In a falling head permeability test, the sample used is $15cm$ long having a cross$-$sectional area of $31c{m}^2.$ Calculate the time required for a drop of head from $15$ to $5cm$ if the cross$-$sectional area of the stand pipe is $1c{m}^2.$ The sample of soil is made of three layers. The thickness of the first layer from the top is $7cm$ and has a value of $k_1=3{10}^{-2}c\frac{m}{sec},$ the second layer of thickness $2cm$ has $k_2=5{10}^{-4}c\frac{m}{sec}$ and the bottom layer of thickness $6cm$ has $k_3=6{10}^{-2}c\frac{m}{sec}.$ Assume that the flow is taking place perpendicular to the layers.