Buoyant Force in Falling Sphere Resistance Method Calculator

Buoyant Force Formula:

\[ F_B = \frac{\pi}{6} \times \rho \times [g] \times d^3 \]

Buoyant Force (F_B):

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1. What is Buoyant Force in Falling Sphere Resistance Method?

The buoyant force is the upward force exerted by a fluid that opposes the weight of an object immersed in it. In the falling sphere resistance method, this force plays a crucial role in determining the drag coefficient and viscosity of the fluid.

2. How Does the Calculator Work?

The calculator uses the buoyant force formula:

\[ F_B = \frac{\pi}{6} \times \rho \times [g] \times d^3 \]

Where:

\( F_B \) — Buoyant Force (N)
\( \pi \) — Archimedes' constant (≈3.14159)
\( \rho \) — Density of liquid (kg/m³)
\( [g] \) — Gravitational acceleration (9.80665 m/s²)
\( d \) — Diameter of sphere (m)

Explanation: The formula calculates the upward force experienced by a sphere immersed in a fluid, which is equal to the weight of the fluid displaced by the sphere.

3. Importance of Buoyant Force Calculation

Details: Accurate buoyant force calculation is essential for determining terminal velocity, drag coefficients, and fluid viscosity in the falling sphere method. It helps in understanding fluid dynamics and designing various engineering systems.

4. Using the Calculator

Tips: Enter liquid density in kg/m³ and sphere diameter in meters. All values must be positive numbers greater than zero.

5. Frequently Asked Questions (FAQ)

Q1: What is the falling sphere resistance method?
A: It's an experimental technique used to determine the viscosity of a fluid by measuring the terminal velocity of a sphere falling through it.

Q2: How does buoyant force affect the falling sphere?
A: Buoyant force reduces the effective weight of the sphere, affecting its terminal velocity and the drag force experienced.

Q3: What factors influence buoyant force?
A: Buoyant force depends on the fluid density, volume of the displaced fluid, and gravitational acceleration.

Q4: Can this formula be used for non-spherical objects?
A: No, this specific formula is derived for spherical objects. Different shapes require different volume calculations.

Q5: What are typical applications of this calculation?
A: Used in rheology studies, viscosity measurements, marine engineering, and designing objects that operate in fluids.