Torque Exerted On Inner Cylinder Given Dynamic Viscosity Of Fluid Calculator

Formula Used:

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

Dynamic Viscosity (μ):

Pa·s

Radius of Outer Cylinder (r₂):

Radius of Inner Cylinder (r₁):

Height of Cylinder (h):

Angular Speed (Ω):

rad/s

Torque on Inner Cylinder (T):

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1. What Is Torque On Inner Cylinder?

The torque on inner cylinder refers to the measure of how much a force acting on a cylinder causing it to rotate. It's a crucial parameter in fluid mechanics for measuring viscosity using rotational viscometers.

2. How Does The Calculator Work?

The calculator uses the formula:

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

Where:

\( T \) — Torque on inner cylinder (N·m)
\( \mu \) — Dynamic viscosity (Pa·s)
\( r_2 \) — Radius of outer cylinder (m)
\( r_1 \) — Radius of inner cylinder (m)
\( h \) — Height of cylinder (m)
\( \Omega \) — Angular speed (rad/s)
\( \pi \) — Mathematical constant (≈3.14159)

Explanation: This formula calculates the torque required to rotate the inner cylinder in a coaxial cylinder viscometer, which is directly related to the fluid's dynamic viscosity.

3. Importance Of Torque Calculation

Details: Accurate torque calculation is essential for determining fluid viscosity, designing mechanical systems involving rotating cylinders, and analyzing fluid behavior in industrial processes.

4. Using The Calculator

Tips: Enter all values in appropriate SI units. Ensure radius of outer cylinder is greater than radius of inner cylinder. All values must be positive numbers.

5. Frequently Asked Questions (FAQ)

Q1: What is dynamic viscosity?
A: Dynamic viscosity refers to the internal resistance of a fluid to flow when a force is applied. It's measured in Pascal-seconds (Pa·s).

Q2: Why is the radius difference important?
A: The difference between outer and inner cylinder radii determines the gap where the fluid flows, which affects the shear rate and thus the torque measurement.

Q3: What is angular speed?
A: Angular speed refers to the rate of change of angular displacement, measured in radians per second (rad/s).

Q4: When is this calculation used?
A: This calculation is primarily used in rotational viscometers to measure fluid viscosity in various industries including petroleum, chemical, and food processing.

Q5: Are there limitations to this formula?
A: This formula assumes Newtonian fluid behavior, laminar flow, and no end effects. It may not be accurate for non-Newtonian fluids or turbulent flow conditions.