Source : E. B. Wylie, V. L. Streeter, Fluid Transients, McGraw-Hill, 1978, § 9-4, fig. 9-20 (Propson's tests, University of Michigan)
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?
A constant-head reservoir feeds a 1,228 m copper tube. At the downstream end, a servo valve reduces the velocity from 0.34 to 0.03 m/s within three wave round trips (4.44 s), following an opening law designed to keep the pressure rise low. Head is measured at the valve and at mid-length. In CBELIER the tube is split into two reaches at measuring point M; the opening law is imposed by a scenario.
| Data | Value | Status |
|---|---|---|
| Tube length (4,030 ft) | 1,228 m | PUBLISHED |
| Inside diameter (0.95 in) | 24.1 mm | PUBLISHED |
| Initial and final velocity (1.1 → 0.1 ft/s) | 0.34 → 0.03 m/s | PUBLISHED |
| Manoeuvre duration (3L/a) | 4.44 s | PUBLISHED |
| Upstream reservoir head (139 ft, ± 1 ft) | 42.37 m | READ FROM FIGURE |
| Initial head at the valve (106 ft, ± 1 ft) | 32.31 m | READ FROM FIGURE |
| Valve opening law τ(t) (± 0.03) | 7 points | READ FROM FIGURE |
| Wave speed 3L/Tf (consistent with 2,709 ft/s in fig. 9-22) | 830 m/s | DERIVED |
| Friction: roughness derived from the 139 − 106 ft drop | 0.025 mm | DERIVED |
| Zero-head outlet, 10 m dummy downstream pipe | — | ASSUMED |
| Indicator | CBELIER | Reference | Difference |
|---|---|---|---|
| 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 | — | — |
The maximum at the valve, the design quantity, is reproduced within 1 %. The largest differences lie in the steep fall around t = 4 s, where a shift of a few hundredths of a second is enough, and both the opening law and the curves are read from a figure.