Horizontal Capsule Tank Volume Formula

We consider a capsule as a sphere, with diameter \(d\), split into two halves and separated by a cylinder of the same diameter \(d\) and height \(a\). Here, \(r\) is defined as \(\frac{d}{2}\).

The volume of a sphere is given by \(V_{\text{sphere}} = \frac{3}{4} \pi r^3\), and

the volume of a cylinder is \(V_{\text{cylinder}} = \pi r^2 a\).

Therefore, the total volume of the capsule can be expressed as:

\(V_{\text{capsule}} = \pi r^2 \left( \frac{3}{4} r + a \right)\).

For the volume of fill in a horizontal capsule, we use different methods for the cylinder and sphere sections.

For the horizontal cylinder section, we use the circular segment method.

For the sphere section, we use the volume of a spherical cap, which is calculated as:

\(V_{\text{spherical cap}} = \frac{1}{3} \pi h^2 (3R - h)\),

where \(R\) is the radius of the sphere and \(h\) is the height of the spherical cap.