EN 752-4:2012 open-channel gutter and swale design via Manning's equation — normal depth iteration, Froude number, velocity limits. Combined with Q = C·i·A Rational Method for pipe network sizing and HGL check.
Free preview: Q, Tc, C, DN, y_n, Fr. Upgrade to Pro or Civil for pipe sizing table, HGL analysis, and export.
The gutter/swale section design follows EN 752-4:2012 §6.4 (Drain and Sewer Systems Outside Buildings — Hydraulic Design and Environmental Considerations). Manning's equation is used for normal depth calculation. Velocity limits are per EN 752-4 Table 3: minimum 0.3 m/s (self-cleansing for gutters) to 3.0 m/s maximum (erosion). Pipe sizing uses the Rational Method Q=CiA with Manning circular pipe full-flow, with DN candidates 150–900 mm.
Normal depth y_n is the depth at which Manning's uniform-flow equation Q = (1/n)·A·R^(2/3)·S^(1/2) is satisfied. For each section type (triangular, trapezoidal, rectangular), A and hydraulic radius R = A/P are functions of y. The calculator uses Newton-Raphson iteration to solve for y_n given Q, n, and S.
The Froude number Fr = V / sqrt(g·A/T) classifies the flow regime. Fr < 1 is subcritical (tranquil) flow — stable and typical for urban drainage. Fr > 1 is supercritical (rapid) flow which can cause hydraulic jumps and surging. EN 752-4 recommends subcritical flow (Fr < 1) in urban drainage channels.
Triangular: kerb gutters and road channels (z = side slope run:rise, e.g. z=25 for typical UK road gutter). Trapezoidal: grass-lined swales and roadside ditches (z = 2–4 typical). Rectangular: concrete channels and lined drains. The calculator supports all three. For trapezoidal, specify both base width b and side slope z.
The gutter section handles the overland flow path and surface drainage. Once flow reaches a catchpit or inlet, it enters the underground pipe system. The pipe sizing uses Q=CiA runoff from the catchment area, Manning's equation for full circular flow, and selects the minimum standard DN (150–900 mm) that satisfies the design Q with self-cleansing velocity ≥ 0.6 m/s.
The Hydraulic Gradient Line (HGL) check verifies that the pipe does not surcharge under design flow. HGL = inlet invert + elbow loss (K=0.9 at 90° bend) + friction loss (S×L). The pipe crown elevation (cover + D) must exceed the HGL rise. PASS = no surcharging. FAIL = pipe operating under pressure — increase slope or DN.