Radius Of Inner Cylinder Given Torque Exerted On Outer Cylinder Calculator

Formula Used:

\[ r1 = \left( \frac{To}{\mu \cdot \pi^2 \cdot \Omega / (60 \cdot C)} \right)^{1/4} \]

Torque on Outer Cylinder (To):

N·m

Dynamic Viscosity (μ):

Pa·s

Angular Speed (Ω):

rad/s

Clearance (C):

Radius of Inner Cylinder (r1):

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1. What is Radius of Inner Cylinder?

The Radius of Inner Cylinder refers to the distance from center to inner cylinder's surface, crucial for viscosity measurement in rotational viscometers and other fluid dynamics applications.

2. How Does the Calculator Work?

The calculator uses the formula:

\[ r1 = \left( \frac{To}{\mu \cdot \pi^2 \cdot \Omega / (60 \cdot C)} \right)^{1/4} \]

Where:

\( r1 \) — Radius of Inner Cylinder (m)
\( To \) — Torque on Outer Cylinder (N·m)
\( \mu \) — Dynamic Viscosity (Pa·s)
\( \Omega \) — Angular Speed (rad/s)
\( C \) — Clearance (m)
\( \pi \) — Mathematical constant pi (≈3.1416)

Explanation: This formula calculates the radius of the inner cylinder based on the torque exerted on the outer cylinder, fluid viscosity, angular speed, and clearance between cylinders.

3. Importance of Radius Calculation

Details: Accurate radius calculation is essential for designing rotational viscometers, analyzing fluid flow between concentric cylinders, and understanding torque transmission in mechanical systems.

4. Using the Calculator

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

5. Frequently Asked Questions (FAQ)

Q1: What is the typical range for inner cylinder radius?
A: The radius typically ranges from a few millimeters to several centimeters, depending on the specific application and scale of the equipment.

Q2: How does clearance affect the radius calculation?
A: Smaller clearance increases the denominator in the formula, resulting in a larger calculated radius for the same torque input.

Q3: What units should be used for angular speed?
A: Angular speed must be in radians per second (rad/s). If you have RPM, convert using: Ω = RPM × 2π / 60.

Q4: Can this formula be used for non-Newtonian fluids?
A: This specific formula is derived for Newtonian fluids. For non-Newtonian fluids, more complex models are required.

Q5: What are common applications of this calculation?
A: This calculation is commonly used in viscometer design, lubrication analysis, and studies of fluid flow between rotating cylinders.