Speed Of Outer Cylinder Given Torque Exerted On Outer Cylinder Calculator

Formula Used:

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

Torque on Outer Cylinder (T_o):

N·m

Dynamic Viscosity (μ):

Pa·s

Radius of Inner Cylinder (r₁):

Clearance (C):

Angular Speed (Ω):

Unit Converter ▲

Unit Converter ▼

From:	To:

1. What is the Angular Speed Calculation?

The Angular Speed calculation determines the rotational speed of the outer cylinder based on the torque exerted, dynamic viscosity, inner cylinder radius, and clearance between cylinders. This is particularly important in fluid mechanics and engineering applications involving rotational systems.

2. How Does the Calculator Work?

The calculator uses the formula:

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

Where:

\( \Omega \) — Angular Speed (rad/s)
\( T_o \) — Torque on Outer Cylinder (N·m)
\( \mu \) — Dynamic Viscosity (Pa·s)
\( r_1 \) — Radius of Inner Cylinder (m)
\( C \) — Clearance (m)
\( \pi \) — Mathematical constant pi (≈3.14159)

Explanation: The formula calculates the angular speed by considering the torque applied, fluid viscosity, geometric dimensions, and the clearance between cylinders.

3. Importance of Angular Speed Calculation

Details: Accurate angular speed calculation is crucial for designing and analyzing rotational systems, optimizing performance, and ensuring proper operation in various engineering applications.

4. Using the Calculator

Tips: Enter torque in N·m, dynamic viscosity in Pa·s, radius in meters, and clearance in meters. All values must be positive and valid.

5. Frequently Asked Questions (FAQ)

Q1: What is angular speed?
A: Angular speed refers to the rate of change of angular displacement, measured in radians per second.

Q2: Why is clearance important in this calculation?
A: Clearance affects the fluid flow and shear stress between cylinders, directly impacting the angular speed calculation.

Q3: What units should be used for input values?
A: Use consistent SI units: N·m for torque, Pa·s for viscosity, and meters for radius and clearance.

Q4: Are there limitations to this formula?
A: This formula assumes Newtonian fluid behavior and may have limitations with non-Newtonian fluids or extreme operating conditions.

Q5: Can this calculator be used for industrial applications?
A: While useful for educational and preliminary calculations, industrial applications may require more comprehensive analysis and validation.