🏄 Calibration of a Standing Wave Flume
A venturi flume in the 5 m tilting channel: the throat contraction forces the flow through critical depth, so one upstream head reading fixes the discharge — no downstream gauge needed. A hydraulic jump (the standing wave) rides just downstream of the throat. Measure head and discharge over a range of flows, determine the flume coefficient Cf, and draw its calibration curve.
Aim
To determine the coefficient of discharge for a standing-wave flume both by calculation and graphically, and to calibrate the flume by preparing its calibration curve.
Theory
critical flow at throat: Q = Cf·1.705·B·H3/2 • H = upstream head above the hump crest • 1.705 = (2/3)3/2·√g
The side contraction and bed hump reduce the specific energy margin until the flow passes through critical conditions in the throat. Because critical depth and discharge are uniquely related, the flume acts as a flow-measuring structure — a "venturi" for open channels. Downstream, the supercritical stream jumps back to the subcritical tailwater through a standing wave. Modular (free-flow) operation requires the jump to stay downstream of the throat; drowning it spoils the unique H–Q relation.
Experimental set-up
Glass-walled (Perspex) rectangular tilting-bed flume, 5 m long × 10.3 cm wide × 60 cm deep, fed by a pump; standing-wave flume insert with side contraction and hump; pointer gauge; measuring tank with stopwatch.
Flume width T = 10.3 cm Throat width B = 6.0 cm Hump height z = 2.0 cm Bed slope S₀ = 0
Procedure — perform it here
Observations & Computations
Tank area At = 0.25 m². Q = At·Δlevel/t. Cf = Q / (1.705·B·H3/2).
| No. | H (cm) | H3/2 (m3/2) | Δlevel (cm) | t (s) | Q (L/s) | Cf |
|---|---|---|---|---|---|---|
| No observations yet — set a flow, take a tank reading, then Record. | ||||||
Calibration curve — Q vs H3/2
Discussion & Precautions
Why does critical flow make the flume a flow meter?
At the critical condition the specific energy is a minimum for the given discharge, and depth and discharge are uniquely linked (q² = g·yc³). Once the throat forces the flow through critical, the upstream energy head alone fixes Q — no second gauge, no rating shifts from downstream conditions, as long as the flume runs free (modular).
What is the standing wave, and why must it stay downstream?
It is the hydraulic jump by which the supercritical jet leaving the throat rejoins the subcritical tailwater. If the tailwater rises enough to push the jump into the throat, the flow there is no longer critical — the flume is "drowned" and the one-to-one H–Q relation is lost.
Why is Cf slightly less than 1?
Friction in the approach and contraction, non-uniform velocity distribution, and streamline curvature over the hump all slightly reduce the effective energy head, so real flumes deliver a few percent less than the ideal critical-flow formula — typically Cf ≈ 0.95–0.98.
Precautions: set the flume bed to zero slope and record the bed (datum) pointer reading first; confirm the standing wave is visible downstream of the throat at every flow; read the upstream gauge where the surface is calm, clear of the drawdown; time the tank rise over at least 60 s.