Tank level and volume calculator
A horizontal cylinder does not fill linearly. Its level-to-volume curve is the circular segment formula, and it catches out anyone who assumes a straight line.
kg/m3
Volume at that level
3.8L
- Percentage full
- 40.00 %
- Total capacity
- 9.4
- Ullage
- 5.7
- Mass of product
- 3204.4 kg
- Hydrostatic pressure at the bottom
- 10.003 kPa
- Wetted cross-section, horizontal tank
- 1.9681 m2
Show the working
- Tank orientation = 1
- Diameter = 2
- Height or length = 3
- Measured level = 1.2
- Product density = 850
- radius = 2 / 2 = 1
- clamped_level = clamp(1.2, 0, 1 > 0 ? 3 : 2) = 1.2
- vertical_volume = pi * 1^2 * 1.2 = 3.769 91
- theta = 1 > 0 ? 2 * acos(clamp((1 - 1.2)/1, -1, 1)) : 0 = 3.544 31
- Wetted cross-section, horizontal tank = 1^2 / 2 * (3.544 31 - sin(3.544 31)) = 1.968 11
- horizontal_volume = 1.968 11 * 3 = 5.904 34
- Volume at that level = 1 > 0 ? 3.769 91 : 5.904 34 = 3.769 91
- Total capacity = 1 > 0 ? pi * 1^2 * 3 : pi * 1^2 * 3 = 9.424 78
- Percentage full = 9.424 78 > 0 ? 3.769 91/9.424 78*100 : 0 = 40
- Mass of product = 3.769 91 * 850 = 3204.42
- Ullage = 9.424 78 - 3.769 91 = 5.654 87
- Hydrostatic pressure at the bottom = 850 * g0 * 1.2 / 1000 = 10.0028
Values are shown to six significant figures here; the arithmetic itself runs on exact fractions and is only rounded where a number is printed.
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The formula
- vertical: V = pi r^2 h
- horizontal: segment area = (r^2/2)(theta - sin theta), with theta = 2 arccos((r - h)/r)
Half full in a horizontal tank really is half the volume, but a quarter of the height is only 19.6% of the volume.
A hydrostatic level transmitter reads the head pressure directly, which is why the product density has to be right.