Impulse Turbine

In an impulse turbine, energy is extracted from a jet of liquid. The energy of a parcel of water m moving at velocity V is E = 1/2 m V². If water enters the turbine at speed V₀ and exits at speed V₁, the initial energy, E₀ = 1/2 m V₀² and final energy, E₁ = 1/2 m V₁² can be calculated by the above formula.

The efficiency is the portion of this energy that is transferred to the wheel, Eff = (E₁ - E₀) / E_0. So determining the efficiency entails calculating the final velocity, V₁, and final energy, E₁.

The final velocity is determined by the wheel speed, U. If the wheel is not turning, the water will bounce off at the same speed, the initial velocity and final velocity will be equal, the initial energy and final energy will be equal and the efficiency will be zero. Likewise, if the wheel speed, U, is the same as the water velocity V, the initial and final velocities will be equal, initial and final energies will be equal, and the efficiency will again be zero.

Maximum efficiency occurs when the wheel speed is half the water jet speed. In this case, as seen from the viewpoint of the wheel, the water jet hits the wheel at V/2 and bounces off at V/2 in the opposite direction. From the viewpoint of the jet, water hits the wheel at speed V and exits at speed 0, thus removing all of its kinetic energy. Efficiency is 100%.

For other values of wheel velocity, U, and jet velocity V₀ :

The exit velocity, V₁ = V₀ - U - U = V₀ - 2U

Substituting in for values of energy for values of U, V₀, and V₁ in the efficiency formula:

Eff = (E0 - E1)/E0 = (V₀² - (V₀-2U)²) / V₀²