Equivalently
and in a minerals processing context where the specific gravity of the liquid (water) is taken to be one:
So
and
Then combining with the first equation:
So
Then since
we conclude that
where
: is the solids fraction of the slurry on a volumetric basis
: is the solids fraction of the slurry on a mass basis
: is the mass or mass flow of solids in the sample or stream
: is the mass or mass flow of slurry in the sample or stream
: is the mass or mass flow of liquid in the sample or stream
: is the bulk specific gravity of the solids