Open Channel Normal Depth Calculator

Find the normal depth, velocity, and flow regime for uniform flow in a rectangular or trapezoidal channel using Manning’s equation.

Flow rate

Flow unit

Channel shape

Bottom width b (ft)

Channel slope S

Slope unit

Manning’s nDefault 0.013 for finished concrete.

Normal Depth (Uniform Flow)

Item	Value

How the calculation works

Manning’s equation (US units)
Q = (1.486 / n) × A × R^2/3 × S^1/2
Rectangular: A = b·y, P = b + 2y
Trapezoidal: A = (b + m·y)·y, P = b + 2y·√(1 + m²)
R = A / P (hydraulic radius)
The depth y is found by bisection: Q(y) increases with y, so the solver narrows the bracket until Q(y) matches the target flow.
Velocity V = Q / A
Froude number Fr = V / √(g × D_h), D_h = A / T (T = top width), g = 32.2 ft/s²
Fr < 1 subcritical · Fr = 1 critical · Fr > 1 supercritical

Channel material	Typical Manning’s n
Finished concrete	0.012 – 0.014
PVC / HDPE pipe	0.009 – 0.011
Corrugated metal	0.022 – 0.026
Earth, straight	0.020 – 0.025
Gravel	0.025 – 0.035

Notes & limitations

Manning’s equation with the 1.486 US-units constant is the standard open-channel uniform-flow relation (Chow, Open-Channel Hydraulics; Chin, Water-Resources Engineering). Normal depth assumes uniform flow — long prismatic channel, constant slope, no backwater.

Normal depth only exists under uniform-flow conditions. Near drops, constrictions, culverts, or downstream controls the real depth follows a gradually-varied-flow profile instead.
Supercritical results (Fr > 1) are sensitive to small changes in slope and roughness — confirm with a gradually-varied-flow check before designing on them.
The n value dominates the answer. Pick it for the actual channel condition (age, sediment, vegetation), not just the material.
This tool does not check freeboard or channel capacity above the computed depth — size the channel with freeboard per project criteria.

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