Sluice Gate Discharge
Sluice Gate Discharge
Sluice gates are the workhorse flow-control device on irrigation canals, spillways, and industrial channels — a vertical plate raised a small amount above the channel floor lets water accelerate underneath it, and the resulting discharge can be predicted from the gate opening and the upstream water level. Getting this relationship right lets an operator set a gate opening to deliver a target flow without needing a separate flow meter. Because the discharge coefficient absorbs contraction and energy-loss effects that are hard to compute from first principles, it is almost always taken from calibration data or hydraulic tables for a given gate geometry; using a generic value on an atypical gate shape is a common source of error in irrigation scheduling.
Sluice gate discharge is Q = Cd*b*a*sqrt(2*g*H), a discharge coefficient times the flow area times the velocity from the upstream head. where C_d2 is the discharge coefficient, b_gate is the gate (channel) width, a_gate is the gate opening height, g_g is gravitational acceleration, and H_head is the upstream head above the gate opening.
Inputs
C_d2 := 0.6=0.6
b_gate := 2 m=2 m
a_gate := 0.3 m=300 mm
g_g := 9.81 m/s^2=9.81 m/s^2
H_head := 1.5 m=1.5 m
The gate opening times the width gives the flow area the water squeezes through, and the sqrt(2gH) term is the velocity that upstream head can theoretically produce; Cd corrects for the vena contracta and other real losses.
Q_gate := C_d2·b_gate·a_gate·sqrt(2·g_g·H_head)=1.95 m^3/s
Results
A discharge in the range of a few cubic metres per second is typical for a moderate irrigation or spillway gate at this opening and head, and doubling the opening a roughly doubles Q while doubling the head H only increases Q by about 41%, so gate opening is the more sensitive control. If the metered flow in the field disagrees with this prediction, the discharge coefficient — not the geometry — is usually the first thing to recalibrate.
Assumptions & limitations
- Free (unsubmerged) discharge assumed — no significant tailwater effect.
- Steady, uniform approach flow with the gate opening small relative to upstream depth.
- Discharge coefficient is empirical and geometry-specific.
- Two-dimensional flow assumed; end effects at the channel walls are neglected.