$($After A$.$ Casagrande.$)$

$6\mathrm{.}5$ A falling$-$head permeability test is to be performed on a soil whose permeability is estimated to be $9\mathrm{.}7{10}^{-7}\frac{m}{sec}.$ What diameter standpipe should you use if you want the head to drop from $35\mathrm{.}4$ cm to $21\mathrm{.}8$ cm in about $5$ min $?$ The sample's cross section is $15c{m}^2$ and its length is $10$ cm $.($After Taylor, $1948.)$