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A bed of sand consists of three horizontal layers of equal thickness. The magnitude of the coefficient of permeability

for both upper and lower layer is $4*10^{-4}mm/s$ and for middle layer it is $6*10^{-2}mm/s$. what is the ratio of average permiability of bed in horizontal to that of vertical direction.

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$K_h$ = coefficient of permeability in horizontal direction $K_v$ = coefficient of permeability in vertical direction $K_h = \frac{K_1H_1+K_2H_2+K_3H_3}{H}$ $H_1=H_2=H_3=\frac{H}{3}$ $K_h = \frac{1}{3}(K_1+K_2+K_3)$ $= 0.020 cm/sec$ $\frac{H}{K_v} = \frac{H_1}{K_1}+\frac{H_2}{K_2}+\frac{H_3}{K_3}$ $\frac{3}{K_v} = (2500 + 16.67 + 2500)$ $\frac{1}{K_v} = 1672.22$ $K_v = 5.980 * 10^{-4}$ $\frac{K_h}{K_v} = 33.44$

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