Torque On Cylinder Given Angular Velocity And Radius Of Inner Cylinder Calculator

Formula Used:

\[ Torque = \frac{Dynamic\ Viscosity \times 2 \times \pi \times (Radius\ of\ Inner\ Cylinder^3) \times Angular\ Velocity \times Length\ of\ Cylinder}{Thickness\ of\ Fluid\ Layer} \] \[ T = \frac{\mu_{viscosity} \times 2 \times \pi \times (R^3) \times \omega \times L_{Cylinder}}{\delta_{fluid}} \]

Dynamic Viscosity:

Pa·s

Radius of Inner Cylinder:

Angular Velocity:

rad/s

Length of Cylinder:

Thickness of Fluid Layer:

Torque:

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1. What is Torque on Cylinder?

Torque on a cylinder refers to the rotational force required to overcome the viscous resistance when a cylinder rotates in a fluid. It is a crucial parameter in fluid mechanics and engineering applications involving rotating machinery.

2. How Does the Calculator Work?

The calculator uses the formula:

\[ T = \frac{\mu \times 2 \times \pi \times R^3 \times \omega \times L}{\delta} \]

Where:

\( T \) — Torque (N·m)
\( \mu \) — Dynamic Viscosity (Pa·s)
\( R \) — Radius of Inner Cylinder (m)
\( \omega \) — Angular Velocity (rad/s)
\( L \) — Length of Cylinder (m)
\( \delta \) — Thickness of Fluid Layer (m)

Explanation: This formula calculates the torque required to rotate an inner cylinder within an outer cylinder with a fluid layer between them, considering the fluid's viscous properties.

3. Importance of Torque Calculation

Details: Accurate torque calculation is essential for designing rotating machinery, determining power requirements, and analyzing fluid behavior in confined spaces. It helps engineers optimize system performance and efficiency.

4. Using the Calculator

Tips: Enter all values in SI units. Dynamic viscosity in Pa·s, dimensions in meters, angular velocity in rad/s. All values must be positive and non-zero for accurate results.

5. Frequently Asked Questions (FAQ)

Q1: What is dynamic viscosity?
A: Dynamic viscosity is a measure of a fluid's resistance to flow under an applied force. It quantifies the internal friction between fluid layers.

Q2: Why is the radius cubed in the formula?
A: The radius is cubed because torque depends on the volume of fluid being sheared, which increases with the cube of the radius in cylindrical systems.

Q3: What applications use this calculation?
A: This calculation is used in viscometers, bearing design, mixing equipment, and any system where a cylinder rotates within a fluid-filled space.

Q4: How does fluid thickness affect torque?
A: Thinner fluid layers generally require more torque for the same rotational speed due to higher shear rates in the fluid.

Q5: Can this formula be used for non-Newtonian fluids?
A: This specific formula is designed for Newtonian fluids. Non-Newtonian fluids require more complex models that account for their variable viscosity.