In a volume of pure fluid with density ρ and viscosity μ the mass conservation is defined by the continuity equation

with the fluid velocity v. For an incompressible fluid it simplifies to:

For a porous medium Equation 2-9 must be corrected by the porosity εp because the fluid volume is only a fraction of the total volume, hence

Note that v refers to the velocity of the fluid within the pores also called seepage or interstitial velocity. More commonly used to describe the flow through a porous medium is the superficial velocity or Darcy velocity u:

Q (SI unit: m/s) is the volume flow rate of the fluid and A(SI unit: m2) is the cross-sectional area of the porous medium. The cross-sectional area for the pore spaces which is available for the fluid to flow is related to the porosity by Aε = εpA such that the Darcy velocity and seepage velocity relate as follows:

And Equation 2-10 can be written as:

or when a volumetric mass source Qm(SI unit: kg/m3/s) is present:

Note that Qm is a mass source per unit volume of the porous medium (not per unit pore volume).