Manning's Flow & Size the Water a Channel Carries

Manning's equation gives the velocity in an open channel as V = (1/n) × R^(2/3) × S^(1/2), where n is the roughness coefficient, R is the hydraulic radius (flow area divided by wetted perimeter) and S is the channel bed slope. Discharge is then Q = A × V, the flow area times the velocity. The tool computes the area, wetted perimeter, hydraulic radius, velocity and discharge for a trapezoidal channel from your dimensions.

For a trapezoidal channel it sets the flow area to (bottom width + side slope × depth) × depth, and the wetted perimeter to bottom width + 2 × depth × √(1 + side slope²). The hydraulic radius is area ÷ wetted perimeter. A side slope of 0 makes it a rectangular channel, so the same tool covers both shapes — just set the side slope to zero for a vertical-walled channel or lined flume.

n captures how rough the channel surface is and how much it slows the flow; smoother surfaces have a lower n and carry more water. Typical values are about 0.011–0.013 for smooth concrete, 0.013–0.017 for ordinary lined canals, 0.020–0.030 for earthen channels, and 0.030–0.050 or more for weedy or rocky ones. Choosing n for the channel's real condition — including vegetation and maintenance — is the largest source of uncertainty in the result.

The side slope is the horizontal run per unit of vertical rise of the bank — a side slope of 1.5 means the bank goes out 1.5 m horizontally for every 1 m of depth (often written 1.5:1). Steeper, more stable soils take a smaller value; loose or sandy soils need a flatter (larger) side slope to stay put. Enter 0 for vertical walls, as in a lined rectangular flume.

Discharge tells you how much water the channel carries, but velocity tells you whether the channel will survive. Too slow and silt and weeds settle out, shrinking capacity; too fast and the bed and banks erode. A common design window for earthen irrigation channels is roughly 0.3–0.9 m/s — fast enough to stay clean but slow enough not to scour. The tool reports velocity so you can check it against that window.

Discharge rises with a larger cross-section (more width or depth), a steeper bed slope, or a smoother lining (lower n). Increasing depth helps most because it raises both the flow area and the hydraulic radius. Lining an earthen channel with concrete can roughly double its capacity for the same size by cutting n. The tool lets you change each input and watch the discharge respond.

Manning's equation is an empirical formula for steady, uniform, turbulent flow in open channels, which covers most irrigation canals, field drains and natural waterways at design flow. It assumes the slope and section are roughly constant over the reach and that flow is fully turbulent. For rapidly varied flow, very steep chutes or pressurised pipes it does not apply, but for everyday farm channel design it is the standard method this tool uses.

Yes — this tool works in SI units, so enter widths and depths in metres and the bed slope as a dimensionless fraction (for example a 1-in-1000 slope is 0.001). The discharge comes out in cubic metres per second and the velocity in metres per second. The Manning coefficient itself is the SI form; if you have a value from an imperial-unit source it is the same n, because n is taken as dimensionless across both systems in common practice.