What is the range of specific speed for Pelton wheels?

Short Answer:

The specific speed of a Pelton wheel is a numerical value that helps to compare the performance of different turbines. It is used to select the most suitable type of turbine for a given head and discharge. The specific speed of a Pelton wheel is generally low because it is an impulse turbine that works under a very high head and low discharge conditions.

The range of specific speed for Pelton wheels lies between 10 to 35 (metric units) or 0.5 to 3.0 (dimensionless form). This range indicates that Pelton wheels are suitable for high head and low flow rate conditions, typically found in mountain or hilly regions.

Detailed Explanation :

Range of Specific Speed for Pelton Wheels

The specific speed is an important parameter used in the design and selection of hydraulic turbines. It helps to classify turbines according to the head, discharge, and rotational speed required for a given output power. The Pelton wheel is an impulse turbine, which operates under a high head and low discharge. Because of this, its specific speed is comparatively low.

Definition of Specific Speed:
The specific speed of a turbine is defined as the speed at which a geometrically similar turbine would run to produce one unit power under a unit head. Mathematically, it is given by:

Where,
= Specific speed of turbine
= Actual speed of turbine in rpm
= Power developed by the turbine in kW
= Head of water in meters

The value of specific speed helps engineers to decide the type of turbine suitable for a particular site depending on the available head and discharge.

Range for Pelton Wheels

For Pelton wheel turbines, the typical range of specific speed is:

  • Metric Units: 10 to 35
  • Dimensionless Units: 0.5 to 3.0

This range shows that Pelton wheels are designed to work efficiently at very high heads (up to 1000 meters or more) and small discharges. The lower value of specific speed means the turbine runs at a slower speed for the given head and power, which is suitable for high-head, low-flow conditions.

Reason for Low Specific Speed

The low specific speed of Pelton wheels is mainly due to the following reasons:

  1. High Head and Low Discharge: Pelton wheels use the potential energy of water stored at high altitudes. Since discharge is small, the power developed per unit head is less, resulting in a low specific speed.
  2. Impulse Nature: It works by converting the entire available head into kinetic energy before striking the buckets. Hence, the velocity of the jet is very high, but the rotational speed of the wheel remains comparatively low.
  3. Single or Double Jet Operation: Pelton wheels generally use one or two jets, which also limits the discharge rate and keeps the specific speed low.
  4. Heavy Runner Construction: The runner is large and heavy to handle the high-speed jet, so it cannot rotate very fast, which again contributes to the low specific speed.

Comparison with Other Turbines

To understand the range more clearly, it is helpful to compare it with other types of turbines:

  • Pelton Wheel: 10 to 35 (for high head, low discharge)
  • Francis Turbine: 60 to 300 (for medium head and discharge)
  • Kaplan Turbine: 300 to 1000 (for low head, high discharge)

From this comparison, we can see that the Pelton wheel has the lowest specific speed, making it ideal for power plants where water falls from great heights, such as in mountain hydroelectric stations.

Importance of Specific Speed Range

The range of specific speed helps in:

  • Selection of Proper Turbine Type: Engineers use the value of specific speed to decide whether to use a Pelton, Francis, or Kaplan turbine.
  • Design Optimization: It helps in designing the runner, number of jets, and size of buckets to achieve the best performance.
  • Performance Prediction: Specific speed also indicates the expected efficiency and speed characteristics of the turbine under various load conditions.
  • Standardization: The range provides a basis for standardizing turbine dimensions and performance parameters.

Example:

If a Pelton wheel operates under a head of 600 m and produces 5000 kW of power at a speed of 400 rpm, its specific speed can be calculated as:

 

This value lies within the typical range (10 to 35), confirming that the turbine is a Pelton wheel type.

Conclusion:

The specific speed of a Pelton wheel indicates its suitability for high-head and low-discharge conditions. The typical range of specific speed for Pelton wheels is 10 to 35 (metric) or 0.5 to 3.0 (dimensionless). Its low value results from the impulse nature of operation, high head requirement, and small discharge. This range helps engineers select the right turbine and ensures efficient energy conversion in hydroelectric power plants located in hilly or mountainous regions.