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Velocity Of Sphere In Falling Sphere Resistance Method Calculator

Formula Used:

\[ U = \frac{F_D}{3 \cdot \pi \cdot \mu \cdot d} \]

N
Pa·s
m

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1. What is the Falling Sphere Resistance Method?

The Falling Sphere Resistance Method is a technique used to determine the viscosity of a fluid by measuring the terminal velocity of a sphere falling through it under the influence of gravity, or conversely, to calculate the velocity given other parameters.

2. How Does the Calculator Work?

The calculator uses the formula:

\[ U = \frac{F_D}{3 \cdot \pi \cdot \mu \cdot d} \]

Where:

Explanation: This formula calculates the velocity of a sphere moving through a viscous fluid based on the drag force acting upon it, the fluid's viscosity, and the sphere's diameter.

3. Importance of Velocity Calculation

Details: Calculating the velocity of a sphere in a fluid is essential for understanding fluid dynamics, designing industrial processes, and in various scientific experiments involving fluid mechanics.

4. Using the Calculator

Tips: Enter drag force in newtons (N), viscosity in pascal-seconds (Pa·s), and diameter in meters (m). All values must be positive numbers.

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 spheres in highly viscous fluids.

Q2: How does temperature affect the calculation?
A: Temperature significantly affects fluid viscosity. Ensure viscosity values correspond to the actual temperature conditions of your experiment.

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

Q4: What are typical values for fluid viscosity?
A: Water at 20°C has viscosity of about 0.001 Pa·s, while honey can have viscosity around 10 Pa·s, and oils range between these values.

Q5: How accurate is this calculation method?
A: The calculation is theoretically accurate for ideal conditions but may require corrections for wall effects, non-Newtonian fluids, or higher Reynolds numbers.

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