, drawdown, soil, and underdrain requirements with the bioretention underdrain calculator and the locally adopted stormwater BMP criteria.
Permissible velocities for grass-lined channels
Maximum velocities (ft/s) for established vegetation on erosion-resistant soils, by retardance class and longitudinal slope. Use the next-lower value for easily eroded soils, and confirm against your local design manual.
| Retardance class | Typical vegetation | Slope 0–5% | Slope 5–10% | Slope > 10% |
|---|---|---|---|---|
| A | Very dense, unmowed grass (> 24 in) | 8.0 ft/s | 7.0 ft/s | 6.0 ft/s |
| B | Tall fescue / native mix (8–24 in) | 7.0 ft/s | 6.0 ft/s | 5.0 ft/s |
| C | Bermuda / Kentucky bluegrass (6–12 in) | 6.0 ft/s | 5.0 ft/s | 4.0 ft/s |
| D | Short mowed grass (2–6 in) | 5.0 ft/s | 4.0 ft/s | 3.0 ft/s |
| E | Very short / sparse grass | 4.0 ft/s | 3.0 ft/s | 2.5 ft/s |
Source: FHWA HEC-22 (Table 7-5) and USDA NRCS guidance for retardance classes after Chow (1959). For SI, multiply by 0.3048 to convert ft/s to m/s.
Frequently asked questions
What is a vegetated (grass) swale and what does this calculator do?
A vegetated swale is a shallow, grass-lined open channel that conveys stormwater while filtering and infiltrating runoff. This calculator solves Manning’s equation for the normal (uniform-flow) depth, mean velocity, hydraulic radius, Froude number and capacity of a trapezoidal swale at your design flow, then checks the velocity against permissible-velocity limits for the chosen vegetation so you can confirm the grass lining will not erode.
How is Manning’s n chosen for a grass-lined swale?
For grass linings Manning’s n is not a single fixed value — it falls as flow gets faster and deeper because the grass bends over. The calculator first picks a retardance class (A–E) from the vegetation type (Chow 1959, Table 5-6), then iterates Manning’s n against the product of velocity and hydraulic radius (the VR product) using HEC-22 Table 7-6 relationships. Class C medium-grass turf, for example, ranges from about n = 0.25 at low VR down to n ≈ 0.05 at high VR.
What flow velocity is safe for a grass swale?
Permissible velocity depends on the vegetation’s retardance class, the longitudinal slope and the soil. On erosion-resistant soils HEC-22 Table 7-5 gives roughly 6 ft/s for Class C grass on 0–5% slopes, dropping to 4 ft/s on slopes over 10%; denser Class A vegetation tolerates up to about 8 ft/s. As a rule of thumb, keep velocity below about 5 ft/s (1.5 m/s) for ordinary turf. Above the permissible limit you should flatten the slope, widen the channel, use denser vegetation, or switch to a hard or reinforced lining.
Why does the calculator report the Froude number and residence time?
The Froude number tells you the flow regime: subcritical (Fr < 1) is calm and stable and is preferred for swales, while supercritical (Fr > 1) is fast and turbulent and can scour the grass. Residence time (swale length ÷ velocity) is the contact time available for filtration and settling; roughly 5–9 minutes is a common minimum target for water-quality treatment, so a longer or flatter swale improves treatment.
What This Solves
Sizes a grass-lined or vegetated open channel (swale) to convey stormwater at non-erosive velocities using Manning's equation with vegetation-adjusted roughness.
Best Used When
- You are designing a vegetated stormwater conveyance channel for a parking lot, roadway, or low-impact development site
- You need to calculate flow depth, velocity, and residence time for a grass swale
- You want to verify that flow velocities are low enough to prevent erosion and allow pollutant settling
Do NOT Use When
- You are designing a hard-lined or riprap-lined channel instead of a vegetated swale — Use Manning's Channel Calculator
- You need detailed guidance on channel lining selection and permissible shear stress — Use Channel Lining Design Calculator
- You need a surface trench drain with grates rather than an open vegetated channel — Use Trench Drain Calculator
Key Assumptions
- Flow is uniform and steady along the swale length
- Vegetation is healthy and maintained at the specified height and density
- Manning's roughness is based on empirical correlations for grass retardance classes
- The cross-section (bottom width, side slopes) is constant along the swale
- Infiltration during flow is not accounted for (conservative for capacity)
Input Quality Notes
Vegetation type and grass height directly affect roughness. Use conservative (higher) roughness values for design, and verify that the selected vegetation can be established and maintained on-site.
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Last verified: February 2026