Turbines

Turbines extract energy from flowing fluids. Learn impulse vs reaction turbines, hydraulic turbines (Pelton, Francis, Kaplan), steam and gas turbines, power and efficiency, specific speed and turbine selection.

Most of the world's electricity comes from turbines — water, steam, gas or wind turning a shaft that drives a generator. Jet engines use turbines to drive their compressors.

The design depends on how much head (pressure) and flow is available: high head and low flow needs a very different machine from low head and huge flow.

An analogy

A pinwheel in the wind or a water wheel in a stream: the fluid pushes blades, turning the shaft. Modern turbines are highly refined versions of the same idea.

Impulse vs reaction

Impulse turbines convert all pressure to a high-speed jet in a nozzle; the jet hits buckets at atmospheric pressure (Pelton). Reaction turbines let pressure drop across the rotating blades themselves, which are fully submerged (Francis, Kaplan, most steam and gas turbine stages).

Hydraulic turbine selection

Pelton: high head (> 250 m), low flow. Francis: medium head (40–600 m) — most common in large dams. Kaplan/propeller: low head (< 40 m), high flow, adjustable blades. Specific speed guides the choice. Large hydro turbines exceed 94 % efficiency.

Steam and gas turbines

Steam expands through many stages of fixed nozzles and moving blades, with blades growing longer as pressure falls. Gas turbines expand hot combustion gas at 1300–1600 °C; roughly half their output drives the compressor.

Velocity triangles and losses

Blade design uses velocity triangles and Euler's equation to set blade angles. Losses: profile, secondary flow, tip leakage, exit kinetic energy, and moisture (steam). Degree of reaction splits the enthalpy drop between stator and rotor; 50 % reaction stages are common.

Formulas

• Hydro power: P = η ρ g Q H
• Jet velocity (Pelton): V = C_v √(2 g H), optimum u ≈ 0.46–0.5 V
• Specific speed (power): N_s = N √P / H^(5/4)
• Steam/gas turbine power: Ẇ = ṁ (h₁ − h₂)

Worked example: Hydro plant output

Given: Q = 10 m³/s, H = 50 m; η = 90 %

Find: Power.

• P = 0.9 × 998 × 9.81 × 10 × 50 = 4.41 MW

Answer: ≈ 4.4 MW

Worked example: Pelton jet

Given: Net head 400 m; C_v ≈ 1

Find: Jet speed and ideal bucket speed.

• V = √(2 × 9.81 × 400) = 88.6 m/s
• u ≈ 0.46 × 88.6 = 40.8 m/s

Answer: 88.6 m/s jet, ≈ 41 m/s buckets

Common mistakes

• Wrong: Using gross head. — Right: Use net head = gross head − penstock losses.
• Wrong: Choosing a Pelton for low head. — Right: Match turbine type to head/specific speed.

Applications

• Hydropower: From micro-hydro (kW) to Three Gorges (22.5 GW) — plus pumped storage.
• Thermal power plants: Steam turbines up to 1.7 GW per unit; gas turbines in combined cycles.
• Aviation & marine: Turbofans, turboprops, turboshafts and turbochargers.

Key takeaways

• P = ηρgQH; steam/gas: ṁΔh.
• Impulse (Pelton) vs reaction (Francis, Kaplan).
• Select by head/specific speed.
• Pelton buckets run at ~half jet speed.

Going further

• Pumped storage: Reversible Francis pump-turbines store grid energy with 70–80 % round-trip efficiency.
• Blade cooling: Gas-turbine blades use internal passages and film cooling to survive gas hotter than their melting point.
• Draft tubes: Diffusers after reaction turbines recover exit kinetic energy and allow the turbine to sit above tailwater.