Volume Flow Rate of Acute Angled Francis Turbine Given Work Done Per Second on Runner Calculator

Formula Used:

\[ Q_f = \frac{W}{\rho_f \times (V_{w1} \times u_1 + V_{w2} \times u_2)} \]

Work Done Per Second by Francis Turbine:

Watt

Density of Fluid in Francis Turbine:

kg/m³

Whirl Velocity at Inlet of Francis Turbine:

m/s

Velocity of Vane at Inlet For Francis Turbine:

m/s

Whirl Velocity at Outlet of Francis Turbine:

m/s

Velocity of Vane at Outlet For Francis Turbine:

m/s

Volume Flow Rate For Francis Turbine:

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1. What is the Volume Flow Rate of Acute Angled Francis Turbine?

The Volume Flow Rate of Acute Angled Francis Turbine represents the volume of fluid that passes through the turbine per unit of time. It is a crucial parameter in turbine design and performance analysis, indicating the turbine's capacity to handle fluid flow.

2. How Does the Calculator Work?

The calculator uses the formula:

\[ Q_f = \frac{W}{\rho_f \times (V_{w1} \times u_1 + V_{w2} \times u_2)} \]

Where:

\( Q_f \) — Volume Flow Rate For Francis Turbine (m³/s)
\( W \) — Work Done Per Second by Francis Turbine (Watt)
\( \rho_f \) — Density of Fluid in Francis Turbine (kg/m³)
\( V_{w1} \) — Whirl Velocity at Inlet of Francis Turbine (m/s)
\( u_1 \) — Velocity of Vane at Inlet For Francis Turbine (m/s)
\( V_{w2} \) — Whirl Velocity at Outlet of Francis Turbine (m/s)
\( u_2 \) — Velocity of Vane at Outlet For Francis Turbine (m/s)

Explanation: This formula calculates the volume flow rate based on the work done by the turbine and the fluid dynamics parameters at both inlet and outlet of the turbine.

3. Importance of Volume Flow Rate Calculation

Details: Accurate volume flow rate calculation is essential for turbine efficiency analysis, power generation optimization, and proper turbine sizing for specific hydraulic conditions.

4. Using the Calculator

Tips: Enter all required parameters with appropriate units. Ensure positive values for work done and density, and non-negative values for velocity components. The denominator must not be zero for valid calculation.

5. Frequently Asked Questions (FAQ)

Q1: What is the significance of whirl velocity in this calculation?
A: Whirl velocity represents the tangential component of fluid velocity, which directly contributes to the torque and work transfer in the turbine.

Q2: How does vane velocity affect the volume flow rate?
A: Vane velocity affects the momentum transfer between the fluid and the turbine blades, influencing the work done and consequently the volume flow rate.

Q3: What are typical values for these parameters in real turbines?
A: Values vary significantly based on turbine size and design, but typically range from: work done (kW to MW), density (1000 kg/m³ for water), velocities (1-100 m/s).

Q4: Why is the denominator term important?
A: The denominator represents the total momentum transfer per unit volume, which determines how effectively the turbine converts fluid energy into mechanical work.

Q5: Can this formula be used for other types of turbines?
A: This specific formula is designed for Francis turbines. Other turbine types may require different formulas based on their specific working principles.