Density Of Fluid In Falling Sphere Resistance Method Calculator

Density of Fluid Formula:

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

Density of Fluid (ρ):

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1. What is the Density of Fluid in Falling Sphere Resistance Method?

The falling sphere resistance method is used to determine the density of a fluid by measuring the buoyant force acting on a sphere of known diameter immersed in the fluid. This method is based on Archimedes' principle and provides an accurate way to measure fluid density.

2. How Does the Calculator Work?

The calculator uses the formula:

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

Where:

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

Explanation: The formula calculates fluid density by relating the buoyant force acting on a sphere to the volume of fluid displaced and gravitational acceleration.

3. Importance of Fluid Density Calculation

Details: Accurate fluid density measurement is crucial in various engineering applications, fluid dynamics studies, quality control processes, and scientific research where precise knowledge of fluid properties is required.

4. Using the Calculator

Tips: Enter buoyant force in Newtons (N) and sphere diameter in meters (m). Both values must be positive numbers. The calculator will provide the fluid density in kg/m³.

5. Frequently Asked Questions (FAQ)

Q1: What is buoyant force?
A: Buoyant force is the upward force exerted by a fluid on an object immersed in it, equal to the weight of the fluid displaced by the object.

Q2: Why is sphere diameter important in this calculation?
A: The sphere diameter determines the volume of fluid displaced, which is directly related to the buoyant force and thus the density calculation.

Q3: What are typical density values for common fluids?
A: Water has a density of about 1000 kg/m³, while air is approximately 1.2 kg/m³ at sea level. Other fluids vary based on composition and temperature.

Q4: How does temperature affect fluid density?
A: Most fluids expand when heated, decreasing their density. The relationship is described by the coefficient of thermal expansion.

Q5: What are the limitations of this method?
A: The method assumes ideal conditions, spherical objects, and may be affected by fluid viscosity, surface tension, and measurement precision.