Horizontal Cylinder Tank Volume Calculator

Total Volume (m³):

Filled Volume (m³):

Total Volume (U.S. Gallons):

Filled Volume (U.S. Gallons):

Total Volume (Imp. Gallons):

Filled Volume (Imp. Gallons):

Total Volume (Liters):

Filled Volume (Liters):

Total Volume (Cubic Feet):

Filled Volume (Cubic Feet):

Tank Volume (bbl):

Filled Volume (bbl):

Total Volume of the Horizontal Cylinder Tank

The total volume $V_{\text{tank}}$ of a cylinder-shaped tank is determined by multiplying the area $A$ of its circular end by its length $l$ . The area $A$ of the circular end is given by $\pi r^2$ , where $r$ is the radius, which is equal to half the diameter or $\frac{d}{2}$ . Thus, the total volume of the tank is:

$V_{\text{tank}} = \pi r^2 l$ Filled Volume of a Horizontal Cylinder Tank

To calculate the filled volume of a horizontal cylinder tank, we first need to find the area $A$ of the circular segment that corresponds to the filled portion and then multiply it by the length $l$ .

For a circular segment, the shaded area $A$ is given by:

$A = \frac{1}{2} r^2 (\theta - \sin\theta)$

where $\theta$ is in radians and is calculated as:

$\theta = 2 \arccos\left(\frac{r}{m}\right)$

Here, $m$ represents the vertical distance from the center of the circle to the chord defining the segment's base.

Thus, the volume of the circular segment $V_{\text{segment}}$ is:

$V_{\text{segment}} = \frac{1}{2} r^2 (\theta - \sin\theta) l$

Case 1: Fill Height Less Than Half the Diameter

If the fill height $f$ is less than half the diameter $d$ (i.e., $f < \frac{d}{2}$ ), we use the segment created by the filled height directly, and the filled volume $V_{\text{fill}}$ is:

$V_{\text{fill}} = V_{\text{segment}}$

Case 2: Fill Height Greater Than Half the Diameter

However, if the fill height $f$ is greater than half the diameter $d$ (i.e., $f > \frac{d}{2}$ ), we need to calculate the segment corresponding to the empty portion of the tank and subtract it from the total volume to get the filled volume. In this case:

$V_{\text{fill}} = V_{\text{tank}} - V_{\text{segment}}$

where $V_{\text{segment}}$ now represents the volume of the empty segment.