Open Channel Manning Calculator

Flow area A, wetted perimeter P and top width T are derived from the chosen section geometry before applying the SI form V = (1/n) R^(2/3) S^(1/2). For a rectangle A = b y and P = b + 2y; for a trapezoid with side slope z, A = (b + z y) y and P = b + 2 y sqrt(1 + z^2); for a triangle A = z y^2. For a part-full circular pipe the subtended angle is theta = 2 arccos(1 - 2y/d), giving A = (d^2/8)(theta - sin theta) and P = d theta / 2. Two different geometric depths then appear: Manning uses the hydraulic radius R = A/P, while the Froude number uses the hydraulic depth D = A/T, and the two are equal only for a wide rectangular section. Earth channels are normally cut at side slopes of 1.5:1 to 2:1 for bank stability, steepening toward 1:1 only in rock. The most efficient trapezoid is the half hexagon at z = 0.577, which maximises R for a given area. Circular conduits reach maximum velocity near a relative depth y/d of 0.81 and maximum discharge near 0.94, so a sewer flowing full carries slightly less than one flowing just short of full. Sanitary sewers are graded for at least 0.6 m/s to stay self-cleansing. Limitations: uniform flow is assumed, no freeboard is added, a single n is applied around the whole wetted perimeter so compound sections with floodplains must be subdivided, and above about 10 percent slope air entrainment makes the predicted velocity too high.

The geometric quantities this calculator evaluates trace back to Antoine Chezy, who in 1769 introduced the ratio of flow area to wetted perimeter while studying a canal intended to bring water to Paris. Systematic experiments on how the lining material changes resistance came from Henri Darcy and Henry Bazin, whose Dijon channel tests published in 1865 produced the first catalogue of roughness organized by surface type, covering masonry, planks, gravel and earth. Emile Ganguillet and Wilhelm Kutter published a widely used but cumbersome resistance formula in 1869, and Robert Manning offered the far simpler two-thirds power form in 1889, published in 1891, which in metric units is written directly as V = (1/n) R^(2/3) S^(1/2) with no conversion constant. The twentieth century added the framework that makes the Froude number meaningful alongside Manning. Boris Bakhmeteff set out the specific energy concept in Hydraulics of Open Channels in 1932, which established critical depth and the subcritical versus supercritical classification used to interpret channel behaviour. Ven Te Chow consolidated the field in Open-Channel Hydraulics in 1959, including the tables of geometric elements for rectangular, trapezoidal, triangular and circular sections that this calculator reproduces algebraically instead of by lookup. Routine computation moved to software when the US Army Corps of Engineers Hydrologic Engineering Center released HEC-2 in 1968 and its successor HEC-RAS in the mid-1990s, yet the required inputs remain unchanged: section geometry, a roughness coefficient and a slope.