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Mechanical EngineeringP0

Partially Filled Horizontal Tank Volume Calculator

Calculate liquid volume in a partially-filled horizontal cylindrical tank from fill level.

Inputs
Enter your values below

From tank bottom, not exceeding diameter

Result
Liquid Volume
—
Enter values and click Calculate
Formula
(r² × acos((r − h) ÷ r) − (r − h) × √(2 × r × h − h²)) × length × 1000
Result unit: L

Liquid volume = Cross-sectional area × Length. Cross-section = r²·arccos((r−h)/r) − (r−h)·√(2rh−h²) (circular segment formula). ×1000 converts m³ to liters. Where r = radius, h = fill height.

Introduction

Calculate the liquid volume in a partially filled horizontal cylinder using the circular segment area formula. This is the standard method for dipstick-to-volume conversion for horizontal fuel tanks, water trucks, and bulk storage.

Calculation Example

3m diameter × 6m horizontal tank filled to 1m height holds ~12,395 liters (out of 42,412 total at 100%).

Inputs: r=1.5, length=6, h=1
Result: 12395 L

Engineering Applications

  • •Fuel tank gauging
  • •Truck tank dipstick calibration
  • •Bulk storage inventory
  • •Process vessel level measurement

Frequently Asked Questions

How accurate is this?

This gives a theoretical result for a perfect cylindrical shell with flat ends. Real tanks with dished heads or internal baffles require a strapping table calibration.

What volume is at 50% fill?

At h = r (half full), the volume is exactly half the total volume. Due to the circular geometry, fill height is not linear with volume: at 30% height you have ~25% volume, at 50% height you have exactly 50% volume.

Related Calculators

Tank Volume CalculatorCylinder Volume CalculatorStorage Capacity Calculator

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Disclaimer: Calculations are for reference and educational purposes only. Always verify results independently for engineering design. See full disclaimer.