Horizontal Tank with Dished Ends Volume Calculator
Calculate the liquid volume in a horizontal cylindrical vessel with 2:1 elliptical, hemispherical or flat heads at any level.
- Shell: L × [R² acos((R − h)/R) − (R − h)√(2Rh − h²)]
- Two heads together form an ellipsoid: (a/R) × πh²(3R − h)/3, a = head depth = 0.625 m
- Total = 12.441 m³
Level to volume strapping table
| Level % | Level | Volume | Volume % |
|---|---|---|---|
| 0 % | 0 m | 0 m³ | 0.0 % |
| 10 % | 0.25 m | 1.6474 m³ | 4.9 % |
| 20 % | 0.5 m | 4.6188 m³ | 13.8 % |
| 30 % | 0.75 m | 8.3149 m³ | 24.8 % |
| 40 % | 1 m | 12.441 m³ | 37.1 % |
| 50 % | 1.25 m | 16.772 m³ | 50.0 % |
| 60 % | 1.5 m | 21.102 m³ | 62.9 % |
| 70 % | 1.75 m | 25.228 m³ | 75.2 % |
| 80 % | 2 m | 28.924 m³ | 86.2 % |
| 90 % | 2.25 m | 31.896 m³ | 95.1 % |
| 100 % | 2.5 m | 33.543 m³ | 100.0 % |
Dished Head Volume
a is the depth of one head: D/4 for 2:1 elliptical heads, D/2 for hemispherical. The two heads together are treated as one ellipsoid, which is exact for these head types.
Worked example
A 2.5 m × 6 m vessel with 2:1 elliptical heads holds 29.45 m³ of shell plus 4.09 m³ of heads = 33.54 m³ when full; at 1.0 m level it holds about 12.44 m³ (37.1 %).
Frequently Asked Questions
What is a 2:1 elliptical head?
A head whose depth is one quarter of the vessel diameter, giving a 2:1 ratio between its major and minor axes.
What is the volume of a 2:1 elliptical head?
π × D³ ÷ 24 for one head, which is half the volume of a hemispherical head of the same diameter.
Are torispherical heads covered?
Not exactly. Use the 2:1 elliptical option as an approximation, or the manufacturer’s strapping table.
Learn more on the blog
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