Volume of liquid in a tilted tank with hemispherical heads

The calculator below computes volume of liquid in a tilted cylindrical tank with hemispherical heads.

Liquid volume in inclined cylindrical tank with hemispherical heads

Cylinder radius

Cylindrical tank part length

Length of cylindrical tank part (whole tank length except heads)

Liquid level

Level measured near

upper base

lower base

Distance from the base

Distance between liquid level measurement place and nearest base. (0 if level is measured right near the base).

Tilt angle (degrees)

Calculation precision

Digits after the decimal point: 2

Calculate

Liquid level near upper base

 

Liquid level near lower base

 

Liquid volume

 

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The tank length L must be entered without counting head length. Since the head is hemisphere, we assume both head length is equal to cylinder radius R.
Liquid level must be measured near upper or lower head at a distance d from the head and tank body intersection (see the picture), set distance to 0 if you measure the level directly on the head splice. Tilt angle must be set in degrees, enter 0 if the tank is horizontal. It is acceptable any measurement units, as result you get the same cubic unit, e.g. if you measure in inches, the calculator computes volume in cubic inches.

Calculation formula

The tilted tank volume with hemispherical ends consist of two hemispherical ends and one cylinder. The calculator computes these figure volumes step by step and sum the results. Hemisphere section volume formula can be found here : Volume of the hemisphere cut at an angle, cylinder section formula is described here: Tilted cylindrical tank volume.