Question

A soil mass comprises two horizontal layers (of equal thickness and equal width) stacked one above the other. The hydraulic conductivities of the two layers are 5 × 10^-2 cm/s and 3 x 10^-2 cm/s. Considering Darcian flow of water and same hydraulic gradient for both the layers, the effective hydraulic conductivity of the soil mass in cm/s is______.(rounded off to two decimal places).

Hint:

When soil layers are placed \textbf{horizontally (parallel to flow)}, the effective conductivity is the arithmetic mean. For \textbf{vertical layers (series flow)}, the harmonic mean is used.

Answer 1

Correct Answer: 0.04

Step 1: Identify the condition.
Since the layers are \emph{horizontal and parallel to flow}, the flow occurs in parallel system. For parallel flow: \[ K_{eq} = \frac{\sum (K_i \cdot H_i)}{\sum H_i} \] where \(K_i\) are hydraulic conductivities and \(H_i\) are thicknesses. Step 2: Apply equal thickness condition.
Both layers have equal thickness, so: \[ K_{eq} = \frac{K_1 + K_2}{2} \] Step 3: Substitute values.
\[ K_1 = 5 \times 10^{-2} = 0.05\ \text{cm/s}, \quad K_2 = 3 \times 10^{-2} = 0.03\ \text{cm/s} \] \[ K_{eq} = \frac{0.05 + 0.03}{2} = \frac{0.08}{2} = 0.04\ \text{cm/s} \] \[ \boxed{0.04\ \text{cm/s}} \]