A turbine and gate is a hydraulic power assembly that pairs a reaction turbine runner with a ring of pivoting wicket gates — also called guide vanes — that throttle and direct water onto the runner. The gates solve the core problem of matching turbine power output to a varying electrical load without spilling water or stalling the runner. As the governor servomotor rotates the gate ring, each vane swings on its stem, opening or closing the flow passage and changing the angle of attack. A modern Francis unit with this arrangement holds grid frequency within ±0.1 Hz across loads from 20% to 100% of rated MW.
Turbine and Gate Interactive Calculator
Vary wicket-gate opening, head, flow capacity, efficiency, and runner speed to see turbine flow, power, torque, and gate angle.
Equation Used
The calculator estimates turbine output from the hydraulic power equation. Wicket-gate opening sets the approximate flow fraction, then shaft power is calculated from head, flow, and efficiency. Runner torque is found by dividing shaft power by angular speed.
- Water density is 1000 kg/m3 and g is 9.81 m/s2.
- Flow is approximated as proportional to wicket-gate opening.
- Efficiency is entered as total hydraulic-to-shaft efficiency.
- Gate angle is a teaching approximation from 5 deg closed to 40 deg open.
Operating Principle of the Turbine and Gate
Water enters the spiral casing under head, fills the stay-vane ring, and arrives at the wicket gates as a pressurised annular flow. Each wicket gate is an aerofoil-shaped vane pivoting on a vertical stem, and all of them are linked through a single servomotor-driven gate ring so they rotate together. When the governor commands more power, the ring rotates a few degrees and every gate opens slightly, increasing both the flow area and the tangential component of the velocity hitting the runner. Close the gates and the opposite happens — flow drops, swirl drops, and the runner unloads.
The geometry has to be tight. Gate-to-gate spacing must match the runner inlet so the wake from each vane lines up cleanly with a runner blade — get the count wrong and you set up a pressure pulsation at gate-passing frequency that cracks runner crowns. Stem clearance is typically 0.05 to 0.15 mm; if it opens up to 0.5 mm from wear you get leakage flow at zero gate, the runner won't fully stop, and you can't safely dewater the spiral case for inspection. The biggest real-world failure mode is gate linkage shear pin failure during a load rejection — when the breaker opens at full load, the governor slams the gates shut in 4 to 8 seconds, and any sticking vane snaps its shear pin so the rest of the ring can still close. That's by design. A stuck open gate after a load rejection is what causes runaway, and runaway is what destroys turbines.
Why pivoting vanes instead of a single throttle valve upstream? Because a throttle wastes head as turbulence and gives no control over flow angle. The wicket gate doubles as a flow regulator and a guide vane, setting the velocity triangle at the runner inlet. That's why this arrangement dominates Francis and Kaplan installations from 100 kW micro-hydro up to 800 MW units like the ones at Itaipu.
Key Components
- Wicket Gate (Guide Vane): Aerofoil-shaped vane, typically 16 to 24 per ring on a Francis unit, that pivots on a vertical stem to throttle flow and set the inlet swirl angle. Profile is usually a NACA-derived section with a chord of 200 to 600 mm depending on runner size.
- Gate Ring (Shifting Ring): Large-diameter steel ring concentric with the runner shaft that connects every gate's outer lever via a link arm. One servomotor stroke rotates the ring a few degrees, and every gate moves in unison within ±0.5° of position match.
- Servomotor: Hydraulic cylinder running on 4 to 6 MPa governor oil that drives the gate ring. Stroke time is set by the governor — typically 4 to 8 seconds full close on load rejection, longer on normal regulation to avoid water-hammer pressure rise above 1.3× static head.
- Shear Pin / Friction Coupling: Sacrificial element between each gate lever and the gate ring. Designed to fail at roughly 1.5× normal closing torque so a single jammed gate cannot prevent the rest of the ring from closing during emergency shutdown.
- Stay Vanes: Fixed structural vanes upstream of the wicket gates that carry the spiral casing roof load and pre-swirl the flow. Stay-vane count and pitch are matched to the wicket-gate count to avoid harmonic resonance in the runner.
