Calculate flow rate, velocity, and Froude number in open channels using Manning's equation. Supports rectangular, trapezoidal, triangular, and circular shapes.
Manning's equation V = (1/n) R²ᐟ³ S¹ᐟ² is the most widely used formula for estimating steady uniform flow in open channels, storm drains, irrigation canals, and natural streams. Combined with q = VA, it gives the discharge for any channel shape when the bed slope, roughness, and water depth are known.
This calculator supports four cross-section shapes: rectangular, trapezoidal, triangular, and circular (part-full pipe). It computes the flow area, wetted perimeter, hydraulic radius, velocity, discharge, Froude number, specific energy, bed shear stress, and critical depth. The Froude number tells you whether the flow is subcritical (Fr < 1) or supercritical (Fr > 1) — a critical distinction for hydraulic design.
Manning's n presets cover lining materials from glass (n = 0.010) to heavy brush (n = 0.050). Five scenario presets model typical applications: storm drains, irrigation canals, roadside ditches, concrete flumes, and river sections. The depth-vs-flow table shows how capacity grows non-linearly with depth.
Use this calculator when you need a quick normal-flow estimate for a ditch, canal, storm drain, or partially full conduit.
It is useful for preliminary hydraulic sizing, comparing lining roughness, and checking whether a geometry and slope combination keeps the flow in a sensible velocity and Froude-number range. That makes it a practical first-pass tool before you move to a full backwater or unsteady-flow model.
Manning's equation: V = (1/n) × R^(2/3) × S^(1/2) Discharge: Q = V × A Froude number: Fr = V / √(gA/T) Specific energy: E = y + V²/(2g) Bed shear: τ = γRS Where: • V = mean velocity (m/s), n = Manning's roughness • R = A/P = hydraulic radius (m) • A = flow area (m²), P = wetted perimeter (m), T = top width (m) • S = bed slope (m/m), g = 9.81 m/s²
Result: Q = 3.65 m³/s, V = 1.04 m/s, Fr = 0.31
A = (2+1.5×1)×1 = 3.5 m². P = 2 + 2×1×√(1+1.5²) = 5.61 m. R = 3.5/5.61 = 0.624 m. V = (1/0.022)×0.624^(2/3)×0.001^(0.5) ≈ 1.04 m/s, so Q ≈ 1.04 × 3.5 = 3.65 m³/s.
Manning's equation is most useful for steady, uniform gravity flow where slope, roughness, and section shape are already known or can be estimated. It is a strong screening tool for channel capacity, especially when you want to compare how much discharge changes with depth, lining, or bed slope.
The biggest mistakes are using Manning's equation outside its assumptions, mixing geometry inputs, and choosing an unrealistic roughness coefficient. Natural channels are especially sensitive to the chosen n-value, and non-uniform features such as backwater, control structures, or hydraulic jumps require a broader energy or momentum analysis.
It applies to steady, uniform, turbulent flow in open channels and gravity-fed pipes. It is not valid for pressurized pipes, laminar flow, or rapidly varied flow (use energy/momentum equations instead).
Use published tables (Chow 1959, HEC-RAS manual). For lined channels, n is well-defined (0.010–0.015). For natural streams, n depends on bed material, vegetation, and channel irregularity — 0.025 to 0.070+.
Fr < 1: subcritical (slow, deep, tranquil). Fr = 1: critical flow. Fr > 1: supercritical (fast, shallow, shooting). Hydraulic jumps occur at the transition from super- to subcritical.
The calculator uses circular-segment geometry. Peak velocity and discharge in a circular pipe occur at about 81% and 93% full, respectively — not at 100% full.
That requires iterating the depth (normal-depth problem). Use this table to find the depth where Q matches your target, or use successive refinement.
Shear stress τ determines whether the channel lining can resist erosion. Permissible shear for grass is ~30–70 Pa; for bare soil 1–3 Pa; for concrete effectively unlimited.