Input
Example data table
| Condition | b (m) | a (m) | Hu (m) | Hd (m) | Cd | Computed Q (m³/s) |
|---|---|---|---|---|---|---|
| Free | 1.50 | 0.30 | 1.20 | 0.20 | 0.70 | 1.429 |
| Submerged | 2.00 | 0.45 | 1.80 | 1.20 | 0.68 | 2.099 |
| Submerged | 1.00 | 0.25 | 0.90 | 0.60 | 0.65 | 0.394 |
Formula used
This tool estimates discharge through an underflow canal gate using an orifice-style relationship:
- Q = discharge
- Cd = discharge coefficient (field- or literature-based)
- b = gate width
- a = gate opening
- g = gravitational acceleration
- H = effective head driving the flow
- Free (unsubmerged): H = Hu − a/2 (head to gate centerline, practical approximation)
- Submerged (drowned): H = Hu − Hd (differential head across the gate)
How to use this calculator
- Select your unit system (meters or feet).
- Choose the flow condition based on tailwater influence.
- Enter gate width b and opening a.
- Enter upstream and downstream heads (Hu, Hd) above the sill.
- Enter Cd (use measurements when possible).
- Press Calculate Discharge to view results above the form.
- Use Download CSV or Download PDF to save a report.
Technical article
1) What this calculator is for
Canal gates are commonly used to regulate irrigation supply and maintain target water levels. This calculator estimates underflow discharge using a practical orifice-style equation with an adjustable discharge coefficient. It supports free and submerged conditions, so you can quickly compare operational scenarios during routine field checks and commissioning.
2) Field data you should collect
Use a consistent datum at the gate sill. Measure upstream head (Hu) and downstream head (Hd) above the sill, plus gate width (b) and opening (a). For accuracy, record Hu and Hd to the nearest 0.01 m (or 0.03 ft). Photograph the gauge readings and note the timestamp for traceability. If sediment is present, note deposition depth and use the effective opening after cleaning.
3) Discharge coefficient guidance
The coefficient Cd captures contraction, approach turbulence, and gate geometry. For sharp-edged underflow gates, Cd is often in the 0.60–0.85 range, with 0.70 as a practical starting value when no calibration is available. If you have a measured flow (from a flume or current meter), back-calculate Cd and reuse it for similar openings.
4) Reading the outputs
The calculator reports effective head H, area A=b×a, discharge Q, and velocity V=Q/A. Use velocity as a quick sanity check: many lined canals operate comfortably near 1–3 m/s, while higher values may require energy dissipation or abrasion checks. In SI, g=9.80665 m/s² is used internally; US inputs are converted using 1 ft = 0.3048 m.
5) Quality control and reporting
Always verify that H remains positive: for free flow the tool assumes H = Hu − a/2, while submerged flow uses H = Hu − Hd. Compare computed Q against historical deliveries and adjust Cd if persistent bias is observed. Export CSV for spreadsheets, and PDF for site reports with inputs, outputs, and brief notes.
FAQs
How do I choose Cd if I have no calibration?
Start with 0.70 for sharp-edged underflow gates. If you later measure flow with a flume or velocity-area method, back-calculate Cd and update it for the same gate geometry and operating range.
When should I pick free versus submerged flow?
Use free when the downstream level does not control the jet and the gate discharges to a lower tailwater. Use submerged when tailwater is high enough to drown the jet and reduce discharge.
Why does the tool warn that effective head is not positive?
Effective head H must be greater than zero. For free flow, ensure Hu is larger than a/2. For submerged flow, ensure upstream head Hu is greater than downstream head Hd at the same datum.
Does velocity under the gate matter for design?
Yes. V = Q/A helps screen for lining abrasion, cavitation risk, and downstream energy requirements. If velocities are consistently high, consider energy dissipation, gradual transitions, or limiting the opening for stable operation.
Are Hu and Hd measured to the water surface or pressure head?
Use water surface elevations above the sill (same datum), representing hydrostatic head at the gate. Keep measurement points close to the gate to reduce errors from channel slope and local losses.
Can this be used for radial or overshot gates?
It is intended for underflow (sluice-type) gates. Radial and overshot gates can require different coefficients and head definitions. You may still use it for rough checks, but verify with the appropriate standard equation.
What should I include in my report for traceability?
Record date/time, gate ID, b, a, Hu, Hd, assumed flow condition, Cd source, and the computed Q. Export the PDF for a site attachment, and keep the CSV for later comparisons and trend checks.