Groundwater Hydrology

Introduction

Groundwater is the water found underground in the cracks and spaces in soil, sand, and rock. It is stored in and moves slowly through geologic formations of soil, sand, and rocks called aquifers.

Types of Aquifers:

Unconfined Aquifer: The water table is at atmospheric pressure. The upper surface is free to rise and fall.
Confined Aquifer: Sandwiched between two impermeable layers (aquicludes). Water is under pressure greater than atmospheric.
Leaky Aquifer: Bounded by semi-permeable layers (aquitards) allowing some flow.

Darcy's Law

Henry Darcy (1856) formulated the law governing groundwater flow in porous media.

Q = K i A

Where:

$Q$ = Discharge ( $m^3/s$ )
$K$ = Hydraulic Conductivity (m/day or m/s). Depends on properties of fluid and medium.
$i$ = Hydraulic Gradient ( $dh/dl$ ). The slope of the hydraulic head.
$A$ = Cross-sectional area perpendicular to flow ( $m^2$ ).

Transmissivity ( $T$ )

For a confined aquifer of thickness $b$ :

T = K \cdot b

Dimensions: $L^2/T$ (e.g., $m^2/day$ ).

Steady Flow to Wells

1. Confined Aquifer (Theiem Equation)

Assumptions:

Radial flow
Homogeneous, isotropic aquifer
Steady state (equilibrium)

Q = \frac{2 \pi T (h_2 - h_1)}{\ln(r_2/r_1)}

Where $h_1, h_2$ are piezometric heads at radii $r_1, r_2$ from the well.

2. Unconfined Aquifer (Dupuit Equation)

Q = \frac{\pi K (h_2^2 - h_1^2)}{\ln(r_2/r_1)}

Step-by-Step Solution

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Unsteady Flow (Theis Equation)

When pumping starts, the cone of depression expands with time.

s = \frac{Q}{4 \pi T} W(u)

Where $W(u)$ is the Well Function.

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