Vane Angle At Inlet And Outlet At Extreme Edge Of Runner Calculator

Formula Used:

\[ \text{Vane Angle} = \tan^{-1}\left(\frac{\text{Flow Velocity at Inlet}}{\text{Whirl Velocity at Inlet} - \text{Velocity of Vane at Inlet}}\right) \] \[ \theta = \tan^{-1}\left(\frac{V_{fi}}{V_{wi} - u_i}\right) \]

Flow Velocity at Inlet (Vfi):

m/s

Whirl Velocity at Inlet (Vwi):

m/s

Velocity of Vane at Inlet (ui):

m/s

Vane Angle (θ):

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1. What is Vane Angle Calculation?

The vane angle calculation determines the angle at which fluid enters the turbine runner vane. This angle is crucial for optimizing turbine efficiency and performance by ensuring proper fluid guidance through the turbine blades.

2. How Does the Calculator Work?

The calculator uses the following formula:

\[ \theta = \tan^{-1}\left(\frac{V_{fi}}{V_{wi} - u_i}\right) \]

Where:

\( \theta \) — Vane angle at inlet (degrees)
\( V_{fi} \) — Flow velocity at inlet (m/s)
\( V_{wi} \) — Whirl velocity at inlet (m/s)
\( u_i \) — Velocity of vane at inlet (m/s)

Explanation: The formula calculates the angle using inverse tangent function based on the ratio of flow velocity to the difference between whirl velocity and vane velocity.

3. Importance of Vane Angle Calculation

Details: Accurate vane angle calculation is essential for turbine design optimization, ensuring maximum energy transfer efficiency, and preventing flow separation and turbulence that can reduce turbine performance.

4. Using the Calculator

Tips: Enter all velocity values in m/s. Ensure that whirl velocity is greater than vane velocity to avoid division by zero. All values must be positive numbers.

5. Frequently Asked Questions (FAQ)

Q1: What is flow velocity at inlet?
A: Flow velocity at inlet refers to the velocity component of the fluid perpendicular to the vane surface at the entrance point.

Q2: What is whirl velocity?
A: Whirl velocity is the tangential component of fluid velocity in the direction of vane motion at the inlet.

Q3: Why is vane velocity important?
A: Vane velocity represents the peripheral speed of the turbine runner, which affects the relative velocity between fluid and vane.

Q4: What are typical vane angle ranges?
A: Vane angles typically range from 15° to 45° depending on turbine type and design specifications.

Q5: How does vane angle affect turbine efficiency?
A: Optimal vane angle ensures smooth fluid entry, minimizes shock losses, and maximizes energy transfer efficiency in the turbine.