Terminal Fall Velocity Calculator

Terminal Fall Velocity Formula:

\[ V_{terminal} = \frac{D_S^2}{18 \cdot \mu} \cdot (\gamma_f - S) \]

Diameter of Sphere (DS):

Dynamic Viscosity (μ):

Pa·s

Specific Weight of Liquid (γf):

kN/m³

Specific Weight of Liquid in Piezometer (S):

kN/m³

Terminal Velocity (Vterminal):

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1. What is Terminal Fall Velocity?

Terminal velocity is the maximum velocity attainable by an object as it falls through a fluid (air is the most common example). It occurs when the sum of the drag force and buoyancy equals the downward force of gravity acting on the object.

2. How Does the Calculator Work?

The calculator uses the Terminal Fall Velocity equation:

\[ V_{terminal} = \frac{D_S^2}{18 \cdot \mu} \cdot (\gamma_f - S) \]

Where:

\( V_{terminal} \) — Terminal velocity (m/s)
\( D_S \) — Diameter of sphere (m)
\( \mu \) — Dynamic viscosity (Pa·s)
\( \gamma_f \) — Specific weight of liquid (kN/m³)
\( S \) — Specific weight of liquid in piezometer (kN/m³)

Explanation: The equation calculates the terminal velocity of a sphere falling through a fluid, accounting for the balance between gravitational force, buoyant force, and viscous drag force.

3. Importance of Terminal Velocity Calculation

Details: Terminal velocity calculation is crucial in various engineering applications including sedimentation processes, particle separation, fluid mechanics analysis, and environmental studies of particle behavior in fluids.

4. Using the Calculator

Tips: Enter all values in the specified units. Diameter and viscosity must be positive values. The specific weight difference (γf - S) should be positive for downward motion.

5. Frequently Asked Questions (FAQ)

Q1: What factors affect terminal velocity?
A: Terminal velocity depends on the object's size, shape, density, and the fluid's density and viscosity.

Q2: Does this formula work for non-spherical objects?
A: This specific formula is derived for spherical objects. Non-spherical objects require different drag coefficient calculations.

Q3: What is the significance of the 18 in the denominator?
A: The factor 18 comes from the Stokes' law derivation for drag force on a sphere in laminar flow conditions.

Q4: When is this formula applicable?
A: This formula is valid for small spherical particles in laminar flow conditions (low Reynolds numbers typically Re < 0.1).

Q5: How does temperature affect terminal velocity?
A: Temperature affects fluid viscosity and density, which in turn influence the terminal velocity calculation.