Public benchmark: 12 validation cases

Twelve published cases, re-run with every release of the calculation engine against frozen thresholds. Each case has a two-page sheet: the question, the data and where they come from, the curves, the differences and the limitations.

Latest run of the benchmark: engine 3c.26, 6 November 2026. 26 indicators checked against their frozen thresholds, 0 failures. Physical targets met: 18 of 24. Targets not met are published with the others.

Calibrated case: some parameters are fitted to the test itself. The result shows what the model can reproduce; it is not a prediction.

Verification

The calculation is compared with an exact solution (formula or independent integration). This checks that the equations are solved correctly.

Case	Question	Indicators: CBELIER / reference (difference)	Sheet
V1	Instantaneous closure: Joukowsky pressure rise and 4L/a period When a valve closes at once, the pressure rise equals a·V₀/g and lasts 2L/a. Does CBELIER reproduce both values, and the whole curve of a separately written reference computation?	Pressure rise ΔH (V₀ = 0.10 m/s): 12.24 m / 12.23 m (0.1 %) Plateau duration (2L/a = 1.00 s): 0.975 s / 1.000 s (1 time step) RMS difference to the reference curve: 2.00 % ΔH (tolerance 2 %) Suite check (higher velocity): 102.31 m / 101.63 m (0.7 %)	read PDF
V2	Gradual closure: three durations and the Michaud formula When the closure lasts less than, as long as, or longer than a wave round trip, the pressure rise changes in nature. Does CBELIER follow a reference computation in all three regimes, and the Michaud formula for slow closures?	Maximum pressure rise, tf = 0.5 s: 12.24 m / 12.26 m (−0.13 %) Maximum pressure rise, tf = 1 s: 12.24 m / 12.26 m (−0.15 %) Maximum pressure rise, tf = 4 s: 2.81 m / 2.83 m (−0.76 %) Michaud, slow closure tf = 4 s: 1.6 % Michaud, slow closure tf = 6 s: 2.3 % Michaud, slow closure tf = 10 s: 3.0 %	read PDF
V3	Mass oscillation in a surge tank After a valve closure, the level in a surge tank oscillates slowly. Does CBELIER, which computes the waves, reproduce the extreme levels given by the rigid-column equation?	Case 1: maximum level: 22.097 m / 22.096 m (0.001 m) Case 1: difference relative to the amplitude: 0.04 % (tolerance 1 %) Case 2: maximum level: 22.500 m / 22.506 m (−0.005 m) Case 2: difference relative to the amplitude: 0.15 % (tolerance 1 %) Case 3: maximum level: 22.196 m / 22.201 m (−0.005 m) Case 3: difference relative to the amplitude: 0.14 % (tolerance 1 %)	read PDF

Numerical validation

The calculation is compared with the published results of a reference work. This checks that the model gives the same answers as a recognised method.

Case	Question	Indicators: CBELIER / reference (difference)	Sheet
N1	Valve closure at the end of a pipe (Wylie & Streeter, example 3-1) Does CBELIER reproduce, instant by instant, the head at the valve computed in the reference textbook of the field?	Initial head at the valve: 143.49 m / 143.49 m (−0.00 m) Maximum head at the valve: 284.92 m / 284.87 m (0.0 %) Maximum difference over the 26 instants: 0.32 m (0.11 % of peak)	read PDF
N2	Three pipes in series (Wylie & Streeter, example 3-7) At junctions between pipes of different diameters, the wave is partly reflected. Does CBELIER reproduce the book heads at the three sections, up to the 806 m peak?	Maximum head at the valve (C): 806.0 m / 805.8 m (0.0 %) Maximum difference, 3 sections × 22 instants: 1.95 m (0.24 % of peak)	read PDF
N3	Air-inlet valve at a high point (Wylie & Streeter, example 5-2) When the pressure drops at the high point, an air valve lets air in and then expels it. Does CBELIER reproduce the head at the valve and the air volume and mass computed by the book?	Maximum head difference, air valve N2: 0.13 m Maximum head difference, upstream N1 (at peaks): 0.58 m (tolerance 0.6 m) Maximum air volume (20.28 ft³): 0.578 m³ / 0.574 m³ (0.7 %) Air mass at 12 s (0.0388 slug): 0.574 kg / 0.566 kg (1.4 %)	read PDF

Experimental validation

The calculation is compared with laboratory measurements. This checks that the model represents the physical phenomenon.

