Head 15 m Flow 0 m³/s Speed 150 rpm · 50 Hz Power 0 MW Efficiency 0 % Cavitation margin ok FPS 0
Hero Side Runner Tailrace
Water (blue ) flows left to right: penstock → guide vanes (give it swirl) → runner (takes the swirl out, turning it into torque) → draft tube. The shaft turns the generator (copper ); power goes to the grid. White specks near the blade tips = cavitation warning. Drag to rotate, wheel to zoom.
WebGL is not available here — the turbine model on the right still runs.
Kaplan Turbine Cutaway: Velocity Triangles, Euler Head and Cavitation Margin
Follow the water through a propeller-type turbine and see how swirl, blade angle, head and tailwater set power, efficiency and cavitation risk.
Educational model: one mean-radius streamline, simplified losses and a model cavitation criterion. It is not a design or safety tool.
Controls
Auto-Kaplan: on Pause Reset Quality: High
Results
Velocity triangles (mean radius)
u = blade speed, c = absolute water velocity, w = velocity relative to the blade. Inlet (left) is after the guide vanes; outlet (right) leaves the runner. The Euler head is u(cu1 − cu2 )/g.
Power and efficiency versus flow
Cyan = with the Kaplan cam, orange = with the current blade angle held fixed.
Missions
Independent numerical checks
Controls help Drag or one finger: rotate. Wheel or pinch: zoom. Buttons Hero / Side / Runner / Tailrace (keys 1–4) jump to camera presets. Gate opening sets the flow. With Auto-Kaplan off you set the blade angle yourself: too small and the flow is choked, too large and the gate throws the head away. Space pauses the animation; visual speed only slows what you see, not the physics.The science
Euler turbine equation. The runner turns the swirl of the water into torque: specific work w = u·(cu1 − cu2 ), shaft power P = ρ·Q·w·ηmech . At the mean radius u = πDm n/60, ca = Q/A, cu1 = ca /tanα from the guide vanes and cu2 = u − ca /tanβ2 from the blade exit angle.
Head balance. gH = w + losses + gate loss. Losses: conduit and blade friction, exit (draft tube) loss and shock when the relative flow does not match the blade inlet angle. If the blades could use more than the available head, the flow is reduced until the balance closes. The Kaplan cam chooses the blade angle that leaves nothing for the gate to throw away.
Grid frequency. f = n·p/60 with p = 20 pole pairs: 150 rpm gives 50 Hz.
Cavitation. Thoma number σ = (Hatm − Hv − Hs )/H, with Hs the height of the runner above the tailwater. Bubbles can form when σ falls below a critical value that grows with specific speed (here a simple model value, not a design rule) [check against a hydraulic-machinery textbook].
Simplifications. One streamline at the rms radius, free-vortex radial distribution only in the numerical check, no secondary flows, constant loss coefficients, no water hammer or fish passage. Not affiliated with any manufacturer.
Sources of this kind: hydraulic machinery textbooks, acceptance-test standards for hydraulic turbines, open dam and plant data.
Made with Blender (turbine, generator, plant, landscape) and rendered with Three.js.