Manning's Equation Calculator
Uniform flow analysis for open channels — normal depth, discharge, Froude number, and rating curves for rectangular, trapezoidal, triangular, and circular sections.
⚙️ Input Parameters
Q = (1/n) · A · Rh2/3 · S₀1/2
V = Q / A
Fr = V / √(g · yh)
yh = A / T (hydraulic depth)
📊 Results
Ready to Calculate
Select a channel shape, enter the geometry and hydraulic parameters, then click Calculate to get normal depth, velocity, Froude number, and the rating curve.
📚 Theory — Manning's Equation
Manning's equation describes uniform open channel flow — where the water surface is parallel to the channel bed and flow conditions do not change along the channel.
🔧 Manning's n
The roughness coefficient n depends on channel material. Smooth surfaces (PVC: 0.009) have lower n than rough surfaces (riprap: 0.035). Values listed in Chow (1959).
⚖️ Froude Number
Fr = V / √(g·y_h). When Fr < 1: subcritical (tranquil) flow. Fr > 1: supercritical (rapid) flow. Fr = 1: critical conditions at minimum specific energy.
📏 Hydraulic Radius
R_h = A/P_wet — the ratio of cross-sectional flow area to wetted perimeter. It governs friction and determines carrying capacity. Maximised by the hydraulically efficient section.
🌊 Normal Depth
The depth at which uniform flow occurs for given Q, n, S₀, and geometry. Solved iteratively by bisection since Manning's equation is implicit in y for non-rectangular sections.