Mean Velocity Of Sphere Given Dynamic Viscosity Calculator

Formula Used:

\[ V_{mean} = \frac{D_S^2}{18 \times \mu} \]

Mean Velocity (V_mean):

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1. What is Mean Velocity of Sphere?

The Mean Velocity of a sphere refers to the average velocity of a fluid at a point and over an arbitrary time T when a sphere is moving through it. This calculation is particularly important in fluid dynamics and Stokes' law applications.

2. How Does the Calculator Work?

The calculator uses the formula:

\[ V_{mean} = \frac{D_S^2}{18 \times \mu} \]

Where:

\( V_{mean} \) — Mean Velocity (m/s)
\( D_S \) — Diameter of Sphere (m)
\( \mu \) — Dynamic Viscosity (Pa·s)

Explanation: This formula calculates the mean velocity of a sphere moving through a viscous fluid, derived from Stokes' law which describes the force of viscosity on a sphere moving through a fluid.

3. Importance of Mean Velocity Calculation

Details: Calculating mean velocity is crucial for understanding fluid dynamics, designing fluid systems, analyzing particle motion in fluids, and various engineering applications involving fluid-structure interactions.

4. Using the Calculator

Tips: Enter the diameter of the sphere in meters and the dynamic viscosity in Pascal-seconds. Both values must be positive numbers greater than zero for accurate calculation.

5. Frequently Asked Questions (FAQ)

Q1: What is dynamic viscosity?
A: Dynamic viscosity is a measure of a fluid's resistance to flow when an external force is applied. It quantifies the internal friction between fluid layers.

Q2: When is this formula applicable?
A: This formula is derived from Stokes' law and is applicable for small spherical particles moving slowly through a viscous fluid at low Reynolds numbers.

Q3: What are typical units for dynamic viscosity?
A: The SI unit is Pascal-second (Pa·s), but other common units include poise (P) and centipoise (cP).

Q4: Does this formula account for fluid density?
A: No, this particular formula for mean velocity does not include fluid density. It's specifically derived for the relationship between sphere diameter, viscosity, and velocity.

Q5: What are the limitations of this calculation?
A: This calculation assumes laminar flow, spherical particles, and low Reynolds numbers. It may not be accurate for non-spherical particles or turbulent flow conditions.