Pelton turbine: Head, jet and nozzle

Pelton turbine head: it determines the velocity of the jet

In the nozzle almost all of the usable pressure is converted into velocity. How fast the jet leaves the nozzle therefore depends mainly on the head. At 400 metres it is about 89 metres per second, which is just over 319 kilometres per hour.

The head is not measured and applied at the nozzle but at the inlet of the distributor. That is the reference section to which the guarantees refer under the standard for model tests; the losses in the distributor and in the nozzle, about 2 per cent of the energy together, then stand in the loss balance.

For engineers: c₁ = √(2 · g · H), with H as the head in m, referred to the high pressure reference section of IEC 60193, here the inlet of the distributor, and g = 9.81 m/s². For the first estimate the calculation uses the full jet velocity; the losses up to the jet stand, as in Veselý, as a share of the energy in the loss balance. After Josef Erlach they total 1.8 to 2 per cent at nominal opening, about 0.5 per cent in the nozzle and about 1.5 per cent in the distributor. Veselý's loss balance gives 2.0 per cent for the nozzle outlet. Example: H = 400 m gives c₁ = 88.6 m/s.

Formula as text: c_1 = sqrt(2 · g · H). Quantities: c_1 jet velocity in m/s; g gravitational acceleration in m/s², equal to 9.81; H head, referred to the high pressure reference section of IEC 60193, here the inlet of the distributor in m.

Source: IEC 60193, section 1.3.3.1.1 (high pressure reference section); Josef Erlach, 3 October 2026 (jet velocity and reference section).

Pelton turbine discharge: the discharge determines the diameter of the jet

Once the velocity is fixed, the discharge of one nozzle gives the diameter of its jet. More water means a thicker jet. Half a cubic metre per second at a head of 400 metres gives a jet of about 85 millimetres.

The jet must not become too thick in relation to the runner. The characteristic number for this is the specific speed. More under Pelton turbine specific speed.

For engineers: d₀ = √(4 · Q_nozzle / (π · c₁)). Example: Q_nozzle = 0.5 m³/s and c₁ = 88.6 m/s give d₀ = 85 mm.

Formulas as text: Q_nozzle = Q / z; d_0 = sqrt(4 · Q_nozzle / (pi · c_1)). Quantities: Q_nozzle discharge per nozzle in m³/s; Q discharge of the turbine in m³/s; z number of nozzles, no unit; d_0 jet diameter in m; pi the number pi, no unit, equal to 3.1416; c_1 jet velocity in m/s.

Needle of the Pelton nozzle: it controls the discharge, not the velocity

A needle sits in the nozzle. When it moves forward, the opening gets smaller and less water passes through. When it moves back, the jet gets thicker. The velocity depends on the head and stays almost the same while the nozzle is wide open; at a very small opening it drops markedly (Veselý, Fig. 14).

This is why a Pelton turbine is easy to control: the needle sets the power without the jet losing its effect on the bucket. It is not entirely free of loss: the further the needle closes, the more energy stays in the nozzle. At full opening the nozzle reaches its best efficiency, at small openings it drops markedly. This is why nozzles are run open, and at low discharge single nozzles are switched off instead, see Pelton turbine efficiency.

For engineers: Veselý calculates the nozzle efficiency η_n = 1 − (p_t1 − p_t2) / p_t1 from the total pressures at inlet and outlet: 0.86 at a needle stroke of 6 per cent of the nozzle tip diameter (Re 37,000), about 0.99 at 66 per cent; for every Pelton nozzle the maximum lies at full opening.

Formula as text: eta_n = 1 − (p_t1 − p_t2) / p_t1. Quantities: eta_n nozzle efficiency, no unit; p_t1 total pressure at the nozzle inlet in Pa; p_t2 total pressure at the nozzle outlet in Pa.

Source: J. Veselý, Energy losses evaluation for high specific speed Pelton turbine, ČKD Blansko Engineering, pp. 256–257, Fig. 14.

Pelton turbine design point: both are fixed for the design

For the point a machine is designed for, the plant sets the head and the discharge. The opening of the nozzle follows from them, not the other way round. In operation it is the needle that sets the discharge. As the discharge changes, the losses in the penstock change, and with them the head at the nozzle changes a little.

Anyone who calculates a flow has to know this beforehand. If the calculation for the design point is given the position of the needle and the head is left open, it calculates correctly and answers the wrong question.

Josef Erlach, Pelton jet measure: equal amounts of water left and right of the guide vanes

In the nozzle, guide vanes lead the water past the needle. If more water flows on one side of the vanes than on the other, the jet becomes one-sided. Equal amounts on both sides are therefore a precondition for a round, steady jet. It is not the only one: swirl and uneven velocity also disturb the jet.

The aim of the flow calculation is a straight jet behind the nozzle. The proof is the mass flow right and left of the fin, considered at half the length of the nozzle: if it is approximately equal, the jet can become good. For the calculation the discharge is prescribed, not the needle position, because needle and nozzle tip have different shapes and therefore different characteristics depending on the manufacturer.

Source: Josef Erlach, 3 October 2026.

Josef Erlach therefore judges the inflow to a nozzle by two things. The first: does every nozzle get the same amount of water? The second: does the water in the individual nozzle split equally between both sides? The first measure shows whether the distributor divides the water fairly. More under Pelton turbine distributor. The second measure shows whether the jet can become good.