1. What is Rotating Fluid in a Cylinder Velocity?

Definition: This calculator determines the linear velocity of a fluid particle in a rotating cylinder based on angular velocity and radial position.

Purpose: It helps in fluid dynamics analysis, centrifuge design, and rotational flow applications.

2. How Does the Calculator Work?

The calculator uses the formula:

Where:

• \( v \) — Linear velocity (m/s)
• \( \omega \) — Angular velocity (rad/s)
• \( r \) — Radial distance from center (m)

Explanation: The linear velocity increases proportionally with both angular speed and distance from the rotation axis.

3. Importance of Velocity Calculation

Details: Understanding fluid velocity in rotating systems is crucial for designing centrifuges, analyzing vortex behavior, and studying geophysical flows.

4. Using the Calculator

Tips: Enter the angular velocity in radians per second and the radial distance in meters. Both values must be ≥ 0.

5. Frequently Asked Questions (FAQ)

Q1: What is the relationship between angular and linear velocity?
A: Linear velocity equals angular velocity multiplied by the radius (distance from axis).

Q2: What are typical angular velocities in applications?
A: Lab centrifuges: 100-1000 rad/s, Industrial mixers: 1-50 rad/s, Geophysical flows: 0.0001-0.1 rad/s.

Q3: Does this formula work for any fluid?
A: Yes, for rigid-body rotation where all fluid rotates at same ω. For viscous flows, velocity profiles are more complex.

Q4: How does radius affect velocity?
A: Velocity increases linearly with radius - particles farther from center move faster.

Q5: What if I know RPM instead of rad/s?
A: Convert RPM to rad/s by multiplying by π/30 (1 RPM = π/30 rad/s).