Question $6$ a$.$

$5$ Marks

A lyyered soil bed has coefficient of permeability $($k$)$ from ground surface up to $2m$ depth $k1$ as $2{10}^{-4}c\frac{m}{sec},$ from $2m$ to $8m$ depth, $kg=3{10}^{-2}c\frac{m}{sec}$ and from $8m$ to $10m$ depth, $kJ=5{10}^{-4}c\frac{m}{sec}.$ Find $($a$)$The ratio of average coefficient of permeability for borizontal flow $($ka$)$ to its vertical flow $(k_n)$; $($b$)$ the discharge velocity $(v)$ in each layer for horizontal flow, taking hydraulic gradient $($i$)$ as $0\mathrm{.}3$ for all the layers, $($c$)$ rate of discharge $($q$)$ through the soil mass in horizontal flow across the whole cross sectional area for unit $cm$ width.