Calculator inputs
Fill in the fields, then click Calculate. Use optional sections for contraction allowances and approach velocity head.
Formula used
This tool sizes crest length using the standard overflow weir relationship:
- Q = C × Le × H3/2
- Le = Q / (C × H3/2)
Where:
- Q is design discharge (m³/s or cfs).
- C is the weir coefficient (depends on crest shape and approach).
- H is total head over the crest (includes optional velocity head).
- Le is effective crest length (accounts for contractions).
How to use this calculator
- Pick your unit system (Metric or US Customary).
- Enter design discharge Q and head over crest H.
- Set coefficient C based on your spillway standard.
- Optionally add approach velocity to include velocity head.
- Enable contractions for bays and pier/abutment adjustments.
- Click Calculate and export results if needed.
Project context and design intent
Spillway crest length is selected to safely pass the controlling flood without overtopping critical embankments or exceeding allowable upstream levels. This calculator supports early sizing by linking discharge capacity to head and an assumed weir coefficient. Treat results as a starting point for concept layouts, comparative options, and preliminary cost estimates.
Hydraulic basis for crest sizing
The computation uses the overflow weir relationship Q = C × Le × H^(3/2), where Le is the effective crest length and H is the total energy head above the crest. Because H is raised to the 3/2 power, small increases in head can significantly reduce required crest length. Conversely, conservative heads can drive longer crests and wider structures.
Selecting the coefficient and head
The coefficient C depends on crest shape, approach conditions, and flow regime. Use values from your agency standard, model studies, or published guidance for ogee, broad‑crested, or sharp‑crested configurations. Head should represent energy head at the control section; include approach velocity head when approach velocities are meaningful, and confirm tailwater does not submerge the crest at design conditions.
Contractions, bays, and practical layout
For gated spillways, piers and abutments reduce effective length. The optional contraction allowance estimates the difference between gross crest length and effective length using pier and abutment coefficients. The tool also estimates clear bay width from gross length, bay count, and pier thickness, helping you quickly check gate module feasibility and structural spacing.
Verification and reporting workflow
After obtaining a preliminary crest length, validate with a full hydraulic profile, masking effects of approach channel geometry, and site‑specific freeboard requirements. Where available, compare against historic performance, HEC‑RAS or CFD results, and physical model data to confirm discharge coefficients, nappe aeration, and pressure profiles, especially when cavitation risk or seasonal debris loading is expected. Check energy dissipation capacity, downstream erosion protection, and operational constraints. Export the results table for design notes, then refine inputs as survey, hydrology, and layout assumptions mature through design review.
FAQs
1) What crest length does the calculator output?
It reports effective crest length Le from the weir equation and an optional gross crest length Lg after applying pier and abutment contraction allowances. Use Lg for layout sketches and Le for hydraulic capacity checks.
2) How do I choose the coefficient C?
Select C from your spillway standard for the crest type and approach conditions. Ogee and broad‑crested crests commonly use different values. If you are unsure, run sensitivity checks with a low and high C range.
3) Should I include approach velocity?
Include approach velocity when flow enters the control section with measurable speed, such as from a confined channel or gate bay. The calculator adds velocity head V²/(2g) to the entered head, increasing capacity for the same crest length.
4) What do contraction coefficients represent?
Contraction coefficients approximate the reduction in effective length caused by piers and abutments. They are empirical and depend on pier nose shape, gate configuration, and flow alignment. Confirm coefficients with project guidance or model studies when available.
5) Why does crest length change so much with head?
Discharge varies with H^(3/2), so head has a strong influence. Increasing head slightly can raise capacity noticeably, reducing required length. However, head is limited by reservoir levels, freeboard, and structural and operational constraints.
6) Is this suitable for final design?
Use it for preliminary sizing, option comparison, and documentation. Final design should verify submergence, tailwater rating, approach losses, discharge coefficients, and downstream energy dissipation using detailed hydraulic analysis and applicable standards.
Example data table
| Unit | Q | H | C | Bays | Pier t | Le | Lg | Bay width |
|---|---|---|---|---|---|---|---|---|
| Metric | 250 m³/s | 2.0 m | 1.84 | 5 | 0.60 m | 48.037 m | 48.997 m | 9.319 m |
| Metric | 120 m³/s | 1.5 m | 1.84 | 4 | 0.50 m | 35.500 m | 36.190 m | 8.672 m |
| Metric | 500 m³/s | 3.0 m | 2.20 | 6 | 0.70 m | 43.739 m | 44.999 m | 6.916 m |
Examples assume velocity head is zero and contractions are enabled. Use project-specific coefficients for final design.