A falling$-$head permeameter containing a soil sample has falling$-$head tube diameter of $2$ cm$,$ a sample radius of $7\mathrm{.}1$

cm and a sample length of $18\mathrm{.}3$ cm$.$ The initial head is $19\mathrm{.}6$ cm$.$ It falls to $11\mathrm{.}4$ cm over a period of $9\mathrm{.}4$ hours.

Compute the hydraulic conductivity in cm$/$s$.$