- Stem Bushings and Seals: Self-lubricating composite bushings (often PTFE-bronze) carrying the gate stem with 0.05 to 0.15 mm radial clearance. Stem seals keep the spiral case pressure out of the head cover — a leaking stem seal is the most common reason a unit can't be dewatered for inspection.
Who Uses the Turbine and Gate
You find the turbine-and-gate arrangement anywhere a reaction turbine has to follow a varying load on a fixed head. The gates are what make the turbine controllable — without them you'd need an upstream valve and you'd lose efficiency at every part-load point. The same pattern shows up at radically different scales, from 50 kW community micro-hydro plants in mountain villages to the 700 MW Francis units at Three Gorges. Wherever you see a Francis or Kaplan runner driving a synchronous generator on a grid, there's a wicket-gate ring upstream doing the regulation work.
- Large Hydroelectric: 20 Francis units at Itaipu Binacional on the Paraná River, each rated 700 MW with a 24-vane wicket-gate ring closing in 6 seconds on full load rejection.
- Pumped Storage: Reversible Francis pump-turbines at the Bath County Pumped Storage Station in Virginia, where the wicket gates throttle in turbine mode and act as discharge guides in pump mode.
- Run-of-River Plants: Kaplan units at Site C on the Peace River in BC, where wicket gates work in tandem with adjustable runner blades to hold efficiency above 90% across a 7 m head variation.
- Micro-Hydro: Gilkes-supplied 1.2 MW Francis units at small UK hydro schemes such as Mary Tavy, using a 16-gate ring with manual override for off-grid black-start capability.
- Industrial Process: Hydraulic-turbine power recovery on high-pressure letdown in seawater reverse-osmosis desalination plants such as the Sorek plant in Israel, where guide-vane control matches recovered power to brine flow.
- Heritage and Restoration: Restored 1920s S. Morgan Smith Francis turbines at the Lockport hydro plant on the Erie Canal, retrofitted with electro-hydraulic gate servomotors to replace the original mechanical flyball governors.
The Formula Behind the Turbine and Gate
The useful number to compute is the volumetric flow Q passing the wicket-gate ring as a function of gate opening angle. This is what tells you what power you'll get at a given gate position and what the part-load efficiency curve looks like. At the low end of the typical operating range — say 20% gate opening — flow is throttled hard, velocity through the gap is high, and you pay an efficiency penalty from incidence loss at the runner inlet. At the nominal best-efficiency point (BEP), usually 70 to 85% gate opening on a Francis unit, the flow angle off the gate matches the runner blade inlet angle and you sit on the efficiency hill. Push above 95% and the gates start to unblock the stay-vane wakes, flow becomes turbulent, and efficiency rolls off again. The sweet spot on a Francis unit is narrow — that's why pumped-storage operators avoid sustained part-load running.
Variables
| Symbol | Meaning | Unit (SI) | Unit (Imperial) |
|---|---|---|---|
| Q | Volumetric flow through the gate ring | m³/s | ft³/s |
| Ng | Number of wicket gates in the ring | — | — |
| hg | Chord length of one gate (effective gap width along the chord) | m | ft |
| b | Gate height (axial dimension between head cover and bottom ring) | m | ft |
| α | Gate opening angle measured from the closed position | ° (degrees) | ° (degrees) |
| Cv | Discharge coefficient, typically 0.65 to 0.80 for Francis wicket gates | — | — |
| g | Gravitational acceleration | 9.81 m/s² | 32.2 ft/s² |
| H | Net head across the turbine | m | ft |
Worked Example: Turbine and Gate in a 2 MW Francis micro-hydro plant
You are sizing the wicket-gate flow at three operating points for a 2 MW Francis micro-hydro retrofit on the Wahleach Lake penstock in Chilliwack BC, feeding a 16-gate Andritz runner with 0.18 m gate chord, 0.22 m gate height, net head of 95 m, and a discharge coefficient of 0.72. The grid operator wants to know flow and indicative power at 25%, 75%, and 100% gate opening so the protection settings can be tuned for the expected speed-no-load to full-load swing.
