🌀 Turbines: The Machines That Make Almost All Electricity

What you’ll learn

1. One Machine, Nine-Tenths of the PowerRecognise that almost all electricity is made by one machine, and set up the course's central claim: the fluid changes, the turbine does not.In 2024 the world generated about 30,850 TWh of electricity. Coal, gas, hydro, nuclear and wind — everything except solar PV and a sliver of 'other' — reach the grid through a shaft spun by a fluid in a turbine. That is roughly 88% of world electricity from one machine family. The rest of the course treats the turbine as a single machine seen four ways.
2. What a Turbine Actually DoesReplace the intuition that a turbine is 'pushed' with the correct one: it turns the flow, and the torque is the rate of change of the fluid's angular momentum.A turbine does not extract work by being shoved. It extracts work by changing the fluid's angular momentum: the blade row deflects the flow sideways, and the reaction to that deflection is torque on the shaft. Euler's turbomachinery equation says the specific work equals the blade speed times the change in the fluid's swirl velocity — which means a turbine that does not turn the flow does no work, however hard the fluid hits it.
3. Velocity Triangles: Seeing From the BladeUse the relative frame — the velocity triangle — as the working language of turbomachinery, and see why a blade must be twisted along its span.The fluid's velocity as you see it (absolute) and as the moving blade sees it (relative) differ by the blade speed U: V = W + U. Turbine blades are shaped for the relative flow, which is why a blade at rest looks wrong. Because U grows with radius while the axial velocity does not, the relative flow angle changes along the span — which is exactly why a long turbine blade is twisted.
4. Impulse and Reaction: Two Ways to Take the EnergyDistinguish impulse from reaction staging via the degree of reaction, and see the trade each one makes.In a pure impulse stage all the pressure drop happens in the stator; the rotor only turns a high-speed jet at constant pressure. In a reaction stage the pressure also falls across the rotor, so the blade passage acts as a nozzle. Degree of reaction quantifies the split. Impulse gives more work per stage and simple sealing; reaction is gentler and more efficient. De Laval and Parsons built the two archetypes within a year of each other, and both machines are still with us.
5. Why One Stage Is Never EnoughExplain staging: why the blade-speed limit forces a large pressure drop to be taken in many small bites, and how pressure and velocity compounding do it.Work per stage scales with U², but U is capped by blade stress, so a single stage can only take a modest bite of a large pressure drop. De Laval's single wheel needed 30,000+ rpm and gearing. The fix is compounding: many stages in series, each taking a fraction — pressure compounding (Rateau), velocity compounding (Curtis), or Parsons' reaction ladder. This is why a steam turbine is metres long and a Pelton wheel is not.
6. Why the Blades Get BiggerExplain the flared shape of a turbine from mass conservation: as the fluid expands, the flow area must grow, which is why blades lengthen down the machine.Mass flow is constant through a turbine, so ρ·A·V must be constant. As a compressible fluid expands and its density collapses, the flow area must grow to pass the same kilograms — so blades get dramatically longer toward the exhaust. In a large steam turbine the density falls by a factor of hundreds, which is why the last stages carry blades over a metre long and why the machine is trumpet-shaped. Water turbines, being incompressible, do not flare this way.
7. The Blade Is the MachineLocate the real limit of all turbomachinery in the centrifugal stress at the blade root, and understand creep as the constraint that actually decides the design.Centrifugal stress at a blade root scales as ρ·ω²·r² — quadratic in speed — and it is the hard cap on U, which caps work per stage. Worse, the blade is hot, and hot metal under constant load creeps: it slowly stretches until it touches the casing or fails. Creep, not melting and not instantaneous strength, is the limit that decides service life. This is why the machine wants a faster blade and can never have one.
8. Hotter Than MeltingExplain why gas turbine blades run in gas hotter than their own melting point, and how internal, film and barrier cooling buy that margin — at a cost.Efficiency drives turbine inlet temperature up, and the gas turbine now fires hotter than its blades can survive: first-stage blades sit in gas around 1,370 °C, and GE's 9HA fires at up to 1,540 °C. The blade survives because roughly 1–3% of the main flow is bled to cool it, lowering blade temperature by 200–300 °C, with a ceramic thermal barrier coating of 1–200 μm worth up to another 200 °C. Every gram of cooling air is air that skipped the combustor — the cooling is itself a loss you accept to enable a bigger gain.
9. Water: The Head Chooses the MachineSee how head and flow select between Pelton, Francis and Kaplan, and understand cavitation as the incompressible fluid's characteristic threat.Hydro turbines are the same machine again, but water's incompressibility and its low vapour pressure change the consequences. Head selects the type: Pelton for roughly 80–1,600 m, Francis for about 10–300 m, Kaplan for about 2–70 m. High head means a fast jet and a small machine; low head means vast flow and a huge one. Water's unique threat is cavitation: drop the local pressure below vapour pressure and the water boils, then the bubbles collapse and hammer the metal away.
10. Wind: The Turbine With No PipeUnderstand the Betz limit as the consequence of an unducted turbine, and why it caps wind extraction at 59.3%.A wind turbine is the same machine with one constraint removed and a worse one added: there is no duct, so the air is free to go around. Slow the air too much and it simply refuses to enter. Betz's 1919 analysis puts the ceiling at 16/27 — 59.3% — of the wind's kinetic energy, and modern utility turbines reach 75–80% of that, giving power coefficients of about 0.45–0.50. The Betz limit is not a statement about blades; it is a statement about mass conservation in an open flow.
11. Steam: The Biggest Machine in the BuildingSee how the steam turbine's constraints — grid frequency, condenser vacuum and wetness — produce the largest single machines ever built.Steam turbines make the majority of the world's electricity and are the largest of the family: the largest ever built is the 1,770 MW Arabelle. A directly coupled machine must turn at 3,000 rpm (50 Hz) or 3,600 rpm (60 Hz) — grid frequency, not aerodynamics, fixes the speed. That fixed ω, plus the condenser vacuum that makes the steam's density collapse, plus wetness at the exhaust, together determine everything about the machine's shape and its limits.
12. When It Lets GoUnderstand overspeed as the characteristic catastrophic failure of turbomachinery, and see why the governor — not the blade — is the last line of defence.A turbine on the grid is held at synchronous speed by the generator's electromagnetic load. Remove that load instantly — a breaker opens — and a machine designed for one speed accelerates hard, with root stress climbing as ω². Because stress is quadratic, a modest overspeed is a large stress rise, so every large turbine carries an overspeed trip whose only job is to shut off the fluid within seconds. It is the last, unavoidable consequence of a course spent wanting a faster blade.

