A constant$-$head permeability test is conducted on a given soil. The diameter of the specimen is $7\mathrm{.}4$ cm and its length is $15$ cm $.$ Over a time of $4hr12$min,$480c{m}^3$ of water are collected passing through the soil. The water level on the inlet side of the soil is $52$ cm above the datum while the water level on the outlet side of the soil is $28$ cm above the datum. Calculate the coefficient of permeability in cm$/$s$.(20$ points$)$