Francis_turbine - Wikiparency

# Francis turbine A **Francis turbine** is an inward-flow reaction [[Water_turbine|water turbine]]: water enters a spiral casing, is given a swirl by adjustable guide vanes, and passes inward and down through a runner of fixed curved blades, leaving along the axis into a draft tube. Its work per kilogram of water is given by the Euler turbine equation, P = ṁ(u₁U_w1 − u₂U_w2): the runner takes out the whirl the guide vanes put in, and at its best operating point the water leaves with almost no swirl.[^barmeir-6] Francis turbines serve medium to high heads, roughly 40 to 600 m, and are the most common turbines in large [[Hydroelectricity|hydroelectric]] stations.[^doe-turbines] <div class="microsim-player"> <iframe src="https://wikitube-3d-microsims.netlify.app/Francis_turbine.html" width="100%" height="620" frameborder="0" loading="lazy" sandbox="allow-scripts allow-same-origin" allow="accelerometer; gyroscope" title="Francis turbine — p5.js microsim"></iframe> </div> *Microsim (THY-057): open the guide vanes and watch the inlet and outlet velocity triangles; efficiency peaks where the outlet whirl vanishes. ILLUSTRATIVE: two-station velocity triangles and a simple loss model.* Videos: [16:9](https://wikitube-3d-microsims.netlify.app/media/Francis_turbine_16x9.mp4) · [9:16](https://wikitube-3d-microsims.netlify.app/media/Francis_turbine_9x16.mp4) ## Development The Francis turbine is named for James B. Francis, chief engineer of the Locks and Canals company at Lowell, Massachusetts, who in the mid-nineteenth century refined earlier inward-flow designs through careful testing and calculation, producing a turbine that could be designed to match a site's flow and head. ## Components The main parts are the spiral casing, which distributes water around the runner; the stay vanes, which carry the casing's structural loads; the guide vanes or wicket gates, which regulate flow and set its swirl; the runner, whose blades take the swirl out; and the draft tube, which slows the leaving water and recovers part of its kinetic energy as pressure. ## Theory of operation Water enters the runner with a tangential velocity component U_w1 set by the guide vanes and leaves with a component U_w2. The torque on the runner equals the mass flow times the change in angular momentum, and the power is P = ṁ(u₁U_w1 − u₂U_w2), where u₁ and u₂ are the blade speeds at inlet and outlet.[^barmeir-6] In a reaction turbine both the pressure and the velocity of the water fall across the runner, which runs full of water.[^doe-turbines] ## Blade efficiency The blades convert the most energy when the relative flow meets the blade edges without shock at the inlet and the absolute flow leaves without whirl at the outlet (U_w2 ≈ 0). Away from that point, part of the energy leaves as swirl in the draft tube or is lost at the inlet edges, and the efficiency falls; the efficiency-versus-opening curve is therefore a hill with its top at the design flow. ## Degree of reaction The degree of reaction is the share of the energy converted by pressure change within the runner, compared with the total converted. An impulse turbine has a degree of reaction of zero; Francis turbines have an intermediate value, with part of the conversion in the guide vanes and part in the runner.[^barmeir-6] ## Application Francis turbines are used for medium- to high-head sites, about 130 to 2,000 ft (40 to 600 m), in horizontal or vertical arrangements.[^doe-turbines] Because they can run backward as pumps, reversible Francis pump-turbines are the usual machines in [[Pumped-storage_hydroelectricity|pumped-storage]] plants.[^kerlin-9] ## See also - [[Water_turbine]] - [[Pelton_wheel]] - [[Pumped-storage_hydroelectricity]] - [[Hydroelectricity]] ## Citations [^barmeir-6]: Bar-Meir, Genick (2025). *Basics of Fluid Mechanics*, version 0.7.5, §6.3 "Machinery Unitizing Momentum" (Euler turbine equation; Pelton wheel), pp. 253–261. https://open.umn.edu/opentextbooks/textbooks/basics-of-fluid-mechanics [^doe-turbines]: U.S. Department of Energy, Water Power Technologies Office. "Types of Hydropower Turbines." https://www.energy.gov/eere/water/types-hydropower-turbines [^kerlin-9]: Kerlin, Thomas W. (2013). *Future Energy: Opportunities & Challenges*, ch. 9 "Hydroenergy," pp. 203–216 (§9.4 dams and small systems; §9.5 pumped storage; §9.6 river-flow converters). ISA; CC BY 4.0. https://open.umn.edu/opentextbooks/textbooks/future-energy-opportunities-challenges ## General bibliography - Bar-Meir, Genick (2025). *Basics of Fluid Mechanics*, v0.7.5 — [OTL record](https://open.umn.edu/opentextbooks/textbooks/basics-of-fluid-mechanics); on the [[PORTAL_WT!Thury_Hydrodynamics_Compendium|Compendium]] Fluid core shelf. - Kerlin, Thomas W. (2013). *Future Energy: Opportunities & Challenges* — [OTL record](https://open.umn.edu/opentextbooks/textbooks/future-energy-opportunities-challenges); on the [[PORTAL_Thury_Hydrodynamics_Apex_Spine]] and [[PORTAL_Energy]] shelves.  *Connected to the Apex Spine:* Francis turbine → [[Hydropower|Hydropower]] — [[WT!Thury_Hydrodynamics_Compendium|Compendium]] section 15, *Hydropower*.  ## Wikipedia : Wikitube **Strict pair:** [Wikipedia](https://en.wikipedia.org/wiki/Francis_turbine) : [Wikitube](https://en.wikitube.io/wiki/Francis_turbine) · pinned revision [1372086986](https://en.wikipedia.org/w/index.php?oldid=1372086986) · 2026-09-10 ## Previous hub tags Hubs: `Life_Physics`, `Systems`. Portals: [[PORTAL_Thury_Hydrodynamics_Apex_Spine]], [[PORTAL_Energy]]. --- *Thury station wave · 2026-09-10 · drafted · microsim THY-057 (p5.js) · parent [[Hydropower]].*