Laboratory Tilting Hydraulics Flume
Glass-walled rectangular flume (0.30 m width, 8.0 m length) with variable slope control.
Civil Engineering / Hydraulic Jump Energy
FREE TO EXPLORELABORATORY 29 · CIVIL ENGINEERING
Hydraulic Jump Characteristics & Energy Dissipation in Open Channel Flow (Bélanger Equation)
Investigate hydraulic jump formation, measure initial and sequent flow depths, compute head loss and energy dissipation efficiency, and verify the classical Bélanger momentum equation in a tilting flume. Explore interactive structural mechanics, materials simulation, and civil engineering telemetry.
STRUCTURAL MATERIALS · MECHANICS · GEOTECHNICAL · HYDRAULICS · HIGHWAYS · SURVEYING
Your virtual civil engineering laboratory.
MEASURED SEQUENT DEPTH RATIO Y_2/Y_1—
CIVIL INFRASTRUCTURE TELEMETRY
Ready to sample with Predictor F(Fr_1) = 2.5 ratio.
Adjust Predictor F(Fr_1), then execute civil engineering measurement.
Civil engineering telemetry is evaluated rigorously using 64-bit IEEE 754 precision. Residuals reflect ordinary least-squares regression across successive observations. Continuous data structures support high-fidelity structural mechanics and geotechnical continuum modeling.
Civil engineering assumptions and boundary condition limits
The civil engineering physical models apply within the specified calibrated operational window (1.5 to 4.5 ratio). Evaluated in an 8-meter tilting flume with adjustable sluice gate and tailwater weir. Linearized relationship correlates measured depth ratio directly to the Bélanger predictor with slope 1.0000.
Laboratory apparatus & testing equipment.
Upstream Sluice Gate with Precision Rack-and-Pinion
Sharp-edged vertical gate generating high-velocity supercritical flow sheets.
Downstream Adjustable Tailwater Weir
Controls backwater depth to position and stabilize the hydraulic jump in the flume observation zone.
Twin Digital Hook-and-Point Vernier Gauges
Simultaneously measures initial depth y_1 and sequent depth y_2 to ±0.05 mm precision.
Total Head Pitot-Static Tube
Traverses flow depth to record upstream and downstream velocity head profiles.
Electromagnetic Flume Discharge Flowmeter
Measures total volumetric discharge Q to ±0.5% reading accuracy.
FOLLOW THE METHOD
A reason behind every step.
Investigate hydraulic jump formation, measure initial and sequent flow depths, compute head loss and energy dissipation efficiency, and verify the classical Bélanger momentum equation in a tilting flume. Standardized parameter settings: 1.5, 2.0, 2.5, 3.0, 3.5, 4.0 ratio.
01
Flume Bed Leveling & Sluice Gate Calibration
Set flume horizontal; zero hook gauges at flume floor datum; open sluice gate to initial test aperture (e.g. 20 mm).
02
Supercritical Flow Generation
Start recirculation pump; adjust discharge Q to establish high-velocity supercritical flow beneath the sluice gate.
03
Jump Stabilization via Tailwater Control
Raise downstream tailwater weir until a stable, stationary hydraulic jump forms in the middle glass inspection section of the flume.
04
Initial Depth & Velocity Measurement
Position upstream hook gauge immediately upstream of jump roller; record supercritical flow depth y_1; log upstream velocity v_1 = Q / (B · y_1); compute Fr_1.
05
Sequent Depth Measurement
Position downstream hook gauge immediately downstream of the surface roller where water surface becomes smooth and subcritical; record sequent depth y_2.
06
Systematic Variation & Energy Loss Calculation
Adjust gate aperture and pump discharge across six systematic Froude conditions (predictor = 1.5 to 4.5); record y_1, y_2; calculate energy loss ΔE.
YOUR NOTEBOOK · 0 OBSERVATIONS
Turn measurements into civil engineering insight.
Points are your recorded observations. The solid regression line validates Hydraulic Jump Energy mathematical scaling.
LINEAR REGRESSION FIT · y = mx + b
y_2/y_1 = 1.0000 · [0.5(√(1+8Fr_1^2)-1)]
| # | Bélanger Theoretical Predictor F(Fr_1) (ratio) | Measured Sequent Depth Ratio y_2/y_1 (ratio) | Bélanger predictor 0.5·(√(1+8Fr₁²) - 1) | Measured sequent depth ratio y₂/y₁ | Remove |
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CHECK YOUR UNDERSTANDING
Explain what the civil engineering metrics mean.
A hydraulic jump occurs only when the upstream flow is:
The classical Bélanger equation relates conjugate depths in a horizontal rectangular channel according to:
The energy dissipated as heat and turbulence across a rectangular hydraulic jump is given by:
The optimal Froude number range for a well-behaved, highly efficient steady hydraulic jump is:
THEORY AND STRUCTURAL CONTEXT
Civil engineering background & physical principles.
A hydraulic jump is a rapid, highly turbulent open-channel flow phenomenon occurring when supercritical flow (Froude number Fr > 1) abruptly transitions to subcritical flow (Fr < 1). In hydraulic infrastructure—including spillway stilling basins, sluice gate chutes, and canal drop structures—hydraulic jumps are intentionally generated as primary energy dissipators to convert catastrophic kinetic energy into internal thermal turbulence, preventing severe downstream bed scour and riverbank erosion. Applying the one-dimensional momentum conservation equation across the control volume while neglecting boundary friction yields the classical Bélanger equation (1828) relating initial supercritical depth y_1 to subcritical sequent (conjugate) depth y_2: y_2 / y_1 = 0.5 · [√(1 + 8·Fr_1²) - 1], where upstream Froude number Fr_1 = v_1 / √(g·y_1). Specific energy drops dramatically across the jump: head loss ΔE = E_1 - E_2 = (y_2 - y_1)³ / (4·y_1·y_2), representing macro-turbulent roller energy dissipation. Depending on initial Froude number Fr_1, jumps are categorized as undular (1.0 < Fr_1 < 1.7), weak (1.7 < Fr_1 < 2.5), oscillating (2.5 < Fr_1 < 4.5), steady (4.5 < Fr_1 < 9.0), or strong/choppy (Fr_1 > 9.0). In this laboratory flume experiment, supercritical flow is discharged beneath an adjustable sluice gate, and a downstream tailwater weir forces hydraulic jump stabilization to verify conjugate depths and energy dissipation efficiency.
y_2/y_1 = 1.0000 · [0.5(√(1+8Fr_1^2)-1)]
Evaluated in an 8-meter tilting flume with adjustable sluice gate and tailwater weir. Linearized relationship correlates measured depth ratio directly to the Bélanger predictor with slope 1.0000.