Open Channel Flow — 3D

Geometry, Manning uniform flow, velocity distribution & Froude number

Channel shape

Geometry

Bottom width b

Side slope m (mH:1V)

Diameter d

Flow depth y

Bed slope S₀

Flow

Mean velocity V

Uniform flow (Manning)

Manning n

In SI units, : Manning n is the inverse of the Strickler coefficient.

Flow calculator

Solve for

Uses continuity to relate discharge, velocity and area. Enter the other known values with the controls above.

Velocity profile model

Show

Cross-section slice + dimensions Velocity profile arrows Surface drift particles Throw stones (wave / Froude demo)

Worked examples

Aha demo: press Example 3 (waves), switch to the Plan view and watch the ripples: their leading edge fights upstream at c − V = 2.93 m/s — downstream can send "news" upstream, so the flow is downstream-controlled. Now slide V up past c = 4.43 m/s: the circles fold into a Froude wedge of half-angle sin θ = 1/Fr — the open-channel Mach cone. No information travels upstream any more: the flow has gone supercritical.

Geometry elements

Flow area A
Wetted perimeter P
Hydraulic radius R = A/P
Top width T
Hydraulic depth D = A/T

Velocity distribution (checks itself)

Surface velocity uₛ
∫u dA ÷ (V·A)
β = ∫u²dA / V²A
α = ∫u³dA / V³A

Flow & regime

Discharge Q = V·A
Reynolds Re = VR/ν
Wave celerity c = √(gD)
Wave speed downstream V+c
Wave speed upstream V−c
Froude number Fr = V/√(gD)
Froude wedge ½-angle θ

SUBCRITICAL

Uniform-flow reference

Normal depth y_n (Manning)
Critical depth y_c (Fr = 1)
Critical slope S_c
Friction slope S_f at y_n
Bed shear τ₀ at y_n
Gravity drive per metre
Friction resistance per metre
Uniform-flow force balance

MANNING REFERENCE

The normal-depth reference uses the current discharge, bed slope and roughness. Critical depth depends on discharge and geometry only. At normal depth, the force-balance ratio is one.

Water body and channel are drawn to true scale (no exaggeration). The translucent water-surface layer carries the surface shimmer and drift particles; flow regime is shown in the Flow & regime panel. Ripple speeds are exact — radius grows at c while the centre is carried at V; ripple amplitude and the faint surface shimmer are cosmetic. α, β above are computed by numerical integration of the chosen profile — for the linear profile they return the classic linear-profile values α = 2, β = 4/3 exactly.