Calculate the free flow that shoots out from beneath a flat vertical gate (a sluice gate) set across a channel. Adjust the gate opening, upstream depth and gate width to see the discharge, contracted depth, downstream velocity and Froude number update in real time, and check how strongly supercritical the jet becomes.
Parameters
Gate opening a
m
Height of the gap between the gate edge and the channel bed
Upstream depth y₁
m
Depth of the water ponded on the upstream side of the gate
Gate width b
m
Width of the channel (the dimension across the flow)
Discharge coefficient C_d
Empirical coefficient lumping contraction and energy loss. About 0.61 for a sharp-edged gate
Results
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Unit discharge q (m²/s)
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Total discharge Q (m³/s)
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Contracted depth y₂ (m)
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Downstream velocity (m/s)
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Downstream Froude number Fr
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Flow regime
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Sluice gate side section — free-flow animation
Deep, calm upstream water (left) passes through the gap of height a, contracts and becomes a thin, fast supercritical jet (right). The blue streamlines show the contraction.
Total discharge Q and the downstream Froude number Fr₂. C_d: discharge coefficient, a: gate opening, b: gate width, y₁: upstream depth, v₂: downstream velocity, y₂: contracted depth.
$$y_2 = C_c\,a,\qquad v_2 = \frac{Q}{b\,y_2}$$
The flow under the gate emerges supercritical (Fr>1), and the jet contracts to a vena contracta depth y₂ smaller than the opening. C_c: contraction coefficient (about 0.61 for a sharp-edged gate).
What is the Sluice Gate Flow Simulator?
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A "sluice gate" is that flat metal plate in an irrigation canal that slides up and down, right?
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Exactly. A sluice gate is a flat vertical plate set across a channel; you slide it up and down to control the flow of water. It is one of the most basic hydraulic structures there is, used in irrigation canals, flood barriers, weirs and water-treatment works almost everywhere. When you raise the gate a little, the water that was ponded behind it shoots out through the gap underneath.
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The water that shoots out looks completely different from the calm water upstream. What kind of flow is that?
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Good observation. Upstream of the gate the water is deep and slow — that is "subcritical" flow. But the water that escapes through the gap turns into a thin, intensely fast "supercritical" jet. Supercritical means the velocity exceeds the speed at which a small surface wave travels, so a wave can no longer move back upstream. The Froude number Fr marks this boundary: once Fr is above one, the flow is supercritical. Make the gate opening a smaller with the slider on the left and you will see Fr climb sharply.
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In the animation below, the water that leaves the gap pinches in to a narrower stream right away. What is that?
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That is the "vena contracta". The lower edge of the gate is a sharp corner, and the streamlines cannot turn it instantly. So the jet keeps contracting for a short distance after it leaves the gate, reaching a minimum depth somewhat smaller than the gate opening. That minimum is the contracted section, and its depth y₂ is roughly 0.61 times the opening a. So when you compute the downstream velocity or Froude number, you must use this contracted depth y₂, not the gate opening a itself.
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The "discharge coefficient C_d" in the flow formula was also 0.61. Is that also related to the contraction?
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Yes. The discharge coefficient C_d rolls the effect of this contraction, together with the small energy losses through the gap, into a single empirical number. Thanks to it, the discharge can be written compactly as Q = C_d·a·b·√(2gy₁). For a sharp-edged gate it is about 0.61. The discharge is proportional to the gate opening a and proportional to the square root of the upstream depth y₁ — look at the two charts below and you will clearly see that "linear" and "square-root" shape.
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If such a fast jet comes out, is it really fine to release it straight into a river?
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Good question. Releasing it directly would scour the channel bed badly. So engineers usually build a "stilling basin" downstream of the gate and deliberately force a "hydraulic jump". A hydraulic jump is the swirling turbulence where supercritical flow switches abruptly back to subcritical; it dissipates the excess energy and calms the flow before it returns to the river. The downstream Froude number from this tool gives you a first measure of how large that jump and energy-dissipation works need to be.
Frequently Asked Questions
For free flow under a sluice gate the discharge per unit width is q = C_d·a·sqrt(2g·y1), where C_d is the discharge coefficient (about 0.61), a is the gate opening, y1 is the upstream depth and g is gravitational acceleration. The total discharge is found by multiplying by the gate width b, giving Q = C_d·a·b·sqrt(2g·y1). The discharge is proportional to the gate opening a and to the square root of the upstream depth y1.
Because the streamlines cannot turn the sharp lower edge of the gate instantly, the jet that leaves the gate keeps contracting for a short distance and reaches a minimum depth somewhat smaller than the gate opening. That minimum is the vena contracta, the contracted section. For a sharp-edged gate the contraction coefficient is roughly 0.61, so the contracted depth y2 is about 0.61 times the opening. Downstream velocity and Froude number must be evaluated at this contracted depth, not at the gate opening.
The deep, calm water ponded upstream becomes a thin, fast sheet of water once it passes through the narrow gap of height a. Its velocity exceeds the speed of a small surface wave, so the Froude number Fr rises above one and the flow becomes supercritical. Here Fr = v2/sqrt(g·y2), with v2 the downstream velocity and y2 the contracted depth. With the default settings the Froude number exceeds four, giving a clearly supercritical jet.
