Calculation of equivalent water depth in a multi-layered soil profile:

\[d_w = \sum \left(w_i \times \frac{\rho_{b,i}}{\rho_w} \times D_i\right) = \sum (\theta_i \times D_i)\]

Given

\(\rho_w = 1000\text{ kg/m}^3\): 1. \lt strong\gt Upper Layer\lt /strong\gt (\(D_1 = 0.4\text{ m}\)): - Mass wetness \(w_1 = 15\% = 0.15\) - Bulk density \(\rho_{b,1} = 1200\text{ kg/m}^3\) - Volumetric water content \(\theta_1 = 0.15 \times \frac{1200}{1000} = 0.18\) - Water depth in layer 1 \(d_1 = 0.18 \times 0.4\text{ m} = 0.072\text{ m}\) 2. \lt strong\gt Lower Layer\lt /strong\gt (\(D_2 = 0.6\text{ m}\)): - Mass wetness \(w_2 = 25\% = 0.25\) - Bulk density \(\rho_{b,2} = 1400\text{ kg/m}^3\) - Volumetric water content \(\theta_2 = 0.25 \times \frac{1400}{1000} = 0.35\) - Water depth in layer 2 \(d_2 = 0.35 \times 0.6\text{ m} = 0.210\text{ m}\) 3. \lt strong\gt Total Equivalent Water Depth\lt /strong\gt : \[d_w = d_1 + d_2 = 0.072\text{ m} + 0.210\text{ m} = 0.282\text{ m}\]

Darcy's Law for saturated flow:

\[q = -K_{\text{sat}} \frac{dH}{dL}\]

Rearranging to express the ratio of water flux density (

\(q\)) to the hydraulic potential gradient (\(dH/dL\)): \[\frac{q}{\left(-\frac{dH}{dL}\right)} = K_{\text{sat}}\]

This ratio is defined as the Saturated Hydraulic Conductivity (\(K_{\text{sat}}\))\lt /strong\gt of the porous soil medium. Intrinsic permeability (\(k\)) is a geometric property of the porous matrix independent of fluid properties (\(K = \frac{k \rho g}{\mu}\)).

Therefore, the ratio of water flux to potential gradient is the saturated hydraulic conductivity.