Pelton_wheel - Wikiparency

# Pelton wheel A **Pelton wheel** is an impulse [[Water_turbine|water turbine]] in which free jets of water strike split buckets around the rim of a wheel. The whole head is first turned into jet speed in a nozzle, U₁ = C_v√(2gH), and the buckets turn the jet back almost on itself, so that at the right bucket speed — about half the jet speed — the water drops away with little energy left.[^barmeir-6] Invented by Lester Allan Pelton in the 1870s, it is the standard machine for very high heads and low flows.[^doe-turbines] <div class="microsim-player"> <iframe src="https://wikitube-3d-microsims.netlify.app/Pelton_wheel.html" width="100%" height="620" frameborder="0" loading="lazy" sandbox="allow-scripts allow-same-origin" allow="accelerometer; gyroscope" title="Pelton wheel — p5.js microsim"></iframe> </div> *Microsim (THY-056): slide the bucket speed through half the jet speed and watch the efficiency curve peak; raise the head and the jet speeds up with √H. ILLUSTRATIVE: single jet, windage and bearing losses ignored.* Videos: [16:9](https://wikitube-3d-microsims.netlify.app/media/Pelton_wheel_16x9.mp4) · [9:16](https://wikitube-3d-microsims.netlify.app/media/Pelton_wheel_9x16.mp4) ## History Lester Allan Pelton developed his wheel in the 1870s to raise the efficiency of impulse machines; its split bucket, which divides the jet and throws it back to both sides, raised efficiency well above earlier impulse wheels.[^barmeir-6][^doe-turbines] ## Design Buckets or cups are set around the periphery of the wheel. Water forced through a nozzle forms a jet that hits the buckets; a central splitter divides the jet into two equal streams to cancel side loads. The bucket angles are typically about 165°, and part of each bucket's tip is cut away so the jet does not strike the preceding bucket.[^barmeir-6] ## Applications Pelton wheels are used where the head is very high and the flow low, from small off-grid installations on mountain streams to large high-head power stations. Horizontal-shaft machines usually have one or two jets; vertical-shaft machines can have up to six.[^barmeir-6] ## Design rules The jet diameter is kept to a fraction of the wheel diameter, and the number of jets is chosen to pass the design flow. In a worked design example, a wheel for 325 m of head and 775 rpm, with a velocity coefficient of 0.98 and a speed ratio of 0.45, gives a jet speed of about 78 m/s and a wheel diameter of about 0.87 m.[^barmeir-6] ## Turbine physics and derivation The analysis follows the momentum of the jet in the frame of the moving bucket.[^barmeir-6] ### Energy and initial jet velocity The head H becomes jet speed U₁ = C_v√(2gH), with a velocity coefficient C_v near 0.98; the jet carries power ρQU₁²/2.[^barmeir-6] ### Final jet velocity Relative to a bucket moving at u, the jet arrives at U₁ − u and leaves turned through the bucket angle, slowed by friction by a factor k. The water's absolute speed on leaving is what the wheel fails to capture. ### Optimal wheel speed With the speed ratio λ = u/U₁, the efficiency is proportional to λ(1 − λ), which is greatest at λ = 1/2; in practice the best ratio is about 0.46.[^barmeir-6] ### Torque The torque on the wheel is proportional to (U₁ − u): greatest when the wheel is held still and zero when the buckets run as fast as the jet. ### Power Power is torque times angular speed, so it is proportional to u(U₁ − u) — zero at standstill and at runaway, and greatest in between. ### Efficiency Written with the total deflection θ of the jet, η = 2λ(1 − λ)(1 − k cos θ). With θ = 165° and k = 0.9 the maximum hydraulic efficiency is about 93%; with no friction and a full 180° turn it would be 100%.[^barmeir-6] ## System components A Pelton installation comprises an intake, a [[Penstock|penstock]] that carries water down to the powerhouse, one or more nozzles with needle valves to regulate the jets, the wheel, a jet deflector that can divert the jet quickly when load is lost, and a housing that catches the spent water. A reversed "braking jet" can stop the wheel.[^barmeir-6] ## See also - [[Water_turbine]] - [[Francis_turbine]] - [[Water_wheel]] - [[Penstock]] ## References [^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 ### Portal Books - 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. ## External links - [Types of Hydropower Turbines](https://www.energy.gov/eere/water/types-hydropower-turbines), U.S. Department of Energy  *Connected to the Apex Spine:* Pelton wheel → [[Hydropower|Hydropower]] — [[WT!Thury_Hydrodynamics_Compendium|Compendium]] section 15, *Hydropower*.  ## Wikipedia : Wikitube **Strict pair:** [Wikipedia](https://en.wikipedia.org/wiki/Pelton_wheel) : [Wikitube](https://en.wikitube.io/wiki/Pelton_wheel) · pinned revision [1364926093](https://en.wikipedia.org/w/index.php?oldid=1364926093) · 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-056 (p5.js) · parent [[Hydropower]].*