Torque Exerted On Outer Cylinder Calculator

Formula Used:

\[ T_o = \frac{\mu \cdot \pi^2 \cdot \Omega \cdot r_1^4}{60 \cdot C} \]

Dynamic Viscosity (μ):

Pa·s

Angular Speed (Ω):

rad/s

Radius of Inner Cylinder (r₁):

Clearance (C):

Torque on Outer Cylinder (Tₒ):

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1. What is Torque on Outer Cylinder?

The Torque on Outer Cylinder refers to the measure of how much a force acting on a cylinder causing it to rotate. It is a crucial parameter in fluid mechanics and engineering applications involving rotating cylinders.

2. How Does the Calculator Work?

The calculator uses the formula:

\[ T_o = \frac{\mu \cdot \pi^2 \cdot \Omega \cdot r_1^4}{60 \cdot C} \]

Where:

\( T_o \) — Torque on outer cylinder (N·m)
\( \mu \) — Dynamic viscosity (Pa·s)
\( \pi \) — Mathematical constant pi (≈3.1416)
\( \Omega \) — Angular speed (rad/s)
\( r_1 \) — Radius of inner cylinder (m)
\( C \) — Clearance between cylinders (m)

Explanation: This formula calculates the torque required to maintain rotation of the outer cylinder in a concentric cylinder viscometer setup.

3. Importance of Torque Calculation

Details: Accurate torque calculation is essential for designing rotating machinery, measuring fluid viscosity, and understanding fluid behavior in confined spaces between rotating surfaces.

4. Using the Calculator

Tips: Enter dynamic viscosity in Pa·s, angular speed in rad/s, radius in meters, and clearance in meters. All values must be positive and non-zero.

5. Frequently Asked Questions (FAQ)

Q1: What is the significance of the clearance parameter?
A: The clearance determines the gap between the inner and outer cylinders, which significantly affects the shear rate and thus the torque required for rotation.

Q2: How does angular speed affect the torque?
A: Higher angular speeds 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 is primarily used for Newtonian fluids where viscosity remains constant regardless of shear rate.

Q4: Why is the radius raised to the fourth power?
A: The r₁⁴ term comes from the integration of shear stress over the cylindrical surface area, which depends on the geometry of the system.

Q5: What are typical applications of this calculation?
A: This calculation is commonly used in viscometer design, lubrication analysis, and rotating machinery design where fluid films are present.