Given the soil column and the test setup shown in Figure Q$3.$

gure Q$3$

$(1)$ If the diameter of the soil cylinder is $6$ cm and $\backslash (42\mathrm{.}5\backslash$mathrm$\{$~cm$\}^\{3\}\backslash )$ water flows through the soil sample in $5$ min $,$ calculate the coefficient of permeability of the soil.

$(2)$ Determine the elevation, total and pressure heads $($in centimeters$)$ at Point C$.$