Volume Flow Rate Of Obtuse Angled Outlet Bladed Francis Turbine Given Work Done Per Second Calculator

Formula Used:

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

Work Done Per Second (W):

Watt

Density of Fluid (ρf):

kg/m³

Whirl Velocity at Inlet (Vw1):

m/s

Velocity of Vane at Inlet (u1):

m/s

Whirl Velocity at Outlet (Vw2):

m/s

Velocity of Vane at Outlet (u2):

m/s

Volume Flow Rate (Qf):

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1. What is the Volume Flow Rate Calculation?

The volume flow rate calculation for an obtuse angled outlet bladed Francis turbine determines the volume of fluid passing through the turbine per unit time, based on work done per second and various velocity parameters.

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 (m³/s)
\( W \) — Work Done Per Second (Watt)
\( \rho_f \) — Density of Fluid (kg/m³)
\( V_{w1} \) — Whirl Velocity at Inlet (m/s)
\( u_1 \) — Velocity of Vane at Inlet (m/s)
\( V_{w2} \) — Whirl Velocity at Outlet (m/s)
\( u_2 \) — Velocity of Vane at Outlet (m/s)

Explanation: This formula calculates the volume flow rate based on the energy transfer between the fluid and the turbine blades, considering both inlet and outlet conditions.

3. Importance of Volume Flow Rate Calculation

Details: Accurate volume flow rate calculation is crucial for turbine design, performance evaluation, and efficiency optimization in hydroelectric power generation systems.

4. Using the Calculator

Tips: Enter all values in appropriate units (Watt for work, kg/m³ for density, m/s for velocities). Ensure all values are positive and the denominator doesn't equal zero.

5. Frequently Asked Questions (FAQ)

Q1: What is whirl velocity in turbine analysis?
A: Whirl velocity is the tangential component of absolute velocity that contributes to the torque and power generation in turbines.

Q2: Why is the outlet angle important in this calculation?
A: The obtuse outlet angle affects the whirl velocity component and thus influences the energy transfer and volume flow rate calculation.

Q3: What are typical values for these parameters?
A: Values vary significantly based on turbine design and operating conditions. Work done can range from kilowatts to megawatts, while velocities typically range from 5-50 m/s.

Q4: When might the denominator become zero?
A: The denominator becomes zero when Vw1×u1 = Vw2×u2, which indicates no net energy transfer between the fluid and turbine blades.

Q5: How does fluid density affect the calculation?
A: Higher density fluids require more energy for the same volume flow rate, as the formula shows an inverse relationship between density and flow rate.