Question Bank • QB_IDE_EXP_043 NAT • 2 Marks

Section 5: Irrigation and Drainage Engineering

Groundwater Hydrology

Subtopic: Groundwater movement; Darcy's Law

Question Statement:

For the same three horizontal layers (Layer 1: $z_1 = 2.0\text{ m}, K_1 = 5\text{ m/day}$; Layer 2: $z_2 = 3.0\text{ m}, K_2 = 10\text{ m/day}$; Layer 3: $z_3 = 5.0\text{ m}, K_3 = 2\text{ m/day}$), the equivalent hydraulic conductivity for flow perpendicular to the bedding planes ($K_v$) in $\text{m/day}$ is ________ (round off to 2 decimal places).

Answer Key:

3.12

Step-by-Step Solution & Explanation

Equivalent vertical permeability perpendicular to bedding planes: $K_v = \frac{\sum z_i}{\sum \frac{z_i}{K_i}}$ 1. Sum of thicknesses $\sum z_i = 10.0\text{ m}$. 2. Sum of hydraulic resistances: $\frac{z_1}{K_1} = \frac{2.0}{5} = 0.40$ $\frac{z_2}{K_2} = \frac{3.0}{10} = 0.30$ $\frac{z_3}{K_3} = \frac{5.0}{2} = 2.50$ $\sum \frac{z_i}{K_i} = 0.40 + 0.30 + 2.50 = 3.20\text{ day}$ $K_v = \frac{10.0}{3.20} = 3.125\text{ m/day} \approx 3.12\text{ m/day}$
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