Semi Minor Axis of Cut Cylinder given Lateral Surface Area Calculator

Semi Minor Axis Formula:

\[ b = \sqrt{\left(\frac{h_{Long} - h_{Short}}{2}\right)^2 + \left(\frac{LSA}{\pi \cdot (h_{Long} + h_{Short})}\right)^2} \]

Long Height of Cut Cylinder:

Short Height of Cut Cylinder:

Lateral Surface Area:

m²

Tolerance:

Semi Minor Axis (b): m

Tolerance Range (±5%):

1. What is Semi Minor Axis of a Cut Cylinder?

Definition: The semi minor axis is half of the length of the shortest diameter of the elliptical face of a cut cylinder.

Purpose: It helps determine the dimensions and properties of a cut cylinder's elliptical cross-section.

2. How Does the Calculator Work?

The calculator uses the formula:

\[ b = \sqrt{\left(\frac{h_{Long} - h_{Short}}{2}\right)^2 + \left(\frac{LSA}{\pi \cdot (h_{Long} + h_{Short})}\right)^2} \]

Where:

\( b \) — Semi minor axis (meters)
\( h_{Long} \) — Long height of cut cylinder (meters)
\( h_{Short} \) — Short height of cut cylinder (meters)
\( LSA \) — Lateral surface area (square meters)

Explanation: The formula calculates the semi minor axis using the height difference and lateral surface area of the cut cylinder.

3. Importance of Semi Minor Axis Calculation

Details: Accurate calculation of the semi minor axis is crucial for engineering applications involving cut cylinders, such as piping systems and structural components.

4. Using the Calculator

Tips: Enter the long height, short height, lateral surface area, and tolerance percentage (default ±5%). All values must be positive numbers.

5. Frequently Asked Questions (FAQ)

Q1: What is the tolerance percentage for?
A: The tolerance percentage calculates an acceptable range around the calculated value (±5% by default) to account for measurement uncertainties.

Q2: How are the long and short heights measured?
A: Long height is the maximum vertical distance, short height is the minimum vertical distance from base to top of the cut cylinder.

Q3: What units should I use?
A: Use consistent units (meters for lengths, square meters for area) for accurate results.

Q4: Can I use this for partially filled cylinders?
A: Yes, this calculator can be used for partially filled cylindrical tanks where the liquid surface forms an ellipse.

Q5: What if my cylinder isn't perfectly cut?
A: This calculator assumes a clean, planar cut. For irregular cuts, results may be approximate.