The soil profile below a lake with water level at elevation $=0$ m and lake bottom at elevation $=-10$ m is shown in the figure, where $k$ is the permeability coefficient. A piezometer (stand pipe) installed in the sand layer shows a reading of $+10$ m elevation. Assume that the piezometric head is uniform in the sand layer. The quantity of water (in $m^3/s$) flowing into the lake from the sand layer through the silt layer per unit are of the lake bed is

1. $1.5 \times 10^{-6}$
2. $2.0 \times 10^{-6}$
3. $1.0 \times 10^{-6}$
4. $0.5 \times 10^{-6}$