Manning's Open-Channel Flow Calculator

What is Manning's equation?

Manning's equation is the standard empirical formula for the mean velocity of uniform, fully-developed turbulent flow in an open channel:

V = (k / n) · R^2/3 · S^1/2,   Q = V · A

where V is the cross-sectional mean velocity, n is Manning's roughness coefficient, R is the hydraulic radius (wetted area divided by wetted perimeter), S is the longitudinal slope of the channel invert, and k is a unit prefactor: 1.486 for Imperial units (ft, ft/s, cfs) or 1.0 for SI units (m, m/s, m³/s).

Which cross-section shapes are supported?

• Rectangular — specify the bottom width b. Top width T equals b at every depth.
• Trapezoidal — specify the bottom width b and the side slope z (horizontal : vertical). Asymmetric sections (different z left and right) are supported via the side-slope mode toggle.
• Triangular (V-notch) — specify the side slope(s) z. Bottom width is zero and the channel converges to a point at the invert.
• Parabolic — specify the bank-full top width T_full and bank-full depth y_full. The free surface follows T(y) = T_full · √(y / y_full) and the wetted area is A = (2/3) T(y) y.

What does this calculator solve for?

Three solver modes are available:

• Given depth — specify the flow depth y and the calculator returns area, hydraulic radius, velocity, discharge, Froude number, critical depth, and boundary shear stress.
• Given discharge — specify the design discharge Q and the calculator iterates (bisection) to find the normal depth that satisfies Manning's equation.
• Given Q and y — specify both flow depth and design discharge and the calculator solves Manning's equation analytically for the required bed slope S.

What does the PDF report contain?

A fully white-label one-to-two-page engineering report: project header (your company, your logo, your client and job number), the design basis with a labelled cross-section diagram, a results table (depth, area, hydraulic radius, velocity, discharge, Froude number, regime, critical depth, boundary shear stress), three figures (cross-section at design depth, longitudinal profile, and depth–discharge rating curve with the design point highlighted), engineer-facing notes and warnings, a sign-off and stamp block, and a standard disclaimer. The only Thurston attribution is one small line at the bottom of the report.

How is the depth-discharge rating curve generated?

The rating curve plots Manning's equation evaluated across the working depth range of the section at the design slope and roughness. Whenever the section carries a bank-full depth — the parabolic y_full, the top-width trapezoid y_full, or a user-supplied D_bank on rectangular / trapezoidal-by-side-slopes / triangular sections — the curve covers y ∈ (0, y_max]. Otherwise (open sections with no channel-depth ceiling) the curve brackets the design depth. The design point is marked so you can see at a glance how much capacity remains before the section is overtopped.

What are the calculator's limitations?

• Single prismatic section only — no compound channels (main + floodplain), non-prismatic reaches, or transitions.
• Uniform, steady normal flow. The equation does not capture backwater, drawdown, hydraulic-jump, or unsteady transient effects.
• Bank-full overtopping is flagged as a warning whenever a bank-full depth is defined (parabolic y_full, top-width-trap y_full, or a user-supplied D_bank on rectangular / trapezoidal-by-side-slopes / triangular sections). Once y > y_max the prismatic geometry no longer describes the flow and a compound-channel or floodplain analysis is required.
• Manning's equation is least accurate at very low Reynolds numbers (Re < ~2000) where the flow is no longer fully turbulent, and at the narrow-deep limit where the sidewall perimeter dominates the channel resistance.
• Manning's n values are calibrated for clear water at typical environmental temperatures. For sediment-laden flow, slurries, or fluids with markedly different viscosity, use the Custom fluid option and treat the resulting n as approximate.
• Sediment transport, scour, riprap sizing, and vegetated- channel n-with-depth variation are out of scope.

Check the discharge in a 4 ft wide rectangular concrete channel with a steel-formed finish at 0.30% slope when the water is flowing 1.5 ft deep. The calculator settings are:

• Unit system: Imperial
• Solver mode: Given depth y → compute Q and V
• Cross-section: Rectangular
• Bottom width b = 4 ft
• Manning's n = 0.011 (concrete, smooth)
• Slope S = 0.30% (= 0.003 ft/ft)
• Flow depth y = 1.5 ft
• Fluid: Water at 20 C (the default)

The calculator evaluates Manning's equation directly and returns:

• Wetted area A = b · y = 6.0 ft²
• Wetted perimeter P = b + 2y = 7.0 ft
• Hydraulic radius R = A / P ≈ 0.857 ft
• Mean velocity V ≈ 6.7 ft/s
• Discharge Q ≈ 40 cfs
• Froude number Fr ≈ 0.96 — near critical
• Reynolds number Re ≈ 2.1 × 10⁶ (fully turbulent)
• Boundary shear stress τ₀ = γRS ≈ 0.16 lb/ft²

The calculator flags the near-critical Froude number so the designer can verify the downstream control. Switching to Given Q and y → compute required slope S with the same depth and a discharge of 40 cfs returns S ≈ 0.003 ft/ft, confirming the closed-form slope solve is consistent with the forward Manning evaluation.

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