Gravity flow in partially full circular pipe, rectangular, and trapezoidal channels. Solves flow from a measured depth, or normal depth from a design flow. Runs entirely offline; inputs persist in this browser via localStorage.
| Normal depth | — |
| d/D ratio | — |
| Flow area | — |
| Wetted perimeter | — |
| Hydraulic radius | — |
| Velocity | — |
| Flow | — |
| Froude number / regime | — |
| Full-pipe capacity (d/D = 1.0) | — |
| Freeboard remaining | — |
Q = (1.486/n) · A · R^(2/3) · S^(1/2) (US customary; Q in cfs, A in ft², R in ft, S in ft/ft)
Velocity is V = Q/A. Conversions: 1 cfs = 448.83 GPM = 0.6463 MGD.
For flow depth y in a pipe of diameter D, with central angle θ = 2·acos(1 − 2y/D) (radians):
A = (D²/8)(θ − sin θ) P = Dθ/2 R = A/P top width T = D·sin(θ/2)
Rectangular: A = b·y, P = b + 2y. Trapezoidal with side slope z: A = (b + z·y)·y, P = b + 2y√(1+z²), T = b + 2z·y.
Manning's can't be inverted for depth in closed form for these sections, so the tool bisects: it evaluates Q(y) at the interval midpoint and halves toward the target until the depth converges (40 iterations ≈ machine precision, a few microseconds in JS).
For circular pipe, discharge peaks at about d/D ≈ 0.94 and then decreases toward full — the last sliver of depth adds wetted perimeter faster than area. The solver searches only up to the peak; a target flow above the peak is reported as exceeding gravity capacity (the pipe would surcharge).
Fr = V / √(g·A/T), where A/T is the hydraulic depth. Fr < 1 is subcritical (tranquil, downstream control), Fr > 1 is supercritical (rapid, upstream control). Between roughly 0.9 and 1.1 the surface is unstable and wavy — depth measurements in that band are unreliable, and designers generally avoid it.