Presets
Playback
Head, gates and speed
Flow follows the orifice law of the wicket-gate opening and the square root of the head. The runner speed changes the blade speed u in the velocity triangles, and with it the torque the water can deliver.
Model checks
The science
What is modelled
Water passes the adjustable wicket gates with a flow angle set by the gate opening, enters the runner with an absolute velocity c, and leaves almost axially. At each radius the absolute velocity is the vector sum of the blade speed u and the relative velocity w along the blade. The page uses the same flow and power formulas as the 3D page and adds the Euler turbine equation for the runner.
Equations
- Flow:
Q = Cd A (gate) √(2 g H)with Cd = 0.9 and A = 6.8 m². - Power:
P = ρ g Q H η; synchronous frequencyf = p n / 120with 40 poles. - Euler:
g HE = u1 cu1 - u2 cu2, torqueρ Q (r1 cu1 - r2 cu2). - Triangle:
w² = c² + u² - 2 u cu.
Checks run in the page
- Power from mass flow and specific energy against rho g Q H eta.
- Orifice-law scaling with head.
- Inlet triangle closes by the law of cosines.
- Euler power equals rho g Q HE, and the frequency formula.
Honest simplifications
A fixed illustrative geometry (inlet radius 1.58 m, outlet radius 1.9 m, outlet blade angle 22 degrees), a guide angle that varies linearly with the gate, uniform meridional velocity across the blade height, and no friction, leakage or draft-tube model. The overall efficiency is a slider, as on the 3D page; the Euler head is a separate indicator of how well the runner uses the net head. Not a turbine design tool.
What to try
- Press Design point and compare the Euler head with the net head.
- Press Part load: the swirl left in the outlet grows and the Euler head falls.
- Press Over-speed: the Euler torque drops towards zero as the blades run away.