Flow Classification Calculator

Classify open channel flow by Froude number (subcritical / critical / supercritical) and Reynolds number (laminar / transitional / turbulent). Supports rectangular, trapezoidal, circular, and wide (2-D) channel cross-sections.

Open Channel Flow · Hydraulics

Inputs

Channel cross-section:

Specify flow as:

Bottom width b (m)

Flow depth y (m)

Mean velocity V (m/s)

Kinematic viscosity ν (m²/s)

Theory

Froude number — gravitational classification:

Fr = V / √(g × D_h)

D_h = A / T · hydraulic depth using top width T (free-surface width)

For rectangular / wide channels: D_h = y

Regime	Condition	Character
Subcritical	Fr < 1	Tranquil / streaming — downstream controls
Critical	Fr = 1	Maximum discharge for given specific energy
Supercritical	Fr > 1	Rapid / shooting — upstream controls

Reynolds number — viscous classification:

Re = V × R_h / ν

R_h = A / P · hydraulic radius; ν = μ/ρ — kinematic viscosity

Regime	Re (open channel)	Notes
Laminar	< 500	Sheet flow, overland flow; viscous forces dominant
Transitional	500 – 12 500	Intermittent turbulence; design should avoid this range
Turbulent	> 12 500	Normal for rivers, canals, drains; velocity well mixed

Note: open-channel Re thresholds differ from pipe flow (laminar below Re ≈ 2 300) because the hydraulic radius is used instead of diameter.

Channel geometry summary:

Rectangular (b = bottom width):

A = b·y · P = b + 2y · T = b · D_h = y

Trapezoidal (z = H:V side slope):

A = (b + z·y)·y · P = b + 2y√(1+z²) · T = b + 2z·y

Circular (D = diameter, θ = 2·arccos(1 − 2y/D)):

A = (D²/8)(θ − sin θ) · P = Dθ/2 · T = D·sin(θ/2)

Wide (2D) — side walls negligible:

D_h = y · R_h ≈ y · Use when b ≫ y