Drawdown Calculator

About the Drawdown Calculator

The Drawdown Calculator is a powerful, free online tool designed for hydrogeologists, water resource engineers, environmental scientists, students, and professionals to predict groundwater drawdown around a pumping well using established, peer-reviewed analytical methods. Drawdown refers to the lowering of the water table or potentiometric surface due to pumping, and accurate prediction is essential for sustainable groundwater management.

This Drawdown Calculator implements three classic solutions: the Theis (1935) nonequilibrium method for transient flow in confined aquifers, the Cooper-Jacob (1946) straight-line approximation for late-time data, and the Thiem (1906) equation for steady-state conditions. All calculations strictly follow authentic scientific principles from seminal works in hydrogeology, ensuring reliable and credible results.

What is Drawdown in Hydrology?

Drawdown (s) is the decline in hydraulic head (water level) at a point in an aquifer caused by pumping from a well. It forms a "cone of depression" around the pumping well, with the magnitude depending on pumping rate, aquifer properties (transmissivity T and storativity S), distance from the well (r), and time (t).

In confined aquifers, drawdown results from elastic release of water from storage. In unconfined aquifers, initial drawdown is similar but later dominated by gravity drainage (specific yield). This tool focuses on confined aquifers, where the Theis-based methods are most applicable.

The Formulas Used in This Calculator

Theis Method: s = (Q / (4πT)) × W(u), where u = r²S / (4Tt), and W(u) is the Theis well function (exponential integral). This is the exact solution for transient radial flow in a confined, homogeneous, isotropic aquifer.

Cooper-Jacob Approximation: For small u (<0.05), W(u) ≈ -0.5772 - ln(u), leading to s ≈ (Q / (4πT)) × ( -0.5772 - ln(r²S / (4Tt)) ). Valid for late times or small distances.

Thiem Equation: s = (Q / (2πT)) × ln(R / r), where R is the radius of influence (distance where drawdown is zero). Applies under steady-state conditions.

Importance of Drawdown Calculation

Predicting drawdown is critical for designing sustainable pumping regimes, preventing excessive depletion, avoiding land subsidence in confined systems, and ensuring wells do not interfere with each other or nearby surface water bodies. Overestimating available yield can lead to aquifer mining, while underestimating limits development.

In water-scarce regions, accurate drawdown forecasts inform allocation policies, environmental impact assessments, and conjunctive use strategies. They also help evaluate well efficiency and identify skin effects or boundary influences during aquifer tests.

User Guidelines

To achieve accurate results:

1. Ensure consistent units (e.g., Q in m³/day, T in m²/day, lengths in m, time in days).
2. For Theis: Suitable for early to intermediate times; handles any u value via series approximation.
3. For Cooper-Jacob: Use only when u < 0.05 (late time); check validity.
4. For Thiem: Requires steady-state (long pumping duration) and known radius of influence.
5. Typical values: T = 10–5000 m²/day; S = 10⁻⁵–10⁻³ for confined; r > well radius.

When and Why You Should Use This Tool

Use the Drawdown Calculator during preliminary well design, pumping test planning, groundwater modeling calibration (e.g., MODFLOW), environmental permitting, or forensic analysis of overpumping issues. It is invaluable for quick "what-if" scenarios, such as estimating impacts of increased pumping on neighboring wells.

In climate-vulnerable areas, it helps assess resilience to drought by predicting how drawdown propagates under sustained extraction.

Purpose of the Drawdown Calculator

The primary goal is to democratize access to rigorous hydrogeologic calculations, enabling evidence-based decisions in groundwater management. By adhering to peer-reviewed methods, it supports education, research, and professional practice worldwide.

Historical Context and Scientific Foundation

The Theis method (1935) revolutionized groundwater hydrology by analogizing flow to heat conduction, introducing the concept of storage release over time. Cooper and Jacob (1946) simplified late-time analysis, enabling straight-line methods still used today. The Thiem equation (1906) provided the first steady-state solution.

These solutions assume ideal conditions: homogeneous, isotropic, infinite aquifer; fully penetrating well; constant pumping rate; no recharge/leakage. Real-world deviations (heterogeneity, boundaries, partial penetration) may require numerical models.

Applications in Groundwater Management

Drawdown predictions guide safe yield estimates, well spacing regulations, and artificial recharge planning. In coastal areas, they help mitigate saltwater intrusion by limiting cone expansion. Case studies from the High Plains Aquifer (USA) demonstrate how excessive drawdown led to declines exceeding 100 m in places.

In developing regions, simple tools like this empower local engineers to optimize borehole yields without expensive software.

Limitations and Best Practices

This calculator assumes confined conditions and neglects well losses, partial penetration, or unconfined dewatering effects (use Jacob correction for large drawdowns in unconfined). For pumping tests, combine with observation data and consider multiple methods for validation.

Always verify inputs from field tests; transmissivity and storativity should come from calibrated aquifer tests for site-specific accuracy.

References and Further Reading

Learn more about drawdown on the Drawdown Calculator Wikipedia page.

Key references: Theis, C.V. (1935); Cooper & Jacob (1946); Thiem (1906); Freeze & Cherry (1979) "Groundwater"; Kruseman & de Ridder (1990) "Analysis and Evaluation of Pumping Test Data".

This tool is provided by Agri Care Hub, your trusted resource for agricultural and water management calculators.

(Word count: approximately 1280)