Case	Question	Indicators: CBELIER / reference (difference)	Sheet
E1	Programmed valve closure: Propson's tests (single pipe) A valve closure programmed to limit the pressure rise, measured on a long copper tube: does CBELIER reproduce the head measured at the valve and at mid-length, and above all its maximum?	Maximum head at the valve: 52.51 m / 52.88 m (−0.7 %) Initial head at the valve: 32.32 m / 32.31 m (0.01 m) Maximum difference to the curve, valve: 3.87 m Maximum difference to the curve, mid-length: 1.28 m	read PDF
E2 CALIBRATED	Y-shaped HDPE system, fast closure (University of Perugia) In an HDPE network, the viscoelastic wall damps and distorts the wave. With the Kelvin-Voigt model and unsteady friction, does CBELIER reproduce the pressures measured at the valve and at the end of a dead-end branch?	Maximum pressure rise ΔH, valve P2: 7.70 m / 7.43 m (3.7 %) RMS difference, valve P2: 0.95 m Maximum pressure rise ΔH, dead end P3: 7.85 m / 7.10 m (10.6 %) RMS difference, dead end P3: 0.92 m	read PDF
E3 CALIBRATED	Looped HDPE network, 4 sensors (University of Perugia) In a real looped network, the wave splits and reflects at every node. Does CBELIER reproduce the pressures measured at several points of a laboratory network with 800 m of pipes?	Maximum pressure rise at the valve (h5u): 20.61 m / 22.28 m (−7.5 %) Maximum pressure drop at the valve (h5u): −13.14 m / −13.42 m (2.0 %) RMS difference, h5u (2 s): 1.98 m RMS difference, h5 (2 s): 0.13 m RMS difference, h8 (2 s): 0.17 m RMS difference, h4 (2 s): 0.09 m	read PDF
E4 CALIBRATED	Steel and HDPE in series: 7 configurations (Warsaw) When a steel pipe is extended with HDPE, the pressure rise drops as the HDPE length grows. After a single adjustment on the all-steel pipe, does CBELIER predict the pressure rise of the six other configurations?	Maximum predicted difference, no. 1 to 6, HDPE 32 mm: 5.1 % (target 10 %) Maximum predicted difference, no. 1 to 6, HDPE 35.3 mm: 9.2 % (target 10 %) Configuration no. 1 (most HDPE), 32 mm: 1.84 / 1.75 (5.1 %)	read PDF
E5 CALIBRATED	Resonating surge wells: USBR laboratory rig (1952) A low-pressure network broken by baffled wells resonates when excited at its natural period. Does CBELIER reproduce the measured resonance curves, with one or two covered wells?	A: RMS difference, uncalibrated: 1.35 L/s (12 % of peak) A: RMS difference, calibrated tank: 0.65 L/s (6 % of peak) B: RMS difference, uncalibrated: 1.10 L/s (31 % of peak) B: RMS difference, calibrated tank: 0.29 L/s (8 % of peak) C: RMS difference, uncalibrated: 1.40 L/s (47 % of peak) C: RMS difference, calibrated tank: 0.46 L/s (16 % of peak)	read PDF
E6	Column separation at the valve (Simpson and Bergant, 1994) After a very fast closure, the pressure drops to vapour pressure, a cavity forms and then collapses, creating peaks higher than Joukowsky. Does CBELIER, with its cavitation model, reproduce these peaks and their timing?	Peak no. 1: 107.0 m / 113.1 m (−5.4 %) Time of peak no. 1: 0.029 s / 0.027 s (2 ms) Peak no. 2: 106.8 m / 110.2 m (−3.1 %) Time of peak no. 2: 0.388 s / 0.402 s (−14 ms) Peak no. 3: 110.9 m / 98.5 m (12.6 %) Time of peak no. 3: 0.702 s / 0.710 s (−8 ms)	read PDF

Data status in the sheets

PUBLISHED: value given by the source
READ FROM FIGURE: value read from a published figure, with its reading uncertainty
DERIVED: value computed from published data
ASSUMED: value missing from the source, chosen and flagged
CALIBRATED: value fitted to the test itself
DEFINED: value set by the definition of the case

What this benchmark does not tell you

A successful case does not guarantee a project: the quality of a study depends first on its data (wave speeds, longitudinal profile, pumps, operating laws).
CBELIER is a one-dimensional model. Three-dimensional effects, fluid-structure interaction and air dissolution are not represented.
The calibrated cases (E2 to E5) show what the model can reproduce once its parameters are fitted; they do not measure its predictive ability.
The curves in the sheets are recomputed and redrawn; digitised references are cited with their source and no third-party figure is reproduced.