BIZOMAT MAKEOS · Geometry
Horizontal Tank Calibration Chart (Shell and Heads, Volume by Depth)
How much liquid is in this horizontal cylindrical tank with dished heads at my dip reading, what is the full capacity, and what does the depth chart look like?
Contents of a horizontal cylindrical tank with flat, 2:1 ellipsoidal or hemispherical heads: liquid volume in the shell at a depth (as the tank volume tool), the liquid in both heads at the same depth (the two heads together form a sphere or a half-depth spheroid), total and full capacity (full matching the vessel head volume tool), percentage full, liquid mass, the time to fill the rest at a pump rate, and a calibration chart every tenth of the diameter.
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How this tool works
Inputs, units and where to find them
| Input | Unit | Typical source |
|---|---|---|
| Inside diameter | mm | Inside diameter of the shell. |
| Shell length (tangent to tangent) | mm | Length of the cylindrical shell between the head tangent lines. |
| Heads | choice | Shape of the two end heads. |
| Liquid depth (dip) | mm | Liquid depth measured from the bottom of the shell. |
| Liquid density | kg/m³ | Density of the liquid. |
| Filling pump rate | L/min | Flow of the filling pump. |
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: Inside diameter
- What it is
- The inside diameter of the cylindrical shell. It also sets the size of the heads and the greatest possible liquid depth.
- Units and format
- Enter a number in mm: millimetres. The form accepts 0.000001 mm to 10000 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.
- Get it right
- Inside, not outside, diameter: subtract twice the wall from an outside measurement.
What this means: Shell length (tangent to tangent)
- What it is
- The length of the straight cylindrical part of the tank between the two head tangent lines, where the curved heads begin.
- Units and format
- Enter a number in mm: millimetres. The form accepts 0.000001 mm to 100000 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
- Shell volume rises in direct proportion; the head volume does not change.
- Get it right
- Leave the heads out; their volume is added from the head choice.
What this means: Heads
- What it is
- The shape of the two end heads: 2:1 ellipsoidal, hemispherical or flat. Curved heads add liquid at every depth; flat heads add none.
- Units and format
- Choose one of 3 options from the list: 2:1 ellipsoidal; Hemispherical; Flat.
- Example
- The form opens with “2:1 ellipsoidal” selected as a worked example. Choose the option that matches your case.
What this means: Liquid depth (dip)
- What it is
- The liquid depth measured vertically up from the lowest point inside the shell, for example with a dip stick or level gauge.
- Units and format
- Enter a number in mm: millimetres. The form accepts 0 mm to 10000 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
- It cannot exceed the inside diameter; a dip measured down from the top must be converted to depth from the bottom.
What this means: Liquid density
- What it is
- The density of the liquid in the tank, used only to turn the contents volume into a mass.
- Units and format
- Enter a number in kg/m³: kilograms per cubic metre. The form accepts 100 kg/m³ to 3000 kg/m³. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 1000 kg/m³ as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
What this means: Filling pump rate
- What it is
- The flow rate of the pump filling the tank, used for the time to fill the space still empty.
- Units and format
- Enter a number in L/min: litres per minute. The form accepts 0.000001 L/min to 1000000 L/min. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 100 L/min as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- Fill time is inversely proportional to the pump rate.
Method and formulas
- Shell segment area A = r² cos⁻¹[(r − h) ÷ r] − (r − h)√(2rh − h²); shell volume = A L (as the tank volume tool).
- Two hemispherical heads = a sphere: V = π h² (3r − h) ÷ 3; two 2:1 ellipsoidal heads = half of that (a spheroid of half depth); flat heads add nothing.
- Full capacity = π r² L + heads (as the vessel head volume tool); fill time = (full − contents) ÷ pump rate.
- Example: at 400 mm the tank holds 1,107.3 L (28.796% of 3,845.3 L); filling the rest takes 27.38 min.
Limitations
- Level tank; a slope changes the readings, especially near empty and full.
- Inside dimensions; nozzles and internals are not deducted.
- Example values are illustrations. Replace them with values for your actual task.
Typical uses
- Make a dip chart for a fuel or water tank
- Convert a dip reading to litres
- Find the time to fill a tank
Who it is for
- Plant engineers
- Operators
- Fuel and storage managers
What you get
- Shell, head and total volume at the dip
- Full capacity, percentage and mass
- Fill time and calibration chart
Interpreting the result
- The middle of a horizontal tank holds the most per millimetre of dip: readings near the top and bottom change slowly.
References
- Machinery’s Handbook, 29th edition (Industrial Press, 2012), printed pp. 68–69, 82–87. Topic reference; no source tables or recommended settings are reproduced.
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Open the Horizontal Tank Calibration Chart (Shell and Heads, Volume by Depth) calculator