Now, discussion comes, how to relate volumetric vapour content to volumetric liquid content. And we said that we will use equilibrium condition, because liquid water is in equilibrium with water vapour at every instance. Remember that we are considering a transient process. So n is the porosity of the soil and q_v volumetric vapour content. Of course we are again using this expression which we have seen before, and we are using this vapour diffusivity expression which we have developed before. So if we substitute this two into this equation and in the differential with respect to time, we will get this expression, which will relate q_v to q_l and temperature.
So you now reapply principle of conservation of mass which is time derivated to q_v related to gradient of velocity and the source term.
And then we substitute the expression which we developed for velocity to give the conservation of mass.