Tip Velocity of Impeller Given Mean Diameter Calculator

Tip Velocity Formula:

\[ U_t = \pi \times \sqrt{2 \times D_m^2 - D_h^2} \times \frac{N}{60} \]

Tip Velocity (U_t):

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1. What is Tip Velocity of Impeller?

Tip Velocity is the blade speed at the tip of the compressor impeller. It represents the maximum linear velocity of the impeller blades and is a critical parameter in turbomachinery design and performance analysis.

2. How Does the Calculator Work?

The calculator uses the Tip Velocity formula:

\[ U_t = \pi \times \sqrt{2 \times D_m^2 - D_h^2} \times \frac{N}{60} \]

Where:

\( U_t \) — Tip Velocity (m/s)
\( D_m \) — Mean Diameter of Impeller (m)
\( D_h \) — Impeller Hub Diameter (m)
\( N \) — Rotational Speed (rpm)
\( \pi \) — Archimedes' constant (approximately 3.14159)

Explanation: The formula calculates the linear velocity at the impeller tip by considering the geometric dimensions of the impeller and its rotational speed.

3. Importance of Tip Velocity Calculation

Details: Tip velocity is crucial for determining impeller performance, efficiency, and structural integrity. It affects factors such as pressure ratio, flow capacity, and stress levels in the impeller material.

4. Using the Calculator

Tips: Enter mean diameter and hub diameter in meters, and RPM in revolutions per minute. All values must be positive numbers with mean diameter greater than zero.

5. Frequently Asked Questions (FAQ)

Q1: Why is tip velocity important in compressor design?
A: Tip velocity determines the maximum stress on impeller blades and affects the compressor's pressure ratio and efficiency. Higher tip velocities generally allow for higher pressure ratios but increase mechanical stress.

Q2: What are typical tip velocity ranges for different impeller types?
A: For centrifugal compressors, tip velocities typically range from 200-500 m/s, depending on the material and application. Higher values are possible with advanced materials like titanium alloys.

Q3: How does hub diameter affect tip velocity?
A: The hub diameter influences the mean diameter calculation. A larger hub diameter reduces the effective blade length and thus affects the tip velocity for a given rotational speed.

Q4: Can this formula be used for different types of impellers?
A: This formula is primarily used for centrifugal impellers. For axial flow impellers or other configurations, different formulas may be more appropriate.

Q5: What safety factors should be considered regarding tip velocity?
A: Material strength, fatigue limits, and operating conditions must be considered. Tip velocities should be kept below the material's safe operating limits to prevent failure due to centrifugal stresses.