F12. Filtration Formulas
Mean velocity of flow in a filtration process can be calculated if resistance to filtration is known. Filtration resistance is due to cake and cloth.
Where V is volume of liquid flowing in time t, A is filtration area, l is thickness of filter cake, L is the thickness of filter cake offering same resistance as that of cloth, r is specific resistance of cake, μ is viscosity of fluid and -ΔP is total pressure drop. Replacing l by vV/A we can get
Where v is a ratio of volume of the deposited to the volume of filtrate.
For a period of constant rate filtration, dV/dt = V/t, and the following equation results
For a period of constant pressure filtration, -ΔP is constant, and the following equation results
Pressure difference is built up gradually and during this period filtration is conducted at constant filtration rate for time t1, then.
Where V1 is volume of liquid passing in time t1.
The filter press: The filter press is made in two main forms, the plate and frame and the recessed or chamber press. If filtration is carried out entirely at constant pressure, then
Where B1 and B2 are constants given as