Breadth of Annulus Given Longest Interval and Outer Circle Radius Calculator

Formula Used:

\[ Breadth\ of\ Annulus = Outer\ Circle\ Radius\ of\ Annulus - \sqrt{Outer\ Circle\ Radius\ of\ Annulus^2 - \left(\frac{Longest\ Interval\ of\ Annulus}{2}\right)^2} \]

Breadth of Annulus:

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1. What is the Breadth of Annulus?

The Breadth of Annulus is defined as the shortest distance or measurement between the outer circle and inner circle of an Annulus. It represents the thickness of the ring-shaped region formed by two concentric circles.

2. How Does the Calculator Work?

The calculator uses the formula:

\[ Breadth\ of\ Annulus = Outer\ Circle\ Radius - \sqrt{Outer\ Circle\ Radius^2 - \left(\frac{Longest\ Interval}{2}\right)^2} \]

Where:

Outer Circle Radius — Radius of the larger circle (m)
Longest Interval — Length of the longest chord tangent to the inner circle (m)
sqrt — Square root function

Explanation: The formula calculates the annulus breadth using geometric relationships between the outer radius and the longest chord that can fit within the annulus while being tangent to the inner circle.

3. Importance of Annulus Calculations

Details: Annulus calculations are important in various engineering and architectural applications, particularly in the design of rings, pipes, washers, and other circular components where the thickness of the material needs to be precisely determined.

4. Using the Calculator

Tips: Enter the outer circle radius and longest interval in meters. Both values must be positive numbers. The longest interval should be less than or equal to twice the outer radius for valid results.

5. Frequently Asked Questions (FAQ)

Q1: What is an annulus?
A: An annulus is a ring-shaped region between two concentric circles, resembling a flat circular ring or washer.

Q2: How is the longest interval related to the annulus?
A: The longest interval is the chord of the outer circle that is tangent to the inner circle, representing the maximum distance between two points within the annulus.

Q3: What are the units used in this calculation?
A: The calculator uses meters for all measurements, but the same formula applies to any consistent unit system.

Q4: Can this formula be used for non-concentric circles?
A: No, this specific formula applies only to concentric circles that form a perfect annulus.

Q5: What if I get a negative result?
A: A negative result indicates invalid input where the longest interval exceeds the possible maximum for the given outer radius.