This simulator finds the free-surface normal depth in a rectangular flume using the Manning equation. Adjust discharge, channel width, bed slope, Manning roughness, reach length and sidewall height, and compare the solved normal depth against critical depth, Froude number and the channel's physical wall capacity.
• A real-time 3D cutaway workbench of the flume inlet and distribution screen, the adjustable rectangular bed, transparent sidewalls with the free surface, three traversing point gauges, a bed-lining roughness sample, a normal/critical depth comparator and a free outfall measurement station, with home view, focus-selected-part, full-enclosure toggle, exploded view, auto-rotate, expand and show/hide labels controls. • Six laboratory controls: imposed discharge (0.005–2 m³/s), clear channel width (0.2–3 m), bed slope S₀ (0.0002–0.03 m/m), Manning roughness n (0.009–0.04 s/m⅓), modeled reach length (5–50 m) and sidewall height above bed (0.3–2 m). • Playback controls: pause/resume, 0.1 s and 1 s step advances, and four speeds. • A Curves & measurements tab with a discharge-vs-depth chart (normal-depth marker), a depth/discharge history chart, the full equation set (wetted geometry, Manning equation, Froude number, critical depth, specific energy, conjugate depth) and snapshot readouts. • An Experiments tab with four guided fixtures (mild-slope reference, steep smooth flume, higher resistance, insufficient wall capacity) and a Model verification bench with an independent-check run, timestamped event log and copyable trial report. • A Learn & assess tab with guided lessons, a knowledge-check quiz with reset, and a written model-scope statement with a reference link.
For steady, uniform flow in a prismatic rectangular channel, the SI Manning equation Q = (1/n)·A·R^(2/3)·√S₀ relates discharge to wetted area A, hydraulic radius R = A/P and bed slope S₀. Because A and P both depend on depth y, the simulator numerically searches for the single normal depth that satisfies this relation for the selected discharge, width, roughness and slope — increasing roughness n at fixed discharge raises the solved normal depth, as shown in the 'Higher resistance' experiment.
The Froude number Fr = V/√(gy) then compares mean velocity with shallow-water wave speed: normal depth above critical depth yc = [(Q/b)²/g]^(1/3) is subcritical (Fr < 1), while the 'Steep smooth flume' experiment (low roughness, steep slope) drives Fr above 1.
Freeboard is wall height minus the solved normal depth; a negative value flags that the uniform-flow solution exceeds the physical sidewalls, as in the 'Insufficient wall capacity' experiment — this is a warning, not a solved overflow-routing calculation. The conjugate-depth reference (Fr₁-based momentum relation) is shown only for supercritical flow as an optional comparison — it does not claim a hydraulic jump has actually formed in the flume.
This is a steady-uniform-flow model only: it excludes gradually varied water-surface profiles, inlet/outfall boundary solutions, sediment transport, hydraulic-jump location and overflow routing. The near-critical band |Fr − 1| < 0.03 is a display guide, and bed slope/section dimensions are visually scaled for the drawing.
Normal depth is the flow depth at which the Manning equation Q = (1/n)·A·R^(2/3)·√S₀ balances gravity and bed-friction resistance for steady, uniform flow. The simulator numerically solves for this depth given the selected discharge, channel width, roughness and slope.
Froude number Fr = V/√(gy) compares mean flow velocity with shallow-water wave speed. Fr below 1 (subcritical) means normal depth exceeds critical depth; Fr above 1 (supercritical) means the flow is faster and shallower than critical, as shown in the "Steep smooth flume" experiment.
It flags that the solved normal depth exceeds the sidewall height — a warning that the uniform-flow reference solution is not physically containable at that wall height. The simulator does not calculate overflow routing or the resulting downstream behavior.
No. The conjugate-depth reference uses momentum theory but is shown only as a reference for supercritical flow — this uniform-flow model does not solve for whether or where an actual hydraulic jump occurs.