A pipe with a square cross$-$sectional area contains sand through which fresh groundwater is flowing. The square cross section has a side length of $0\mathrm{.}19$ m$.$ A head drop of $3\mathrm{.}97$ m is imposed on the pipe, which is $4\mathrm{.}02$ m long in the direction of flow. If flow through the sand$-$filled pipe occurs at $9\mathrm{.}8$ L$/$s$,$ determine the permeability of the sand in mm$2.$