Releasing the fast jet that leaves the gate straight into a natural channel would severely scour the bed. Engineers therefore build a stilling basin downstream and deliberately force a hydraulic jump, which dissipates the excess energy and returns the flow to a subcritical state before it is released. The downstream Froude number from this tool gives a first measure of the hydraulic jump and energy-dissipation works that will be required.
Real-World Applications
Irrigation canals and agricultural water management: The most familiar use of a sluice gate is the irrigation canal that distributes water to fields. Opening or closing a division gate by a small amount adjusts the discharge to each branch. Estimating the discharge from the opening and upstream depth, as this tool does, tells you in advance how far the gate must be raised to deliver the required flow. On a main canal with several intakes, operating an upstream gate changes the downstream depth, so the discharge sharing across the whole system must be considered.
River gates and flood control: Sluice gates appear in the drainage gates that prevent floodwater from backing up into tributaries, in the release gates downstream of dams, and in the tidal barriers that stop the upstream run of the tide. On a flood gate the upstream depth is large and the total discharge can reach hundreds of cubic metres per second. The fast supercritical jet produced when the gate opens must not scour the downstream levee or bed, so the stilling basin and bed protection are critical to the design.
Water and wastewater treatment plants: In treatment facilities, sluice gates are widely used to control the inflow into settling tanks and reaction basins and to isolate channels for maintenance. Here the discharge is relatively small and the gate opening is controlled precisely. The choice of discharge coefficient and the treatment of the contraction directly affect the accuracy of the flow measurement.
Hydraulics education and CAE verification: Sluice gate flow condenses the core concepts of open-channel hydraulics — energy conservation, momentum conservation, contraction, supercritical flow and the hydraulic jump — into a single subject. Before solving a free-surface flow with detailed CFD, a section-averaged estimate like this tool gives a first read on the discharge and downstream Froude number, letting you judge plausibility before investing in mesh and turbulence models. If a CFD result differs from this estimate by an order of magnitude, it is a sanity check pointing to a boundary-condition or free-surface error.
Common Misconceptions and Pitfalls
The biggest pitfall is using the free-flow formula when the gate is actually submerged downstream. The formula Q = C_d·a·b·√(2gy₁) used here is for "free flow", meaning the supercritical jet leaving the gate is open to the atmosphere and not held back by the downstream water level. When the downstream depth rises high enough to drown the jet, the flow becomes "submerged", and the discharge then depends not on the upstream depth y₁ alone but on the difference between the upstream and downstream water levels. For the same gate opening, submerged flow carries less discharge. Always check the downstream water level and decide whether the flow is free or submerged.
Next, confusing the contracted depth y₂ with the gate opening a. When computing the downstream velocity v₂ or the Froude number Fr, using the gate opening a directly as the depth underestimates the velocity and gives too small a Froude number. The real jet contracts after leaving the gate and pinches down to y₂ ≈ 0.61·a. Because the velocity is computed as Q/(b·y₂), simply using y₂ instead of a changes the velocity by roughly a factor of 1.6. When evaluating the energy of the downstream jet, always base it on the contracted depth.
Finally, assuming the discharge coefficient C_d is always 0.61. The value 0.61 is a representative figure for a sharp-edged gate when the upstream depth is much larger than the gate opening. The real C_d varies with the ratio of opening to upstream depth a/y₁, with the shape of the gate's lower edge (sharp or rounded), with the inclination of the gate, and with the approach velocity upstream. As the opening approaches the upstream depth, C_d departs from 0.61, and a thick gate or a rounded edge weakens the contraction and raises the coefficient. For measurements that need accuracy, an experimental relation or a calibrated coefficient is essential.
How to Use
Enter gate opening a (m) — the vertical distance between sluice gate and channel bed.
Set channel width b (m) — typically 2–10 m for irrigation or hydropower applications.
Input upstream depth y₁ (m) — water level measured above the channel bed upstream of the gate.
Adjust discharge coefficient C_d (0.61–0.65 for sharp-edged gates) to account for vena contracta and friction losses.
Click Calculate to obtain unit discharge q, total discharge Q, contracted depth y₂, downstream velocity, Froude number, and flow regime classification.
Worked Example
A rectangular irrigation channel with width b = 3 m, upstream depth y₁ = 1.8 m, and sluice gate opening a = 0.45 m operates with C_d = 0.62. The simulator calculates: unit discharge q = 2.84 m²/s, total discharge Q = 8.52 m³/s, contracted depth y₂ = 0.28 m (approximately 62% of gate opening), downstream velocity v₂ = 10.17 m/s, and Froude number Fr = 3.84 indicating supercritical free-jet flow. This supercritical regime requires stilling basins or energy dissipators to prevent bed scour downstream.
Practical Notes
Discharge coefficient C_d varies with gate geometry: sharp rectangular gates use 0.61–0.64; rounded or cylindrical gates reach 0.75–0.80. Calibrate against field measurements if available.
When Fr exceeds 1.0, expect a hydraulic jump; position stilling basins 0.5–2.0 m downstream depending on Q and channel roughness to dissipate energy safely.
Gate opening control affects sediment transport significantly — smaller openings increase velocity concentration, risking erosion; larger openings diffuse flow across the channel width.
For gates with submergence (backwater), apply submerged-flow correction factors (typically 0.85–0.95 × free-flow discharge).