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Theis Transient Aquifer Drawdown & Well Function Calculator

The Theis equation is the cornerstone of transient groundwater hydraulics, modeling non-steady radial flow toward a pumping well in confined aquifers.

Calculated Result
0.751 m

Aquifer Drawdown (s)

Dimensionless Parameter (u)

5.0000e-3

Well Function W(u)

4.7211

Transmissivity (T)

500 m²/day

Calculation Breakdown

  1. Calculate dimensionless Boltzmann variable u = (r²·S) / (4·T·t)u = (100² * 0.001) / (4 * 500 * 1) = 5.0000e-3
  2. Evaluate exponential integral well function W(u)W(u) = 4.7211
  3. Determine unsteady aquifer drawdown s = (Q / 4πT) · W(u)s = (1000 / (4π * 500)) * 4.7211 = 0.751 m

Drawdown vs Distance from Well

Interactive visualization based on your current inputs

Drawdown
0.00.30.60.91.325 m50 m100 m200 m500 mDistance (m)Drawdown (m)

What Is the Theis Transient Aquifer Drawdown & Well Function Calculator?

The Theis equation is the cornerstone of transient groundwater hydraulics, modeling non-steady radial flow toward a pumping well in confined aquifers.

How Does the Theis Transient Aquifer Drawdown & Well Function Calculator Work?

The calculation evaluates user-provided measurements using recognized domain equations, converts between measurement units, and adjusts for real-world efficiency factors.

Theis Transient Aquifer Drawdown & Well Function Calculator Formula & Variables

The core mathematical equation utilized by this calculator is expressed as:

s = \frac{Q}{4\pi T} W(u), \quad u = \frac{r^2 S}{4 T t}

The well function W(u) represents the exponential integral describing cone-of-depression propagation through porous geologic formations.

How to Use the Theis Transient Aquifer Drawdown & Well Function Calculator

  1. Enter your primary measurements in the input fields above.
  2. Select your preferred units (e.g. metric or imperial) if applicable.
  3. Review or adjust operational assumptions such as field efficiency.
  4. Click Calculate to instantly generate the full results breakdown and visual chart.
  5. Use the Reset button at any time to clear the form and test a new scenario.

Step-by-Step Example Calculation

1,000 m³/day Municipal Well at 100m

Input Values:

pumpingRateM3PerDay:1000
transmissivityM2PerDay:500
storativityFraction:0.001
radialDistanceM:100
elapsedTimeDays:1

Understanding Your Result

Your calculated result represents the realistic operational capacity or baseline output under the specified conditions. Comparing theoretical and effective outputs reveals the direct impact of turns, overlap, and practical downtime.

Factors That Affect the Result

Field terrain, operator experience, equipment maintenance, overlap margin, and weather conditions can significantly influence real-world output.

When Should You Use This Calculator?

Use this calculator whenever you need quick, verified estimates for job planning, budgeting, equipment sizing, or project timelines.

Assumptions & Limitations

  • Assumes homogeneous, isotropic, infinite confined aquifer of uniform thickness.

Frequently Asked Questions

Calculation Accuracy & Reference Note

This calculator implements verified, deterministic mathematical equations based on published standards. Results should be treated as professional engineering estimates; always verify critical operations with local equipment manuals and site inspections.

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