Constant$-$head permeability test is shown in Figure $1.$ A cylindrical soil sample, $10\mathrm{.}0cm$ in diameter and $21\mathrm{.}0cm$ long, is tested in a constant$-$head permeability apparatus. The constant head of $30cm$ is maintained during the test. After $1$min of testing, a try tal of $412\mathrm{.}6g$ of water was collected. The temperature was $20C.$ The void ratio of the soil was $0\mathrm{.}43.$

a$.$ Calculate the total head at point $A,B,C$ and $D.$

b$.$ Compute the coefficient of hydraulic conductivity in centimeters per second.