Diameter Of Sphere Given Resistance Force On Spherical Surface Calculator

Formula Used:

\[ DS = \frac{F_{resistance}}{3 \times \pi \times \mu \times V_{mean}} \]

Resistance Force (F_resistance):

Newton

Dynamic Viscosity (μ):

Pascal Second

Mean Velocity (V_mean):

Meter per Second

Diameter of Sphere (DS):

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1. What is the Diameter of Sphere Formula?

The formula calculates the diameter of a sphere based on resistance force, dynamic viscosity, and mean velocity. It's derived from Stokes' law and fluid dynamics principles for spherical objects in viscous fluids.

2. How Does the Calculator Work?

The calculator uses the formula:

\[ DS = \frac{F_{resistance}}{3 \times \pi \times \mu \times V_{mean}} \]

Where:

\( DS \) — Diameter of Sphere (Meter)
\( F_{resistance} \) — Resistance Force (Newton)
\( \pi \) — Archimedes' constant (≈3.1416)
\( \mu \) — Dynamic Viscosity (Pascal Second)
\( V_{mean} \) — Mean Velocity (Meter per Second)

Explanation: The formula relates the sphere's diameter to the resistance force it experiences in a viscous fluid, considering the fluid's viscosity and flow velocity.

3. Importance of Sphere Diameter Calculation

Details: Accurate sphere diameter calculation is crucial for fluid dynamics studies, particle size analysis, engineering applications, and understanding drag forces in viscous fluids.

4. Using the Calculator

Tips: Enter resistance force in Newtons, dynamic viscosity in Pascal Seconds, and mean velocity in Meters per Second. All values must be positive and non-zero.

5. Frequently Asked Questions (FAQ)

Q1: What is the physical significance of this formula?
A: This formula helps determine the size of spherical objects based on the drag force they experience when moving through a viscous fluid.

Q2: When is this formula applicable?
A: The formula applies to small spherical particles moving at low Reynolds numbers in viscous fluids (Stokes' flow regime).

Q3: What are the limitations of this formula?
A: The formula assumes laminar flow, spherical particles, and low Reynolds numbers. It may not be accurate for non-spherical objects or turbulent flow conditions.

Q4: How does viscosity affect the result?
A: Higher viscosity fluids create more resistance, requiring larger diameter values for the same resistance force and velocity.

Q5: Can this be used for air and water?
A: Yes, but the formula works best for highly viscous fluids. For low viscosity fluids like air and water, the formula is most accurate for very small particles or very low velocities.