Source : E. B. Wylie, V. L. Streeter, Fluid Transients, McGraw-Hill, 1978, example 5-2, program D-1 and results D-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?
Two 610 m pipes connect a varying inflow, 16·(0.75 − 0.25·sin 0.3t) ft³/s, to a downstream reservoir, through an air valve at the high point (elevation 10.36 m). The book computes with one reach per pipe and a 0.5 s step; so does CBELIER.
| Data | Value | Status |
|---|---|---|
| Pipes: L, D, wave speed | 2 × 610 m; 0.61 m; 1,219 m/s | PUBLISHED |
| Friction factor; initial flow | 0.02; 0.34 m³/s | PUBLISHED |
| Air valve: elevation; inlet Cd; outlet Cd; opening | 10.36 m; 0.65; 0.975; 0.02 ft² | PUBLISHED |
| Downstream reservoir | 9.75 m | PUBLISHED |
| Time step; reaches per pipe | 0.5 s; 1 | PUBLISHED |
| Indicator | CBELIER | Reference | Difference |
|---|---|---|---|
| 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 % |
The head at the air valve follows the book within 0.15 m, the upstream head within 0.6 m at the oscillation peaks; the maximum air volume and the air mass are reproduced within 2 %. The air-valve law (four-regime compressible orifice) is therefore consistent.