Given
- Ng = 16 gates
- hg = 0.18 m
- b = 0.22 m
- Cv = 0.72 —
- H = 95 m
- αfull = 32 ° (corresponds to 100% rated opening)
Solution
Step 1 — compute the head-driven velocity term, which is constant across all gate positions for a fixed head:
Step 2 — at nominal 75% gate opening, α = 0.75 × 32° = 24°, and sin(24°) = 0.407. Compute Q at the BEP:
That flow on 95 m head with a typical 90% turbine-generator efficiency gives roughly P = ρ × g × Q × H × η = 1000 × 9.81 × 8.12 × 95 × 0.90 ≈ 6.8 MW available — well above the 2 MW rating, which is correct because the unit is rated at a partial gate to leave overload margin.
Step 3 — at the low end of the typical operating range, 25% gate opening, α = 8°, sin(8°) = 0.139:
At this opening the runner is well off BEP — incidence loss at the blade inlet pushes turbine efficiency down to roughly 72%, and you'll feel it as draft-tube surge: a low-frequency 1 to 2 Hz pressure pulsation that you can hear as a thump in the powerhouse. Sustained running here cracks the draft tube cone over years.
Step 4 — at 100% gate opening, α = 32°, sin(32°) = 0.530:
That's 30% above the BEP flow. You can run there briefly but the gates are now shading the stay-vane wakes, runner cavitation risk climbs sharply, and efficiency drops back to roughly 85%. Most operators cap continuous operation at 95% gate.
Result
Nominal flow at 75% gate opening is 8. 12 m³/s, which is the design BEP for this Andritz runner on 95 m head. In practice you'll see the unit settle here under steady grid load with no audible draft-tube rumble and a smooth ammeter trace. Across the operating range the flow swings from 2.77 m³/s at 25% gate (rough running, draft-tube surge audible) through 8.12 m³/s at the sweet spot to 10.57 m³/s at 100% (efficient but cavitation-prone for sustained operation). If your measured flow at 75% gate is more than 5% below 8.12 m³/s, check three things in order: (1) gate position feedback offset — the LVDT on the servomotor commonly drifts 1 to 2° per year and the gates aren't actually where the governor thinks they are; (2) stay-vane fouling from log debris caught upstream, which silently throttles the casing; (3) Cv drop from gate trailing-edge erosion — once the trailing edge wears past 3 mm radius, discharge coefficient drops from 0.72 toward 0.65 and you lose 10% flow at the same opening.
Choosing the Turbine and Gate: Pros and Cons
The wicket-gate-and-runner pairing isn't the only way to regulate a hydraulic turbine. Pelton wheels use a deflector and spear valve, Turgo units use a spear nozzle, and crossflow turbines use a single guide vane on a hinge. Each picks a different point on the speed/cost/maintenance curve, and the choice is usually forced by head and flow rather than preference.
| Property | Wicket Gate (Francis/Kaplan) | Spear Valve (Pelton) | Hinged Guide Vane (Crossflow) |
|---|---|---|---|
| Head range | 20 to 700 m | 200 to 1800 m | 2 to 200 m |
| Flow regulation accuracy | ±0.5° of position, very fine | ±0.2 mm spear stroke, fine | Coarse, ±5% flow steps |
| Part-load efficiency at 30% load | 62 to 70% | 85 to 88% (per nozzle, with multi-nozzle staging) | 70 to 75% |
| Closing time on load rejection | 4 to 8 seconds | Spear 20 to 60 s, deflector 1 to 2 s | 3 to 10 seconds |
| Number of moving parts in regulator | 20 to 30 (gates, links, ring, servo) | 2 (spear + deflector per nozzle) | 1 to 2 |
| Capital cost (per kW) | High | Medium | Low |
| Servicing interval (gate or valve overhaul) | 8 to 12 years | 5 to 8 years (spear tip wear) | 10 to 15 years |
| Best fit application | Grid-connected Francis/Kaplan, 1 MW to 800 MW | High-head impulse, 500 kW to 400 MW | Off-grid micro-hydro, 5 to 500 kW |
Frequently Asked Questions About Turbine and Gate
That's incidence loss, and it's baked into the geometry — not a fault. At BEP the flow angle leaving the wicket gate matches the runner blade inlet angle within a few degrees. Close the gates and the absolute flow angle becomes more tangential, but the runner blade inlet angle is fixed (on a Francis — Kaplan units adjust the runner blades to compensate). The mismatch shows up as separation on the suction side of the runner blade and you lose head to turbulence rather than work.
