= Solution
{c}
The <hydrostatic pressure> gives $p_x=\rho gh_x$, independent of depth. Thus <Darcy's law> gives $u=-Kh_x$ and the horizontal <volume flux per unit width> is
$$
\boxed{q(x,t)=\int_0^hu\,dz=-Khh_x,\qquad
K=\frac{k\rho g}{\mu}.}
$$
The coefficient $K$ is the <hydraulic conductivity>, with units of <velocity>. For a column of unit horizontal area, the stored water volume is $\phi h$, and rainfall supplies <volume flux> $R$. The local <mass conservation> equation is $\phi h_t+q_x=R$. Therefore the <Boussinesq equation for an unconfined aquifer> is
$$
\boxed{\phi h_t=K(hh_x)_x+R.}
$$
This assumes rainfall is entirely converted into recharge and neglects unsaturated storage and losses before the water reaches the <water table>.
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