| Case | Type | L (m) | H (m) | Cd | H2 (m) | Q free (m³/s) | Q corrected (m³/s) |
|---|---|---|---|---|---|---|---|
| A | Ogee | 20.00 | 1.50 | 2.10 | 0.40 | 77.159 | 72.881 |
| B | Sharp | 6.00 | 0.45 | 0.62 | 0.10 | 1.524 | 1.454 |
| C | Broad | 12.00 | 0.80 | 1.70 | 0.00 | 14.605 | 14.605 |
- Sharp-crested (rectangular): Q = (2/3)·Cd·L·√(2g)·He^(3/2)
- Ogee / Broad-crested rating form: Q = Cd·L·He^(3/2)
- Optional submergence (Villemonte-style): Qs = Qf·(1 − (H2/H)^n)^β
- Select your unit system to match field measurements.
- Choose the spillway or weir type that matches crest geometry.
- Enter effective crest length and upstream head over crest.
- Provide a discharge coefficient from standards or calibration.
- Enable velocity head only when approach velocity is known.
- Enable submergence when downstream level affects overflow.
- Click Calculate, then download the CSV or PDF report.
1) Why spillway discharge matters
Spillway capacity controls the maximum reservoir release during floods and helps prevent overtopping. For many dams, the design flood can require discharges ranging from tens to thousands of cubic meters per second, depending on catchment size, reservoir routing, and freeboard. Reliable discharge estimates support gate operation planning, emergency action triggers, and safe downstream conveyance.
2) Head definition and measurement
Discharge is highly sensitive to the upstream head over crest because the governing equations scale with the head to the 3/2 power. A 10% increase in head typically raises free-flow discharge by roughly 15%. Use consistent reference levels, correct for approach flow when velocity head is significant, and document how the head was measured (staff gauge, pressure sensor, or survey).
3) Coefficients and crest geometry
Coefficients represent real losses and crest shape effects. Ogee and broad-crested crests are often rated using a compact form Q = Cd·L·H^(3/2), where the coefficient embeds geometry and energy effects. Sharp-crested sections use Q = (2/3)·Cd·L·√(2g)·H^(3/2). Select coefficients from approved standards or calibrated rating curves.
4) Submergence and drowned flow
When the downstream water level rises, the nappe can become submerged and the effective discharge decreases. The optional Villemonte-style reduction factor uses the ratio H2/H with exponent n and parameter β. As H2/H approaches 1.0, the reduction factor trends toward zero, indicating strong drowning and the need for operational or hydraulic review.
5) Reporting and quality checks
Good practice includes recording unit system, crest length assumptions, coefficient source, and any submergence adjustment. Compare specific discharge Q/L to typical crest loading ranges used for similar structures, and confirm that inputs stay within the validity range of your selected equation. Exporting CSV and PDF reports supports peer review, audit trails, and site records.
1) Which spillway type should I select?
Choose the option that matches crest geometry and rating practice: sharp-crested for thin-plate overflow, ogee for shaped crests, and broad-crested for wide crests where the head-discharge form is used in your standard.
2) What is the difference between H and He?
H is the measured upstream head over the crest. He is the effective head when velocity head is included: He = H + Va²/(2g). Use He only when approach velocity is known and meaningful.
3) How do I pick a discharge coefficient (Cd)?
Use a coefficient from your design manual, model studies, or a calibrated rating curve for the specific crest and approach conditions. Record the source and keep the coefficient consistent with the selected equation form.
4) When should I apply submergence correction?
Apply it when downstream tailwater rises high enough to influence overflow, reducing discharge compared with free flow. Enter downstream head H2 above the crest and review the reduction factor for plausibility.
5) Why does a small head change affect discharge so much?
Most overflow equations scale with head to the 3/2 power. That non-linear relationship means discharge grows faster than head, so accurate head measurement and consistent reference elevations are critical for reliable results.
6) Does crest length include side contractions?
Use the effective overflow length. If end contractions, piers, or training walls reduce flow width, adjust L accordingly. Many standards provide contraction corrections; apply them consistently with your coefficient selection.
7) Can I use this for final dam safety certification?
This tool supports preliminary checks and reporting. Final certification should follow the governing standard, include routing and tailwater analysis, and be reviewed by qualified professionals using validated coefficients and site data.