🌊 Formation of a Hydraulic Jump
A virtual re-creation of the flume experiment. Set the discharge and sluice-gate opening to launch a fast supercritical stream, then raise the tailgate until the tailwater matches the sequent depth and a stable jump stands still in the test section. Measure it, record six observations, and compute the jump characteristics.
Hands-on Mission
Use the virtual flume like a real lab bench: choose a target jump type, adjust discharge, gate opening and tailwater, then record only stable jumps. Try to collect six valid readings that cover at least three different Froude-number ranges.
Aim
To study the formation of a hydraulic jump in a rectangular channel and to determine the characteristics of the jump — sequent depths, Froude number, height, length and energy loss.
Theory
A hydraulic jump forms when a supercritical stream (Fr > 1) meets a subcritical tailwater of sufficient depth. The stream abruptly rises from its initial depth y₁ to its sequent depth y₂ through a turbulent roller, dissipating energy. For a horizontal rectangular channel the momentum equation gives the Belanger sequent-depth relation:
Fr₁ = V₁/√(g·y₁) • y₂/y₁ = ½(√(1 + 8·Fr₁²) − 1) • ΔE = (y₂ − y₁)³ / (4·y₁·y₂) • L ≈ 6.9(y₂ − y₁)
Classification by Fr₁: 1–1.7 undular · 1.7–2.5 weak · 2.5–4.5 oscillating · 4.5–9 steady · >9 strong jump.
Apparatus
Re-circulating rectangular tilting flume (10 m × 0.30 m × 0.60 m), upstream and downstream sluice gates, pump with delivery valve, pointer gauge, collecting tank & stopwatch, steel ruler.
Procedure — perform it here
Observations & Computations
Width of flume B = 0.30 m. Record at least 6 observations at different discharges / gate settings (only a stable jump can be recorded).
| No. | Q (L/s) | y₁ (cm) | y₂ (cm) | Fr₁ | y₂/y₁ | hj=y₂−y₁ (cm) | L (cm) | ΔE (m) | Type |
|---|---|---|---|---|---|---|---|---|---|
| No observations yet — form a stable jump and press “Record reading”. | |||||||||
Live Plot
Recorded points show how the sequent-depth ratio grows with Froude number. The guide curve is the Belanger relation for a rectangular channel.
Results
Questions & Precautions
What is the purpose of a hydraulic jump and its applications?
It dissipates surplus kinetic energy of supercritical flow, preventing scour downstream of spillways, sluice gates and chutes. It is also used to mix chemicals, aerate water, and raise the downstream water level for irrigation off-takes.
Why can't the energy equation be applied directly across the jump?
The jump is highly turbulent with an unknown, large energy loss in the roller, so energy is not conserved across it. The momentum equation is applied instead, giving the Belanger sequent-depth relation; the energy loss is then found as the difference E₁ − E₂ = (y₂−y₁)³/(4y₁y₂).
Jump types (undular, weak, oscillating, strong)
Undular (Fr₁ 1–1.7): surface undulations, little loss. Weak (1.7–2.5): smooth roller, ~5–18% loss. Oscillating (2.5–4.5): an unstable jet causes surface waves travelling downstream. Steady/strong (>4.5): a well-defined, stable jump dissipating 45–85% of the energy.
Precautions: ensure the sluice gate is seated properly; form the jump near the gate within the test section; vary the flow and adjust the tailgate accordingly; take readings only after the jump is steady.