Content Cylindrical Tank

Overview

Engineering reference data for Content Cylindrical Tank in miscellaneous.

Key Formulas

Unit Conversion

$y = x \cdot k$

Multiply by conversion factor.

Linear Interpolation

$y = y_1 + \frac{(x - x_1)(y_2 - y_1)}{x_2 - x_1}$

Estimate between two known points.

Percentage

$p = \frac{\text{part}}{\text{whole}} \times 100\%$

Part as fraction of whole.

Variables

Liquid Level vs Volume Relationship

The relationship between liquid level and volume in a horizontal cylindrical tank is non-linear. The following reference table shows this relationship for zero-slope (horizontal) tanks and pipes:

Calculation Method

The volume calculation uses an iterative slicing algorithm that sums small sliced volumes along the tank length. This approach is necessary because:

• The cross-sectional area of liquid changes non-linearly with fill level
• Sloped tanks have varying liquid depth along their length
• The method accounts for complex geometries at partial fill levels

For a horizontal tank, the liquid cross-section forms a circular segment defined by:

• Central angle ($\theta$) — the angle subtended by the liquid surface at the pipe center
• Chord length ($c$) — the width of the liquid surface
• Arc length ($s$) — the curved length along the liquid-wall interface

Slope Effects

When a cylindrical tank is sloped at an angle, the liquid distribution becomes uneven along the tank length. The calculation algorithm accounts for:

• The slope angle (in degrees)
• Variable liquid depth from inlet to outlet
• Changes in air volume distribution

The relationship between slope formats:

$\text{Grade (\%)} = \tan(\theta) \times 100 = \text{Gradient} \times 100$

Key Relationships

At 50% fill level, the liquid volume equals exactly 50% of total volume due to symmetry. For levels below 50%, the fill percentage is less than the level percentage; above 50%, the fill percentage exceeds the level percentage.

The air volume in the tank equals:

$V_{\text{air}} = V_{\text{total}} - V_{\text{liquid}}$

Calculator Outputs Summary

The calculation provides these derived quantities from the basic inputs:

• Liquid volume and liquid mass (using density)
• Central angle, chord length, and arc length of the liquid segment
• Cross-sectional area of both liquid and air portions
• Air volume remaining in the tank

Interactive Charts

References

• Original Source