Question Bank • QB_IDE_EXP_042 NAT • 2 Marks

Section 5: Irrigation and Drainage Engineering

Groundwater Hydrology

Subtopic: Groundwater movement; Darcy's Law

Question Statement:

A stratified soil deposit consists of three horizontal layers. Layer 1 has thickness $2.0\text{ m}$ and $K_1 = 5\text{ m/day}$. Layer 2 has thickness $3.0\text{ m}$ and $K_2 = 10\text{ m/day}$. Layer 3 has thickness $5.0\text{ m}$ and $K_3 = 2\text{ m/day}$. The equivalent hydraulic conductivity for flow parallel to the bedding planes ($K_h$) in $\text{m/day}$ is ________ (round off to 1 decimal place).

Answer Key:

5

Step-by-Step Solution & Explanation

Equivalent horizontal permeability parallel to bedding planes: $K_h = \frac{\sum K_i z_i}{\sum z_i}$ Given: • $K_1 z_1 = 5 \times 2.0 = 10.0$ • $K_2 z_2 = 10 \times 3.0 = 30.0$ • $K_3 z_3 = 2 \times 5.0 = 10.0$ Total thickness $Z = 2.0 + 3.0 + 5.0 = 10.0\text{ m}$. $K_h = \frac{10.0 + 30.0 + 10.0}{10.0} = \frac{50.0}{10.0} = 5.0\text{ m/day}$
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