Sheet N1 · Numerical validation

Valve closure at the end of a pipe (Wylie & Streeter, example 3-1)

Source : E. B. Wylie, V. L. Streeter, Fluid Transients, McGraw-Hill, 1978, example 3-1

1. The question

Does CBELIER reproduce, instant by instant, the head at the valve computed in the reference textbook of the field?

2. The case

upstream reservoirL = 600 m, D = 0.5 m, a = 1,200 m/s, f = 0.018valveoutletJ

A reservoir at 150 m feeds a 600 m pipe closed by a valve following τ = (1 − t/2.1)^1.5. The book gives the head at the valve every 0.1 s. CBELIER uses the same mesh (5 reaches, 0.1 s step).

3. Data and status

DataValueStatus
Upstream reservoir150 mPUBLISHED
Pipe: L, D, a600 m; 0.5 m; 1,200 m/sPUBLISHED
Friction factor f0.018PUBLISHED
Initial flow0.477 m³/sPUBLISHED
Closure law τ = (1 − t/2.1)^1.5—PUBLISHED
Roughness giving f = 0.018 at nominal flow0.31 mmDERIVED

4. Results

1001502002500.00.51.01.52.02.5time (s)head (m)CBELIERWylie & Streeter
Head at the valve: CBELIER (line) and book values (circles).

5. Differences

IndicatorCBELIERReferenceDifference
Initial head at the valve143.49 m143.49 m−0.00 m
Maximum head at the valve284.92 m284.87 m0.0 %
Maximum difference over the 26 instants0.32 m—0.11 % of peak

The book curve is reproduced within 0.3 m for a 285 m peak. The residual difference comes from friction: CBELIER recomputes it at every step, the book keeps it constant.

6. Limitations and assumptions