Note:

This formula calculates the Absolute (Dynamic) Viscosity (μ) of a fluid by analyzing the motion of a sphere falling through it. It is derived from the balance between gravitational force, buoyant force, and viscous drag acting on the sphere.

Understanding Parameters:

• Δρ (kg/m³): Difference in density between the sphere and the fluid.
• g (m/s²): Acceleration due to gravity, with a standard value of 9.81 m/s² (Earth-based calculations). Note: While users can change this value, keeping it at 9.81 m/s² ensures accurate calculations for Earth conditions.
• r (m): Radius of the sphere.
• u (m/s): Velocity of the sphere, calculated as u = Distance (d) / Time (t).

How This Formula Works:

When a sphere falls through a fluid, it experiences gravitational force, buoyant force, and viscous resistance. After reaching terminal velocity (steady speed), the forces are balanced, and the viscosity can be calculated using the given formula.

Key Applications:

• Industrial Fluids Analysis: Used to determine viscosity of lubricants, paints, and coatings.
• Pharmaceuticals: Helps in analyzing the flow properties of liquid medicines.
• Food & Beverages: Ensures consistency in liquids like syrups, juices, and dairy products.
• Environmental Studies: Used in measuring viscosity of natural water bodies, crude oil, and wastewater.

Validations & Input Constraints:

• Density Difference (Δρ) must be positive: - Δρ > 0 is required because a negative density difference is physically meaningless. - If Δρ ≤ 0, an error message will be displayed: "Invalid input! Density difference must be a positive number."
• Radius (r) must be positive: - The sphere must have a valid size, so r > 0 is mandatory. - If r ≤ 0, an error message will be displayed.
• Velocity (u) must be positive: - Since velocity is u = d / t, negative or zero values for distance (d) or time (t) are not allowed. - If d ≤ 0 or t ≤ 0, an error will be shown.
• No Negative or Zero Values Allowed: - Any negative input will result in an error message prompting users to enter a valid value.

Conclusion:

This tool allows users to accurately determine the dynamic viscosity of a fluid while ensuring valid input values. Proper validation prevents incorrect calculations and enhances the reliability of fluid viscosity assessments.