Torque On Cylinder Given Radius, Length And Viscosity Calculator

Formula Used:

\[ Torque = \frac{\mu \times 4 \times \pi^2 \times R^3 \times \omega \times L}{\delta} \]

Dynamic Viscosity (μ):

Pa·s

Radius of Inner Cylinder (R):

Revolutions per Second (ω):

Length of Cylinder (L):

Thickness of Fluid Layer (δ):

Torque (T):

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1. What is the Torque on Cylinder Formula?

The Torque on Cylinder formula calculates the torque required to rotate an inner cylinder within an outer cylinder with a fluid layer between them. This is commonly used in viscometry to determine fluid viscosity properties.

2. How Does the Calculator Work?

The calculator uses the formula:

\[ T = \frac{\mu \times 4 \times \pi^2 \times R^3 \times \omega \times L}{\delta} \]

Where:

\( T \) — Torque (N·m)
\( \mu \) — Dynamic Viscosity (Pa·s)
\( R \) — Radius of Inner Cylinder (m)
\( \omega \) — Revolutions per Second (Hz)
\( L \) — Length of Cylinder (m)
\( \delta \) — Thickness of Fluid Layer (m)
\( \pi \) — Mathematical constant (approximately 3.1416)

Explanation: The formula calculates the torque required to overcome the viscous resistance of the fluid between two concentric cylinders when the inner cylinder rotates.

3. Importance of Torque Calculation

Details: Accurate torque calculation is crucial for designing rotating machinery, determining fluid viscosity, and analyzing fluid behavior in confined spaces between rotating surfaces.

4. Using the Calculator

Tips: Enter all values in SI units. Ensure all inputs are positive values. The calculator provides results in Newton-meters (N·m).

5. Frequently Asked Questions (FAQ)

Q1: What is the physical significance of this torque calculation?
A: This calculation helps determine the resistance offered by a fluid to rotational motion, which is essential in designing bearings, seals, and other rotating systems.

Q2: How does fluid thickness affect the torque?
A: Thinner fluid layers generally result in higher torque requirements due to increased shear rates in the fluid.

Q3: What types of fluids can this formula be applied to?
A: This formula works best for Newtonian fluids where viscosity remains constant regardless of shear rate.

Q4: How does cylinder radius affect the torque?
A: Torque increases with the cube of the radius, making it the most significant factor in the calculation.

Q5: What are typical applications of this calculation?
A: This is commonly used in viscometers, lubrication systems, and any application involving fluid between rotating cylinders.