BIZOMAT MAKEOS · Geometry
Cylindrical Tank Contents
How much liquid is in this partly filled cylindrical tank?
Volume of liquid in a horizontal or vertical cylindrical tank at a given depth, with percentage full and remaining capacity.
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How this tool works
Inputs, units and where to find them
| Input | Unit | Typical source |
|---|---|---|
| Tank orientation | choice | How the tank axis is installed. |
| Inside diameter | mm | Inside diameter from the tank drawing or measured shell circumference ÷ π minus wall thickness. |
| Inside length (straight shell) | mm | Straight shell length between flat ends (horizontal) or shell height (vertical). |
| Liquid depth | mm | Measured liquid depth from the lowest inside point. |
What each input means
Open an input to see what it is, its units, the worked example and the common mistakes, with a small diagram.
What this means: Tank orientation
- What it is
- Whether the tank lies on its side with the axis level, or stands upright with the axis vertical. This decides how the liquid depth turns into a volume.
- Units and format
- Choose one of 2 options from the list: Horizontal (axis level); Vertical (axis upright).
- Example
- The form opens with “Horizontal (axis level)” selected as a worked example. Choose the option that matches your case.
- Get it right
- A horizontal tank’s volume does not rise in proportion to depth; a vertical tank’s does.
What this means: Inside diameter
- What it is
- The diameter across the inside of the cylindrical shell, inside the walls, where the liquid sits.
- Units and format
- Enter a number in mm: millimetres. The form accepts 0.000001 mm to 1000000 mm. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 1200 mm as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- Capacity rises with the square of the diameter.
- Get it right
- Use the inside, not the outside, diameter; if you measured the outside circumference, divide by π and take off twice the wall thickness.
What this means: Inside length (straight shell)
- What it is
- The straight inside length of the cylindrical shell between flat ends: the horizontal length of a lying tank, or the shell height of an upright tank.
- Units and format
- Enter a number in mm: millimetres. The form accepts 0.000001 mm to 1000000 mm. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 3000 mm as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- Liquid volume and capacity rise in proportion to the length.
- Get it right
- The tool treats the ends as flat. Volume in dished or rounded ends is not included and must be added separately.
What this means: Liquid depth
- What it is
- How deep the liquid is, measured straight up from the lowest point inside the tank to the liquid surface, for example with a dip stick.
- Units and format
- Enter a number in mm: millimetres. The form accepts 0 mm to 1000000 mm. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 400 mm as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Get it right
- For a horizontal tank it cannot exceed the inside diameter; for an upright tank it cannot exceed the shell height. A sloping tank gives a false reading.
Method and formulas
- Horizontal: wetted area = r² arccos((r − h) ÷ r) − (r − h)√(2rh − h²); volume = area × length.
- Vertical: volume = π r² × depth.
- Volumes are converted from mm³ to litres (÷ 10⁶).
- Example: a horizontal tank 1200 mm × 3000 mm at 400 mm depth holds 990.02 L, 29.179% of its 3,392.9 L capacity.
Limitations
- Flat ends only; dished or hemispherical heads add volume not included here.
- The tank is assumed level; a slope changes the depth–volume relation.
- Example values are illustrations. Replace them with values for your actual task.
Typical uses
- Build a dip chart for a horizontal tank
- Estimate coolant, oil or fuel stock from a depth reading
- Check tank capacity for a batch
Who it is for
- Maintenance planners
- Process engineers
- Operators
What you get
- Liquid volume
- Percentage full
- Full capacity
- Remaining capacity
Interpreting the result
- Calibrate against a measured fill where stock value matters.
References
- Machinery’s Handbook, 29th edition (Industrial Press, 2012), printed pp. 68–69. Topic reference; no source tables or recommended settings are reproduced.
Learn the Concepts Behind This Tool
These BIZOMAT Library readings explain the method this tool uses, with worked examples.
Method explained here · BIZOMAT original book
Installing a weighing vessel
In Strain Gauges and Load Cells by the Numbers
What it covers: How to size a hopper's load cells from its volume and load sharing, mount them so the vessel can grow and move freely, and stop pipes, chutes and cables from carrying weight past the cells.
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