Open Channel Flow — 3D

OpenHydroLab · Geometry, 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

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

Water body and channel are drawn to true scale (no exaggeration). 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.