Weir Rating (Bottom Intake + Overflow) — TEL Match

1) Global & Datums

Gravity \(g\) (m/s²)

Excel sheet uses 9.78; change if needed.

Upstream apron (Bottom intake) \(z_{a,bi}\) (masl)

Upstream apron (Overflow) \(z_{a,ow}\) (masl)

2) Geometry & Coefficients

Bottom intake crest level \(z_{c,bi}\) (masl)

Bottom intake width \(B_{bi}\) (m)

Cd (Bottom intake)

Overflow crest level \(z_{c,ow}\) (masl)

Overflow weir width \(B_{ow}\) (m)

Cd (Overflow weir)

Discharge formula used (as in the workbook): \(Q=C_d\;B\;H^{3/2}\). Ensure your \(C_d\) is consistent with SI units.

3) Target Discharges

Enter discharge targets. Solver finds water level \(WL\) so that \(Q_{bi}(WL)+Q_{ow}(WL)=Q_{target}\) and reports TEL match.

Label	Q target (m³/s)
NWL
Q2
Q5
Q10
Q25
Q50
Q100
Q200
Q500
Q1000

Detailed Table (replicates workbook columns)

Theory

For water level \(WL\) (masl) and depth above bottom‑intake apron \(y_1=WL-z_{a,bi}\), heads over crests are \(H_{bi}=\max(WL-z_{c,bi},0)\) and \(H_{ow}=\max(WL-z_{c,ow},0)\). Discharges: \[ Q_{bi}=C_{d,bi}\,B_{bi}\,H_{bi}^{3/2},\quad Q_{ow}=C_{d,ow}\,B_{ow}\,H_{ow}^{3/2}. \] Unit discharge under the bottom intake: \(q_{bi}=Q_{bi}/B_{bi}\). Specific energy near the intake (per unit width): \[ E = y_1 + \frac{q_{bi}^2}{2\,g\,y_1^2}. \] Total Energy Line at the intake: \(\mathrm{TEL}_1=z_{a,bi}+E\). With apron‑level difference \(\Delta z_a=z_{a,ow}-z_{a,bi}\), an equivalent TEL at the overflow side is \(\mathrm{TEL}_2=z_{a,ow}+(E-\Delta z_a)\). For a consistent solution \(\mathrm{TEL}_1\approx\mathrm{TEL}_2\). The solver finds \(WL\) such that \(Q_{bi}(WL)+Q_{ow}(WL)=Q_{\text{target}}\).