Terminal Velocity Given Angular Velocity Calculator

Terminal Velocity Given Angular Velocity Formula:

\[ v_{ter} = \frac{m \times r_m \times \omega^2}{6 \times \pi \times \mu \times r_0} \]

Mass of Particle (m):

Radius of Molecule (r_m):

Angular Velocity (ω):

rad/s

Dynamic Viscosity (μ):

Pa·s

Radius of Spherical Particle (r_0):

Terminal Velocity (v_ter):

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1. What is Terminal Velocity Given Angular Velocity?

Terminal Velocity Given Angular Velocity is the maximum velocity attainable by an object as it falls through a fluid when considering the effects of angular velocity. This calculation is important in fluid dynamics and particle motion studies.

2. How Does the Calculator Work?

The calculator uses the formula:

\[ v_{ter} = \frac{m \times r_m \times \omega^2}{6 \times \pi \times \mu \times r_0} \]

Where:

\( v_{ter} \) — Terminal velocity (m/s)
\( m \) — Mass of particle (kg)
\( r_m \) — Radius of molecule (m)
\( \omega \) — Angular velocity (rad/s)
\( \mu \) — Dynamic viscosity (Pa·s)
\( r_0 \) — Radius of spherical particle (m)
\( \pi \) — Archimedes' constant (approximately 3.1416)

Explanation: This formula calculates the terminal velocity of a spherical particle in a viscous fluid when the particle has angular velocity, accounting for the rotational effects on the drag force.

3. Importance of Terminal Velocity Calculation

Details: Calculating terminal velocity with angular velocity is crucial for understanding particle behavior in rotating fluids, designing separation equipment, and studying sedimentation processes in industrial and environmental applications.

4. Using the Calculator

Tips: Enter all values in appropriate SI units. Mass and radii must be positive values. Angular velocity and dynamic viscosity must be greater than zero for meaningful results.

5. Frequently Asked Questions (FAQ)

Q1: What is terminal velocity in fluid dynamics?
A: Terminal velocity is the constant speed that a freely falling object eventually reaches when the resistance of the medium prevents further acceleration.

Q2: How does angular velocity affect terminal velocity?
A: Angular velocity can influence the drag forces acting on a particle, potentially altering its terminal velocity compared to a non-rotating particle.

Q3: What are typical values for dynamic viscosity?
A: Water at 20°C has a viscosity of about 0.001 Pa·s, while honey can have viscosities around 2-10 Pa·s, and air about 0.000018 Pa·s.

Q4: When is this formula applicable?
A: This formula applies to spherical particles in laminar flow conditions where Stokes' law is valid and rotational effects are significant.

Q5: What are the limitations of this calculation?
A: The formula assumes spherical particles, Newtonian fluids, and laminar flow conditions. It may not be accurate for non-spherical particles or turbulent flow conditions.