Questions this course answers

Grounded in trusted sources

• Wikipedia — Electricity generation (2024 world generation by source: coal 10,587 TWh / 34.4%, gas 6,796 / 22.1%, hydro 4,417 / 14.4%, nuclear 2,765 / 8.99%, wind 2,497 / 8.12%, solar 2,130 / 6.92%, other 1,569 / 5.10%; total 30,850 TWh): https://en.wikipedia.org/wiki/Electricity_generation
• Wikipedia — Steam turbine (Parsons 1884, 7.5 kW; ~10,000× scale-up in his lifetime to 50 MW units; largest ever built = 1,770 MW Arabelle; 3,000 rpm at 50 Hz / 3,600 rpm at 60 Hz; de Laval impulse vs Parsons reaction; compounding; ~42% of US generation in 2022): https://en.wikipedia.org/wiki/Steam_turbine
• Wikipedia — Turbine blade (first-stage blades ~1,370 °C; Snecma M88 ~1,590 °C; cooling air 1–3% of main flow, reducing blade temperature 200–300 °C; TBC from the 1970s; directional solidification and single-crystal casting from Pratt & Whitney in the 1960s): https://en.wikipedia.org/wiki/Turbine_blade
• Wikipedia — Gas turbine (GE 9HA firing up to 1,540 °C; TBC 1–200 μm lowering blade temperature by up to 200 °C; simple cycle ~30%; Siemens SGT5-9000HL 64.18% combined cycle, record as of 2024): https://en.wikipedia.org/wiki/Gas_turbine
• Wikipedia — Water turbine (head ranges — Pelton 80–1,600 m, Turgo 50–250 m, Francis 10–300 m, Kaplan 2–70 m; efficiency >90%; Pelton up to 92%; Baihetan 1,000 MW units, largest as of 2021; cavitation pitting): https://en.wikipedia.org/wiki/Water_turbine
• Wikipedia — Betz's law (16/27 = 59.3%; Betz 1919, Lanchester 1915, Zhukowsky 1920; four assumptions; modern turbines reach 75–80% of the limit, C_P ≈ 0.45–0.50): https://en.wikipedia.org/wiki/Betz%27s_law
• Wikipedia — Euler's pump and turbine equation: https://en.wikipedia.org/wiki/Euler%27s_pump_and_turbine_equation
• Wikipedia — Turbine; Pelton wheel; Francis turbine; Kaplan turbine; Cavitation; Creep (deformation); Superalloy; Water hammer; Black start

Every Wunder lesson is built from real, reputable sources — never invented.

Related Science courses