In a uniform soil deposit having a level ground surface, an open standpipe with a constant interior diameter of $5\mathrm{.}0cm$ is installed to a depth of $10mm.$ The standpipe has a flush bottom. The groundwater table is located $4\mathrm{.}0m$ below the ground surface. The standpipe is filled with water to ground surface and the water level is allowed to drop without adding any water to the standpipe. If the water level in the standpipe drops from graund surface to a depth of $0\mathrm{.}9m$ below ground surface in $60$ seconds, calculate the mean coefficient of per m$$ability k of the soil deposit.