Question Bank • QB_IDE_ADV_099
NAT • 2 Marks
Section 5: Irrigation and Drainage Engineering
Groundwater Hydrology
Subtopic: Groundwater movement; Darcy's Law
Question Statement:
A stratified horizontal aquifer consists of three distinct layers:
- Layer 1: thickness $d_1 = 2.0\text{ m}$, hydraulic conductivity $K_1 = 4.0\text{ m/day}$
- Layer 2: thickness $d_2 = 3.0\text{ m}$, hydraulic conductivity $K_2 = 1.0\text{ m/day}$
- Layer 3: thickness $d_3 = 5.0\text{ m}$, hydraulic conductivity $K_3 = 8.0\text{ m/day}$
The equivalent horizontal hydraulic conductivity ($K_h$) for groundwater flow parallel to the bedding planes in meters per day ($\text{m/day}$) is ________ (round off to two decimal places).
Step-by-Step Solution & Explanation
1. Total aquifer thickness:
$D = d_1 + d_2 + d_3 = 2.0 + 3.0 + 5.0 = 10.0\text{ m}$
2. Equivalent horizontal hydraulic conductivity ($K_h$ for parallel flow):
$K_h = \frac{K_1 d_1 + K_2 d_2 + K_3 d_3}{D}$
3. Substituting values:
$K_1 d_1 = 4.0 \times 2.0 = 8.0\text{ m}^2/\text{day}$
$K_2 d_2 = 1.0 \times 3.0 = 3.0\text{ m}^2/\text{day}$
$K_3 d_3 = 8.0 \times 5.0 = 40.0\text{ m}^2/\text{day}$
$\sum K_i d_i = 8.0 + 3.0 + 40.0 = 51.0\text{ m}^2/\text{day}$
$K_h = \frac{51.0}{10.0} = 5.10\text{ m/day}$
(Notice $K_h$ is weighted heavily by the thick, permeable third layer).
Practice In Authentic CBT Exam Interface
Test your skills under authentic timed conditions with live scoring and AIR percentile ranking.
Launch CBT Mock Test