Hi Faby,
I try to extend my explanation. First, let's clarify those equations:
Eq. 3-15 is the horizontal formulation for the unconfined aquifer. It is depth-integrated and yields the (depth-integrated) Darcy velocity, thus it has the unit [m²/s].
The more general formulation is (3-2), however it also contains a buoyancy term. The unit is [m/s], and yields the Darcy velocity.
Eq. 3-16 yields the depth-integrated mass-source term, thus its unit is [kg/m²*s].
The Dupuit approximation is a simplification of 3D settings, practically reducing your first equation to two dimensions, assuming the vertical flow is negligible. The same is valid for any density effects, that's why you don't have any buoyancy term in the 2D formulations (3-10 and 3-15).
Using 3D models in FEFLOW, the Dupuit approximation is not valid. But in 2D horizontal models, these so-called aquifer-averaged-, or horizontal equations are used. The formulations in chapter 3.2 are part of them, so you often find depth-integrated formulas.
Please read chapter 1.5 in the RF for more details.
Bastian
