Page last updated 30/08/2018

Volume of a cylinder
The drum plant is made as a brick
lined cylindlical hole in the ground.
The space between the bricks and
the side of the hole is back-filled
with earth, which is packed firmly
in. The cylindrical shape is very
strong, especially in compression.
The pressure due to the liquid inside
the digester is balanced by the
pressure of the soil on the outside.
The volume of a cylinder is given by
the equation:

Volume of a section of a
sphere (a cap)
The dome plants are made as
sections of a sphere (or close to
that shape). A spherical shape is
even stronger in compression than
a cylinder. Again, soil is used to
compress the outside of the
masonry shape.
This is then able to balance the
pressures due to the liquid and gas
inside the dome.
The relationships between the
different parameters shown in the
diagram are given by the equations
below:

Design Equations for biogas plant designs

where:
R is the radius of the sphere
r is the radius of the cap
h is the height of the cap
φ is the included angle

Diagram of a cylinder

Diagram of a section
of a sphere

which gives:
The volume is:
Rearranging:
The angle (φ) is: