Swale Sizing Calculator

Sizing a swale means finding the flow depth at which the channel just carries the design discharge under normal-depth conditions. Manning equation supplies the relationship: velocity equals 1.49 divided by n, times hydraulic radius to the two-thirds power, times the square root of the longitudinal slope, and discharge is that velocity multiplied by flow area. For a triangular section with side slopes of z horizontal to 1 vertical, the area equals z times depth squared, the wetted perimeter equals 2 times depth times the square root of 1 plus z squared, and the top width equals 2 z d. Discharge therefore rises roughly as depth to the eight-thirds power. There is no algebraic inverse for depth, which is why the solution is obtained by iteration rather than a closed formula. The roughness coefficient carries most of the design uncertainty. Mowed turf runs about 0.025 to 0.030, medium grass 0.030 to 0.040, and dense unmowed meadow 0.040 to 0.060. Roughness in a grass-lined channel is not even constant with depth: n falls sharply once flow depth exceeds the vegetation height and the stems lie over. Practical constraints include longitudinal slopes of 1 to 6 percent, side slopes of 3:1 or flatter so mowing equipment can operate safely, freeboard of 0.25 to 0.5 feet above the design water surface, and velocity kept below roughly 4 to 5 feet per second so the grass lining is not scoured. Water quality swales are sized additionally for residence time, often around 9 minutes at the treatment flow.

The hydraulic core of swale design is the uniform flow formula. Robert Manning, an Irish engineer who served as chief engineer of Ireland's Office of Public Works, presented the relationship to the Institution of Civil Engineers of Ireland in 1889 and published it in 1891, offering it as a simpler fit to existing gauging data than the several competing formulas then in circulation. Philippe Gauckler had proposed an essentially equivalent expression in France in 1867, and Albert Strickler worked out the relation between roughness and grain size in Switzerland in 1923, so the equation is sometimes properly called the Gauckler-Manning-Strickler formula. Grass-lined channels became a distinct design subject through soil erosion control work in the United States following the Dust Bowl. The Soil Conservation Service, established in 1935 and now the Natural Resources Conservation Service, published permissible velocity data and vegetal retardance classes for grassed waterways that remain the backbone of the subject. The Federal Highway Administration issued its roadside channel guidance as Hydraulic Engineering Circular 15, whose editions from the mid-1970s onward shifted the design basis from permissible velocity to permissible tractive shear stress. The water quality role arrived later: the Environmental Protection Agency's Nationwide Urban Runoff Program, reported in 1983, documented pollutant loads in stormwater and prompted state manuals through the 1990s to recommend vegetated swales and bioswales as treatment practices rather than as conveyance alone.