Since the thickness 1 of the deposit varies continuously with the proceeding of the ritering, it will be opportune to write the preceding equation in differential form.
From the relationship (2) and from the successive differential equation we can deduce what ready intuition suggests, and that is to say that the filtering velocity is proportional to the filteringsurface, to say that the existing pressure difference between the face of the panel and inversely proportional to the thickness of the deposit. Be it noted that we have supposed, in the setting of the proceding relationships, that the deposited sludge is incompressible with the increase of the filterng pressure, and that is to say that the diameter of the various capillariess remains unchanged.
ir, on the other hand, the sludge is compressed, if the particles are warped with the increase of the pressure, the capillaries get shrnked and therefore the filtering velocity increase less rapidly than what states the proportionality with the pressure difference AP