Dynamic Viscosity Of Fluid Given Terminal Fall Velocity Calculator

Formula Used:

\[ \mu = \frac{D_S^2}{18 \times V_{terminal}} \times (\gamma_f - S) \]

Diameter of Sphere (DS):

Terminal Velocity (Vterminal):

m/s

Specific Weight of Liquid (γf):

kN/m³

Specific Weight of Liquid in Piezometer (S):

kN/m³

Dynamic Viscosity (μ):

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1. What is Dynamic Viscosity?

Dynamic Viscosity refers to the internal resistance of a fluid to flow when a force is applied. It is a fundamental property that characterizes a fluid's resistance to shear or flow.

2. How Does the Calculator Work?

The calculator uses the formula:

\[ \mu = \frac{D_S^2}{18 \times V_{terminal}} \times (\gamma_f - S) \]

Where:

\( \mu \) — Dynamic Viscosity (Pa·s)
\( D_S \) — Diameter of Sphere (m)
\( V_{terminal} \) — Terminal Velocity (m/s)
\( \gamma_f \) — Specific Weight of Liquid (kN/m³)
\( S \) — Specific Weight of Liquid in Piezometer (kN/m³)

Explanation: This formula calculates the dynamic viscosity of a fluid based on the terminal fall velocity of a sphere through the fluid, taking into account the specific weight difference between the fluid and the liquid in the piezometer.

3. Importance of Dynamic Viscosity Calculation

Details: Accurate viscosity measurement is crucial for understanding fluid behavior in various applications, including industrial processes, lubrication systems, and fluid dynamics research.

4. Using the Calculator

Tips: Enter all values in the specified units. Diameter of sphere and terminal velocity must be positive values. Specific weight values should be entered in kN/m³.

5. Frequently Asked Questions (FAQ)

Q1: What is the significance of terminal velocity in viscosity calculation?
A: Terminal velocity represents the constant speed that a falling object eventually reaches when the resistance of the medium prevents further acceleration, which is directly related to the fluid's viscosity.

Q2: How does sphere diameter affect viscosity measurement?
A: Larger sphere diameters result in higher terminal velocities and thus affect the viscosity calculation. The relationship is quadratic as seen in the formula.

Q3: What are typical dynamic viscosity values for common fluids?
A: Water at 20°C has a viscosity of about 0.001 Pa·s, while honey can have viscosities around 2-10 Pa·s, and motor oils range from 0.1-0.5 Pa·s.

Q4: Why is the specific weight difference important?
A: The difference (γf - S) represents the net buoyant force acting on the sphere, which drives its motion through the fluid and affects the terminal velocity.

Q5: What are the limitations of this method?
A: This method assumes spherical particles, laminar flow conditions, and may not be accurate for non-Newtonian fluids or at very high/low velocities.