# 3.16 Groundwater Flow

Groundwater has always been one of the most important sources of water supply. Virtually all parts of the earth are underlain by water, and wells have been constructed to provide a water supply when surface water was not readily available. Groundwater-bearing formations which are sufficiently permeable to yield usable quantities of water are called aquifers. When an aquifer is not overlain by an impermeable layer it is said to be unconfined. Confined aquifers consist of a water-bearing layer contained between two less permeable layers. This section presents the calculation of the steady flow in the confined or unconfined aquifers. It also presents the well hydraulics in confined or unconfined steady flow.

#### Steady Flow in a Confined Aquifer

If there is the steady movement of ground water in a confined aquifer, there will be a gradient or slope to the potentiometric surface of the aquifer. A portion of a confined aquifer of uniform thickness is shown in the following figure. The potentiometric surface has a linear gradient. There are two observation wells where the hydraulic head can be measured.

Steady Flow in a Confined Aquifer

For flow of this type, Darcy’s law may be used directly.

where q          =          flow rate per unit width of aquifer (m2/d, ft2/d)

K         =          hydraulic conductivity of aquifer (m/d, ft/d) (see Table 3-13)

B          =          aquifer thickness (m, ft)

L          =          flow length (m, ft)

h2         =          head at length L (m, ft)

h1         =          head at the origin (m, ft)

Table 3-13: Soil Properties

 Soil Type Hydraulic Conductivity, K (cm/s) Clayey 10-9 - 10-6 Silty 10-7 - 10-3 Sandy 10-5 - 10-1 Gravelly 10-1 - 102

The aquifer transmissivity is defined as a measure of the amount of water that can be transmitted horizontally through a unit width by the fully saturated thickness of the aquifer under a hydraulic gradient of 1. The transmissivity, T, (m2/d, ft2/d) is the product of the hydraulic conductivity (K) and the saturated thickness of the aquifer (B) as

T BK

#### Steady Flow in an Unconfined Aquifer

Steady Flow in an Unconfined Aquifer

In an unconfined aquifer, the fact that the water table is also the upper boundary of the region of flow complicates flow determinations. This problem was solved by Dupuit who made the following simplifying assumptions: (1) the hydraulic gradient is equal to the slope of the water table and (2) for small water-table gradients, the streamlines are horizontal and the equipotential lines are vertical. Using these assumptions, Depuit developed Equation (102), commonly known as the Dupuit equation.

where q          =          flow rate per unit width of aquifer (m2/d, ft2/d)

K         =          hydraulic conductivity of aquifer (m/d, ft/d) (see Table 3-13)

L          =          flow length (m, ft)

h2         =          head at length L (m, ft)

h1         =          head at the origin (m, ft)

#### Well Hydraulics of Confined Steady Flow

Darcy’s equation can be used to analyze axially symmetric flow into a well. If a well pumps long enough, the water level may reach a state of equilibrium; that is, there is no further drawdown with time. The following figure illustrates the flow conditions for a well in a confined aquifer.

Steady Flow to a Well in a Confined Aquifer

where Q         =          pumping rate (m3/d, ft3/d)

K         =          hydraulic conductivity of aquifer (m/d, ft/d)

B          =          aquifer thickness (m, ft)

T          =          hydraulic transmissivity (m2/d, ft2/d)

h2         =          head at distance r2 from the pumping well (m, ft)

h1         =          head at distance r1 from the pumping well (m, ft)

d2         =          drawdown at distance r2 from the pumping well (m, ft)

d1         =          drawdown at distance r1 from the pumping well (m, ft)

#### Well Hydraulics of Unconfined Steady Flow

The following figure illustrates the flow conditions for a well in an unconfined aquifer. In the case of steady radial flow in an unconfined aquifer, the steady pumping rate is

or

All the terms are consistent with the definitions given above.

Steady Flow to a Well in an Unconfined Aquifer