Sheet N2 · Numerical validation

Three pipes in series (Wylie & Streeter, example 3-7)

Source : E. B. Wylie, V. L. Streeter, Fluid Transients, McGraw-Hill, 1978, example 3-7, program C-1 and results C-2

1. The question

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?

2. The case

upstream reservoir351 m, D 0.30 m483 m, D 0.20 m115 m, D 0.15 mvalveoutletABC

Three pipes in series (351, 483 and 115 m; 0.30, 0.20 and 0.15 m) carry 0.2 m³/s towards a valve closed in 1.8 s. With the book's 0.1 s step, CBELIER adjusts the wave speeds exactly like the book's program (1,170, 1,207.5 and 1,150 m/s).

3. Data and status

DataValueStatus
Lengths351; 483; 115 mPUBLISHED
Diameters0.30; 0.20; 0.15 mPUBLISHED
Friction factors f0.019; 0.018; 0.018PUBLISHED
Wave speed; time step1,200 m/s; 0.1 sPUBLISHED
Initial flow; head at the valve0.2 m³/s; 100 mPUBLISHED
Closure law (TAU column of fig. C-2)1.8 sREAD FROM FIGURE
Roughnesses giving f at nominal flow—DERIVED

4. Results

2004006008000.00.51.01.52.0time (s)head (m)CBELIER, Abook, ACBELIER, Bbook, BCBELIER, Cbook, C
Heads at sections A, B and C: CBELIER (lines) and book values (circles).

5. Differences

IndicatorCBELIERReferenceDifference
Maximum head at the valve (C)806.0 m805.8 m0.0 %
Maximum difference, 3 sections × 22 instants1.95 m—0.24 % of peak

All three sections follow the book within less than 0.25 % of the peak. The mesh is identical to that of the book's program, which confirms the wave-speed adjustment.

6. Limitations and assumptions