Resistance Force On Spherical Surface Calculator

Resistance Force Formula:

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

Resistance Force (F_resistance):

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1. What is Resistance Force on Spherical Surface?

The resistance force on a spherical surface refers to the drag force experienced by a sphere moving through a fluid. This force is equal to the external load applied at equilibrium and is governed by Stokes' law for low Reynolds number flows.

2. How Does the Calculator Work?

The calculator uses the resistance force formula:

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

Where:

\( \pi \) — Archimedes' constant (≈ 3.141592653589793)
\( \mu \) — Dynamic viscosity of the fluid (Pa·s)
\( V_{mean} \) — Mean velocity of the fluid (m/s)
\( D_S \) — Diameter of the sphere (m)

Explanation: This formula calculates the drag force on a sphere in a viscous fluid, valid for low Reynolds number flows where Stokes' law applies.

3. Importance of Resistance Force Calculation

Details: Calculating resistance force is crucial for understanding fluid dynamics around spherical objects, designing filtration systems, analyzing particle sedimentation, and studying colloidal suspensions.

4. Using the Calculator

Tips: Enter dynamic viscosity in Pa·s, mean velocity in m/s, and diameter in meters. All values must be positive numbers greater than zero.

5. Frequently Asked Questions (FAQ)

Q1: What is the range of validity for this formula?
A: This formula is valid for low Reynolds numbers (Re < 0.1) where Stokes' law applies, typically for small particles in viscous fluids.

Q2: How does temperature affect the resistance force?
A: Temperature affects dynamic viscosity (μ), which decreases with increasing temperature for liquids but increases for gases.

Q3: Can this formula be used for non-spherical objects?
A: No, this specific formula is derived for perfect spheres. Different shapes require different drag coefficient formulations.

Q4: What are typical applications of this calculation?
A: Applications include particle sedimentation analysis, viscosity measurements, aerosol science, and microfluidic device design.

Q5: How accurate is this formula in real-world applications?
A: The formula provides excellent accuracy for small, smooth spheres in Newtonian fluids at low Reynolds numbers, but deviations occur for rough surfaces or non-Newtonian fluids.