Surface to Volume Ratio of Cut Cylinder given Volume Calculator

Surface to Volume Ratio Formula:

\[ \frac{A}{V} = \sqrt{\frac{2\pi}{V(h_{long} + h_{short})}} \times \left( \sqrt{\frac{2V}{\pi(h_{long} + h_{short})}} + b + h_{short} + h_{long} \right) \]

Volume of Cut Cylinder:

m³

Long Height:

Short Height:

Semi Minor Axis:

Tolerance:

Surface to Volume Ratio (1/m):

Tolerance Range (±5%):

1. What is Surface to Volume Ratio of Cut Cylinder?

Definition: This ratio measures the total surface area relative to the volume of a cut cylinder, important for understanding material efficiency and heat transfer properties.

Purpose: Used in engineering and physics to analyze properties like heat dissipation, chemical reactivity, and structural efficiency.

2. How Does the Calculator Work?

The calculator uses the formula:

\[ \frac{A}{V} = \sqrt{\frac{2\pi}{V(h_{long} + h_{short})}} \times \left( \sqrt{\frac{2V}{\pi(h_{long} + h_{short})}} + b + h_{short} + h_{long} \right) \]

Where:

\( \frac{A}{V} \) — Surface to Volume Ratio (1/m)
\( V \) — Volume of cut cylinder (m³)
\( h_{long} \) — Long height (m)
\( h_{short} \) — Short height (m)
\( b \) — Semi minor axis (m)

3. Importance of Surface to Volume Ratio

Details: Higher ratios indicate more surface area relative to volume, which is crucial for applications requiring efficient heat transfer or chemical reactions.

4. Using the Calculator

Tips: Enter all dimensions in meters. The tolerance field (default ±5%) calculates an acceptable range around the exact value.

5. Frequently Asked Questions (FAQ)

Q1: What is a typical surface to volume ratio range?
A: Values typically range from 0.1 to 10 1/m depending on the cylinder dimensions.

Q2: Why include a tolerance field?
A: Manufacturing variations often require acceptable ranges rather than exact values.

Q3: How does changing heights affect the ratio?
A: Greater height differences generally increase the surface to volume ratio.

Q4: What's the significance of the semi minor axis?
A: It determines the elliptical shape of the cut face, affecting both surface area and volume.

Q5: When would I need this calculation?
A: Useful for designing pressure vessels, heat exchangers, or any application where surface area relative to volume matters.