Rule of thumb: a fixed-blade Francis is within 2% of peak only across roughly 65 to 90% gate. If you need flat efficiency from 30 to 100% load, you specified the wrong machine — Kaplan or pump-turbine with double regulation is the answer.
The shear pin (or friction coupling, depending on vintage) on that gate's link arm did exactly what it's designed to do. Something jammed the gate — usually a piece of debris between the gate and the discharge ring, or a corroded stem bushing — and the closing torque on the gate ring exceeded the shear pin rating, so the pin snapped and decoupled that one gate from the ring. The other 15 or 23 gates then closed normally.
This is a deliberate sacrificial design. A stuck-open gate after a load rejection still leaks flow, but it cannot prevent the rest of the ring from closing, which is what would cause runaway. Replace the shear pin, find what jammed the gate, and inspect the stem bushing clearance — if it's above 0.3 mm radial you have a wear problem that will keep eating shear pins.
250 m is in the overlap zone where both work, and the deciding factors are flow variability and part-load duty. If your stream is steady year-round, a Francis with wicket gates gives you a smaller, cheaper machine and higher peak efficiency — around 92% versus 88% for the Pelton. If your flow varies seasonally by more than 3:1, go Pelton with two or three nozzles. You can shut off nozzles individually and keep each running nozzle near its peak efficiency, where a Francis is dragged off BEP across the whole flow range.
Maintenance also matters off-grid: Pelton spear tips need attention every 5 to 8 years on silty water, but the wicket-gate ring on a Francis is a 20-part assembly that needs a crane to service. For a remote site with no road access, the simpler machine usually wins.
Spec is usually ±0.5° gate-to-gate at any commanded position. Get to 2° offset and you've created a non-uniform flow distribution around the runner inlet — one sector sees more flow than the rest, and the runner sees a once-per-revolution unbalanced load. You'll measure it as elevated 1× shaft vibration, typically rising from baseline 2 mm/s to 5 to 8 mm/s RMS on the guide bearing.
The cause is almost always wear or backlash in the gate link arms or the regulating ring pivots. Pull the gate-position feedback during a slow gate ramp and look for one gate that lags or leads the others — that's the worn linkage.
You hit the part-load draft-tube vortex — a corkscrew vapour rope spinning in the draft tube cone at roughly 0.25 to 0.35 times runner speed. It forms when the wicket gates throttle hard enough that residual swirl exits the runner and organizes into a precessing vortex. The pressure pulsation couples into the penstock and you can feel it as a 1 to 2 Hz building thump throughout the powerhouse.
You cannot fix this with the gates alone — it's a runner/draft-tube geometry issue. Standard mitigations are air admission through the head cover (breaks up the vortex), a fin in the draft tube cone, or simply avoiding sustained operation between roughly 30 and 50% load. Most modern governors have a forbidden-zone setting for exactly this reason.
Penstock water hammer. When you decelerate the water column quickly, the kinetic energy converts to a pressure rise governed by the Joukowsky equation — and a long penstock can easily generate a pressure rise above the burst rating of the pipe if you close too fast. The closing time is sized so that 2L/a (the wave reflection time, where L is penstock length and a is the wave speed of about 1200 m/s in steel) is less than the closing time, keeping the rise to roughly 1.3× static head.
On a 600 m penstock that's a 1 second reflection time, and you typically pick 5 to 6 seconds closing time to stay safely below the pipe rating. If you must close faster — for a runaway prevention case — you fit a pressure-relief valve or a bypass that opens as the gates close.
References & Further Reading
- Wikipedia contributors. Water turbine. Wikipedia
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