Dynamic Viscosity Of Fluid Flow Given Torque Calculator

Dynamic Viscosity Formula:

\[ \mu = \frac{15 \times T \times (r_2 - r_1)}{\pi^2 \times r_1^2 \times r_2 \times h \times \Omega} \]

Torque on Inner Cylinder (T):

N·m

Radius of Outer Cylinder (r₂):

Radius of Inner Cylinder (r₁):

Height of Cylinder (h):

Angular Speed (Ω):

rad/s

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 measure of a fluid's resistance to shear or flow and is an important property in fluid dynamics and engineering applications.

2. How Does the Calculator Work?

The calculator uses the formula for dynamic viscosity in cylindrical Couette flow:

\[ \mu = \frac{15 \times T \times (r_2 - r_1)}{\pi^2 \times r_1^2 \times r_2 \times h \times \Omega} \]

Where:

\( \mu \) — Dynamic Viscosity (Pa·s)
\( T \) — Torque on Inner Cylinder (N·m)
\( r_2 \) — Radius of Outer Cylinder (m)
\( r_1 \) — Radius of Inner Cylinder (m)
\( h \) — Height of Cylinder (m)
\( \Omega \) — Angular Speed (rad/s)
\( \pi \) — Archimedes' constant (approximately 3.14159)

Explanation: This formula calculates the dynamic viscosity of a fluid between two concentric cylinders when the inner cylinder rotates with a known torque and angular speed.

3. Importance of Viscosity Calculation

Details: Accurate viscosity measurement is crucial for designing fluid systems, predicting flow behavior, selecting appropriate lubricants, and understanding fluid transport phenomena in various engineering applications.

4. Using the Calculator

Tips: Enter all values in the specified units. Ensure that the outer radius is greater than the inner radius, and all values are positive. The calculator will compute the dynamic viscosity in Pascal-seconds (Pa·s).

5. Frequently Asked Questions (FAQ)

Q1: What is the difference between dynamic and kinematic viscosity?
A: Dynamic viscosity (μ) measures a fluid's internal resistance to flow, while kinematic viscosity (ν) is dynamic viscosity divided by density (ν = μ/ρ).

Q2: What are typical viscosity values for common fluids?
A: Water at 20°C has μ ≈ 0.001 Pa·s, while honey has μ ≈ 10 Pa·s, and air has μ ≈ 0.000018 Pa·s.

Q3: How does temperature affect viscosity?
A: For liquids, viscosity generally decreases with increasing temperature. For gases, viscosity generally increases with temperature.

Q4: What are the limitations of this calculation method?
A: This method assumes laminar flow, Newtonian fluid behavior, and no end effects. It may not be accurate for non-Newtonian fluids or turbulent flow conditions.

Q5: What engineering applications require viscosity measurements?
A: Viscosity measurements are essential in lubrication engineering, pipeline design, chemical processing, food production, and pharmaceutical manufacturing.