Guide · Gates and turnouts
How much water a headgate passes: the orifice equation
A slide gate or headgate that is open part way and submerged behaves like an orifice. The flow depends on two things you can measure with a tape: the size of the opening and the difference in water level across the gate.
Short answer: Q = Cd × A × √(2 × g × h). A is the gate opening in square feet, h is the water-level difference across the gate in feet, g is 32.2 ft/s², and Cd is about 0.61 for a sharp-edged rectangular opening. A 1 sq ft opening under 0.75 ft of head passes about 4.2 cfs.
The equation
- Cd — discharge coefficient. 0.61 matches the U.S. Bureau of Reclamation reference conditions for a fully contracted rectangular orifice.
- A — open area of the gate: width times how far it is raised, in square feet.
- h — differential head. For a submerged gate, upstream water surface minus downstream water surface. For a free-flowing gate, upstream water surface minus the center of the opening.
Worked example
A 2 ft wide slide gate is raised 6 inches. The canal stands 0.75 ft higher than the ditch below the gate.
Why head matters less than you expect
Flow goes with the square root of head. To double the flow through the same opening you need four times the head difference. Opening the gate further is almost always the more effective move, because flow rises in direct proportion to area.
| Head difference | Flow through 1 sq ft (Cd 0.61) |
|---|---|
| 0.25 ft | 2.4 cfs |
| 0.50 ft | 3.5 cfs |
| 0.75 ft | 4.2 cfs |
| 1.00 ft | 4.9 cfs |
| 2.00 ft | 6.9 cfs |
When 0.61 is wrong
- Suppressed contraction. If the opening sits on the floor or against a side wall, the jet cannot contract on that side and the coefficient rises.
- Rounded or bell-mouthed entrances pass more water than a sharp edge.
- Trash, silt, and bent frames pass less.
- Zero or reversed head means zero forward flow. A gate cannot deliver water the canal is not standing high enough to push.
For water accounting, a gate needs a field rating: measure actual flow at several openings and heads and fit your own coefficient. A measured rating always outranks a textbook value.
Leaky gates
A closed gate that does not seal is still an orifice, just a small one. Estimate the gap as an equivalent open area and run the same equation. A gap equal to 2 percent of a 1 sq ft gate under 0.75 ft of head leaks about 0.085 cfs — roughly 38 gpm, or 55,000 gallons a day.
Planning estimate, not a stamped design. These are steady-state equations. Real accuracy depends on surveyed elevations, current channel and pipe condition, calibrated gate ratings, and pump curves. Verify in the field and get qualified engineering review before final construction or official operation.
Related guides
- Ditch sizing with Manning's equation — to confirm the ditch below the gate can carry what the gate delivers.
- cfs, gpm, acre-feet, and miner's inches.
Sources
- U.S. Bureau of Reclamation, Water Measurement Manual, Chapter 9: submerged orifices.
Model the gate in the drawing
FieldFlowCAD treats every headgate as an orifice with an editable discharge coefficient and a leak-area setting, and reports flow in gpm, cfs, gallons per day, and acre-feet per day.