Francis Turbine Speed Ratio Calculator

Francis Turbine Speed Ratio Formula:

\[ K_u = \frac{u_1}{\sqrt{2 \cdot g \cdot H_i}} \]

Velocity of Vane at Inlet (u₁):

m/s

Acceleration Due to Gravity (g):

m/s²

Head at Inlet (Hᵢ):

Speed Ratio (Kᵤ):

Unit Converter ▲

Unit Converter ▼

From:	To:

1. What is the Francis Turbine Speed Ratio?

The Francis Turbine Speed Ratio (Kᵤ) is the ratio of tangential velocity to the theoretical velocity. It is a crucial parameter in the design and analysis of Francis turbines, which are widely used in hydroelectric power generation.

2. How Does the Calculator Work?

The calculator uses the Francis Turbine Speed Ratio formula:

\[ K_u = \frac{u_1}{\sqrt{2 \cdot g \cdot H_i}} \]

Where:

\( K_u \) — Speed Ratio of Francis Turbine
\( u_1 \) — Velocity of Vane at Inlet (m/s)
\( g \) — Acceleration Due to Gravity (m/s²)
\( H_i \) — Head at Inlet of Francis Turbine (m)

Explanation: The formula calculates the ratio between the actual tangential velocity of the vane at the inlet and the theoretical velocity derived from the available head.

3. Importance of Speed Ratio Calculation

Details: Accurate speed ratio calculation is essential for optimizing turbine efficiency, ensuring proper turbine design, and maintaining stable operation under various load conditions in hydroelectric power plants.

4. Using the Calculator

Tips: Enter velocity of vane at inlet in m/s, acceleration due to gravity in m/s² (default is 9.81 m/s²), and head at inlet in meters. All values must be positive.

5. Frequently Asked Questions (FAQ)

Q1: What is the typical range for Francis Turbine Speed Ratio?
A: The speed ratio typically ranges between 0.6-0.9 for optimal Francis turbine performance, though this can vary based on specific design parameters.

Q2: How does speed ratio affect turbine efficiency?
A: The speed ratio significantly impacts turbine efficiency. An optimal speed ratio ensures maximum energy transfer from water to the turbine blades.

Q3: Can this calculator be used for other turbine types?
A: No, this specific formula is designed for Francis turbines. Other turbine types (Kaplan, Pelton) have different speed ratio formulas.

Q4: What factors influence the velocity of vane at inlet?
A: Vane velocity is influenced by turbine rotational speed, blade design, and the specific geometry of the turbine runner.

Q5: Why is acceleration due to gravity included in the formula?
A: Gravity acceleration is fundamental to calculating the theoretical velocity derived from the available hydraulic head, as it relates to the potential energy of the water.