Hydraulic Efficiency of Francis Turbine with Obtuse Angled Outlet Blade Calculator

Formula Used:

\[ \eta_h = \frac{V_{w1} \cdot u_1 - V_{w2} \cdot u_2}{g \cdot H_f} \]

Whirl Velocity at Inlet of Francis Turbine (Vw1):

m/s

Velocity of Vane at Inlet For Francis Turbine (u1):

m/s

Whirl Velocity at Outlet of Francis Turbine (Vw2):

m/s

Velocity of Vane at Outlet For Francis Turbine (u2):

m/s

Acceleration Due to Gravity (g):

m/s²

Net Francis Turbine Head (Hf):

Hydraulic Efficiency of Francis Turbine (ηh):

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1. What is the Hydraulic Efficiency of Francis Turbine?

The Hydraulic Efficiency of Francis Turbine is the measure of the amount of work input that is converted into useful work output. It represents how effectively the turbine converts hydraulic energy into mechanical energy.

2. How Does the Calculator Work?

The calculator uses the formula:

\[ \eta_h = \frac{V_{w1} \cdot u_1 - V_{w2} \cdot u_2}{g \cdot H_f} \]

Where:

\( V_{w1} \) — 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)
\( g \) — Acceleration Due to Gravity (m/s²)
\( H_f \) — Net Francis Turbine Head (m)

Explanation: The formula calculates the hydraulic efficiency by comparing the work done by the water on the turbine runner to the available hydraulic energy.

3. Importance of Hydraulic Efficiency Calculation

Details: Accurate hydraulic efficiency calculation is crucial for evaluating turbine performance, optimizing energy conversion, and identifying potential improvements in turbine design and operation.

4. Using the Calculator

Tips: Enter all velocity values in m/s, acceleration due to gravity in m/s² (default 9.81), and net head in meters. All values must be positive and non-zero except outlet velocities which can be zero.

5. Frequently Asked Questions (FAQ)

Q1: What is the typical range of hydraulic efficiency for Francis turbines?
A: Modern Francis turbines typically achieve hydraulic efficiencies between 90-95% under optimal operating conditions.

Q2: Why are both inlet and outlet velocities considered?
A: Both velocities are considered to account for the energy transfer between the water and the turbine blades at both entry and exit points.

Q3: What factors affect hydraulic efficiency?
A: Factors include blade design, flow conditions, head variation, surface roughness, and operating point relative to best efficiency point.

Q4: How does obtuse angled outlet blade affect efficiency?
A: Obtuse angled outlet blades help in reducing exit losses and improving energy recovery, thereby increasing overall hydraulic efficiency.

Q5: Can hydraulic efficiency exceed 100%?
A: No, hydraulic efficiency cannot exceed 100% as it represents the ratio of useful output to input energy, which is always less than unity due to various losses.