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The formula \( N = N_u \times \sqrt{H} \) calculates the working speed of a hydroelectric turbine based on its unit speed and the fall height of water. This relationship is fundamental in turbine design and operation for hydroelectric power generation.
The calculator uses the formula:
Where:
Explanation: The working speed is directly proportional to the unit speed and the square root of the fall height. This relationship accounts for the fundamental physics of hydroelectric power generation.
Details: Accurate calculation of turbine working speed is crucial for optimal power generation efficiency, proper turbine selection, and ensuring the turbine operates within its designed parameters for maximum performance and longevity.
Tips: Enter unit speed in Radian per Second and fall height in Meters. Both values must be positive numbers greater than zero for accurate calculation.
Q1: What is unit speed in turbine terminology?
A: Unit speed is defined as the speed of a geometrically similar turbine working under a head of 1m. It's a standardized measure used for comparing different turbine designs.
Q2: Why does working speed depend on the square root of fall height?
A: The square root relationship comes from the fundamental physics of fluid dynamics and energy conversion, where the velocity of water flowing under gravity is proportional to the square root of the head.
Q3: What factors affect the working speed of a hydroelectric plant?
A: Working speed depends on various factors including turbine design, type of turbines used, head and flow rate of water, and the desired electrical output requirements.
Q4: Are there limitations to this formula?
A: This formula provides a fundamental relationship but may need adjustments for specific turbine designs, efficiency factors, and real-world operating conditions that affect performance.
Q5: How is this calculation used in practical applications?
A: This calculation is used in turbine selection, power plant design, performance prediction, and optimization of hydroelectric power generation systems.