Manning Open Channel Flow Calculator
Manning’s equation for trapezoidal, rectangular, triangular and part-full circular channels: solve for discharge, normal depth, slope or bottom width, with velocity, Froude number, critical depth and slope, shear stress, an erosion check and a rating table.
How it works
V = (k/n) × R^(2/3) × S^(1/2), k = 1.486 (US) or 1 (SI); Q = V × A; R = A ÷ P; trapezoid: A = by + ½(z₁ + z₂)y², P = b + y(√(1+z₁²) + √(1+z₂²)); circle: θ = 2·acos(1 − 2y/D), A = D²(θ − sin θ)/8, P = Dθ/2; Froude Fr = V ÷ √(g·A/T); critical depth: Q²T = gA³; shear τ = γRS; specific energy E = y + V²/2g
Manning’s equation ties the speed of water in an open channel to three things: how steep it is, how big and efficiently shaped the flow section is (the hydraulic radius, area over wetted perimeter), and how rough the surface is (the n value, from about 0.011 for plastic pipe to 0.08 for brush). Velocity times area gives the discharge. Pick what to solve for: the flow a channel carries at a given depth, the normal depth a design flow will reach, the slope needed, or the bottom width needed; the depth and width are found by iteration, the slope directly. The calculator handles trapezoids with equal or unequal side slopes, rectangles, V-ditches and part-full circular pipes. The checks follow: velocity against the lining’s erosion limit (grass swales fail above 5–6 ft/s, bare earth much sooner), the boundary shear stress γRS used in lining design, the Froude number with the unstable near-critical range, and the critical depth and critical slope that tell you whether the channel is mild or steep. The rating table shows discharge across a range of depths, and freeboard is added above the water surface for waves, debris and sediment.
Worked example
A trapezoidal grass swale with a 2 ft bottom and 3:1 sides flowing 1 ft deep at 1% slope (n = 0.030): area 2 × 1 + 3 × 1² = 5 ft², wetted perimeter 2 + 2 × √10 = 8.32 ft, hydraulic radius 0.60 ft, velocity (1.486/0.030) × 0.60^(2/3) × 0.1 = 3.53 ft/s and 17.6 cfs — subcritical (Fr 0.79) and below the 5.5 ft/s grass limit. Solving the other way, a design flow of 20 cfs in the same swale reaches a normal depth of about 1.06 ft. The critical depth for 17.6 cfs is about 0.89 ft, so the 1% slope is mild.
Sources: Chow, V.T. — Open-Channel Hydraulics (1959), Manning n tables · FHWA HEC-15 — Design of Roadside Channels with Flexible Linings · USGS — Guide for selecting Manning’s roughness coefficients (WSP 2339)
Frequently asked questions
How do I find the depth for a given flow?
Choose “Solve for: Depth” and enter the design flow. The calculator iterates Manning’s equation until the discharge matches and reports that normal depth, with the velocity, Froude number and erosion check at that depth. The same works for the slope or bottom width needed.
Which n for a mown grass swale?
0.030–0.035 for short grass at moderate depth; n rises to 0.05–0.10 in tall grass at shallow depth (retardance classes), which is what makes grass swales slow and erosion-resistant. Use “Custom n” for any value from a reference table.
What do critical depth and critical slope tell me?
Critical depth is the depth at which the flow has its minimum specific energy (Froude = 1). If the normal depth is above it the channel is mild and the flow subcritical; below it, the channel is steep and the flow supercritical, with standing waves and a hydraulic jump where it slows down. The critical slope is the slope at which normal depth equals critical depth.
Can I use it for a storm sewer or culvert flowing part full?
Yes, choose the circular pipe shape. A pipe carries its peak flow at about 94% of its diameter, slightly more than when flowing full, so the depth solver stops there and tells you when a flow exceeds the pipe’s capacity. Inlet and outlet control in culverts need a separate check.
Related calculators
Preliminary engineering estimate using standard textbook formulas; final design must be checked by a licensed engineer against local codes, soils and rainfall data.