Short Answer:

The efficiency of a Pelton wheel is the ratio of the useful mechanical energy obtained from the turbine to the total energy supplied by the water jet. It measures how effectively the turbine converts the kinetic energy of water into mechanical energy. The efficiency mainly depends on the design, head, jet velocity, and bucket speed.

Generally, the overall efficiency of a Pelton wheel ranges from 85% to 90% under ideal operating conditions. This high efficiency is achieved when the bucket velocity is about half of the jet velocity and the water jet strikes the bucket properly without energy losses.

Detailed Explanation:

Efficiency of a Pelton Wheel

The efficiency of a Pelton wheel represents how well the turbine converts the kinetic energy of the water jet into mechanical energy on the runner. The main purpose of measuring efficiency is to determine the performance and effectiveness of the turbine. Since Pelton wheels are used in high head and low discharge conditions, their design is focused on minimizing losses and maximizing energy conversion.

The efficiency of a Pelton wheel can be expressed as the ratio of the power output from the turbine to the power input of the water jet supplied through the nozzle. Mathematically, it can be written as:

η = (Power Output / Power Input) × 100%

Where,

Power Output = Useful mechanical energy developed on the runner shaft.
Power Input = Energy of the water jet striking the buckets per second.

Types of Efficiency in Pelton Wheel

There are three main types of efficiencies that describe the performance of the Pelton wheel:

Hydraulic Efficiency (ηh):
It is the ratio of the power developed by the runner to the power supplied by the water jet.

This efficiency shows how effectively the water jet transfers its energy to the turbine buckets.

Mechanical Efficiency (ηm):
It is the ratio of the power available at the turbine shaft to the power developed by the runner.

Mechanical efficiency accounts for frictional and mechanical losses in bearings and the shaft system.

Overall Efficiency (ηo):
It is the product of hydraulic and mechanical efficiencies.

This represents the total efficiency of the Pelton wheel, indicating how much of the water’s energy is ultimately converted into usable mechanical energy at the shaft.

Derivation of Hydraulic Efficiency

Consider a water jet striking the bucket with a velocity , and the bucket moves with a tangential velocity .
Let the velocity of water at the outlet be , and the deflection angle of the jet be (usually between 160° and 170°).

The work done per second on the runner is:

Where,

= Density of water
= Cross-sectional area of the jet
= Jet velocity
= Bucket velocity
= Angle of deflection of the jet

The power supplied by the water jet is:

Thus,

For maximum efficiency, the derivative of efficiency with respect to is made zero, which gives:

This means that maximum efficiency occurs when the bucket speed is half of the jet velocity.

Substituting , the maximum hydraulic efficiency is obtained as:

If ,

But in practical conditions, the deflection angle is around 165°, giving a hydraulic efficiency of around 90%.

Factors Affecting Efficiency

Several factors influence the efficiency of a Pelton wheel:

Jet Velocity and Head:
Higher head increases the kinetic energy of the jet, improving efficiency up to an optimum point.
Bucket Velocity Ratio:
Efficiency is highest when bucket velocity is about half of jet velocity.
Deflection Angle:
The efficiency depends on the smooth deflection of the jet. A larger angle (160°–170°) provides higher efficiency.
Frictional Losses:
Losses in bearings, buckets, and nozzle decrease the overall efficiency.
Design of Buckets:
Properly designed buckets with smooth surfaces ensure minimal energy loss due to splashing and turbulence.
Jet Alignment:
The nozzle must direct the jet accurately on the bucket splitter for effective energy transfer.

Typical Efficiency Values

Hydraulic Efficiency: 90–92%
Mechanical Efficiency: 95–97%
Overall Efficiency: 85–90%

These high values make the Pelton wheel one of the most efficient impulse turbines for high-head applications.

Conclusion:

The efficiency of a Pelton wheel measures how effectively it converts the kinetic energy of water into mechanical energy on the turbine shaft. For best performance, the bucket velocity should be nearly half of the jet velocity, and losses must be minimized. Under ideal conditions, the Pelton wheel can achieve an overall efficiency of 85–90%. Its high efficiency, simple design, and durability make it widely used in hydroelectric power plants operating under high heads.