Reviewed by: Stephanie Ben-Joseph

Pumping Rate Q (m³/day): Aquifer Transmissivity T (m²/day): Observation Well Distance r (m): Radius of Influence R (m): Calculate Copy Result

Groundwater Pumping and Drawdown

When a well pumps water from an aquifer, the water level in and around the well declines, forming a cone-shaped depression in the potentiometric surface known as a drawdown cone. Understanding the magnitude of drawdown is vital for evaluating well interference, predicting pumping impacts on nearby streams or wetlands, and determining sustainable yields. The Thiem equation offers a simple analytical expression for steady-state drawdown in confined or unconfined aquifers under certain ideal conditions. This calculator implements the Thiem equation to estimate the drop in hydraulic head at a specified distance from a pumping well. Although real-world aquifers exhibit heterogeneity, boundaries, and time-dependent behavior, the Thiem solution provides an accessible starting point for high school and undergraduate studies in hydrogeology.

The Thiem Equation

For a fully penetrating well in a homogeneous, isotropic aquifer of infinite extent, the drawdown at distance $r$ from the well after steady state has been reached is given by the logarithmic expression:

$$s=Q\{2\pi T\}ln\left(Rr\right)$$

where $s$ is drawdown in meters, $Q$ is pumping rate, $T$ is aquifer transmissivity, $R$ is the radius of influence (the distance at which drawdown is effectively zero), and $r$ is the distance from the pumping well to the observation point. The natural logarithm captures the radial nature of groundwater flow; drawdown decreases with distance, but not linearly.

Conceptual Understanding

Transmissivity combines the aquifer’s hydraulic conductivity with its saturated thickness and represents the ease with which water can move horizontally through the formation. High transmissivity aquifers, such as gravel layers, allow groundwater to flow readily and thus exhibit smaller drawdowns for a given pumping rate. Low transmissivity formations, like silt or clay, result in steeper cones of depression. The radius of influence depends on pumping duration, aquifer diffusivity, and boundaries like impermeable layers or recharge zones. In many practical situations, the radius of influence is estimated rather than directly measured, but its value significantly affects calculated drawdown.

Students often visualize the drawdown cone as a three-dimensional funnel surrounding the well. Near the well, hydraulic gradients are steep, and water flows rapidly toward the well screen. Farther away, gradients decrease, and the water table may remain unaffected. When multiple wells operate close together, their cones of depression can overlap, leading to greater drawdown than predicted for a single well, a phenomenon known as well interference.

Example Calculation

Suppose a well pumps $Q=500$ m³/day from an aquifer with transmissivity $T=1000$ m²/day. At an observation well located $r=30$ m away, and assuming a radius of influence $R=300$ m, the drawdown is:

A drawdown of 0.58 m may be acceptable for many wells, but larger pumping rates or lower transmissivities could yield much greater declines, potentially dewatering the well or affecting neighboring users.

Typical Transmissivity Values

The following table lists rough ranges of transmissivity for common aquifer materials, illustrating why geologic setting is critical to drawdown analysis.

Material	Transmissivity (m²/day)
Gravel	>1000
Sand	100-1000
Silt	10-100
Clay	<10

These ranges are approximate but emphasize how an order-of-magnitude change in transmissivity can dramatically alter drawdown for the same pumping rate.

Interpreting Results

The calculator outputs drawdown in meters and assigns a qualitative category:

Drawdown (m)	Category
<1	Low
1-3	Moderate
>3	High

These categories help students gauge the severity of pumping impacts. Large drawdowns may lower the water table enough to reduce spring flows or harm wetlands, highlighting the interconnectedness of groundwater and surface water systems.

Limitations of the Thiem Solution

The Thiem equation assumes steady-state conditions, an aquifer of infinite areal extent, and a fully penetrating well. It neglects transient effects, partial penetration, and anisotropy. In reality, drawdown evolves over time and may be influenced by recharge, leakage, or layered geology. For early-time pumping tests, the Theis solution is more appropriate because it accounts for transient behavior. Additionally, boundaries such as impermeable faults or rivers require image-well techniques or numerical models. Nevertheless, the Thiem equation remains a valuable teaching tool and a first approximation when data are limited.

Students can extend this calculator by incorporating multiple observation wells, time-dependent solutions, or by coupling it with groundwater flow models that simulate complex boundary conditions. Exploring how parameter uncertainty affects drawdown predictions can also build statistical thinking and appreciation for field data collection.

Using the Calculator

Enter the pumping rate, transmissivity, observation distance, and radius of influence. The script computes drawdown using the Thiem formula and reports the result along with the qualitative category. The Copy Result button facilitates transferring the output to worksheets or reports. Experiment with different transmissivities or pumping rates to observe how aquifer properties control the response to pumping.

This tool encourages critical thinking about groundwater sustainability. Excessive drawdown can increase energy costs for pumping, cause land subsidence, or dry up neighboring wells. By quantifying drawdown, planners can balance water needs with aquifer protection, ensuring long-term resource availability.