Thiem's Equilibrium Equation For Steady Flow In Confined Aquifer Calculator

Thiem's Equilibrium Equation:

\[ Q_{sf} = \frac{2\pi K H_a (h_2 - h_1)}{\ln\left(\frac{r_2}{r_1}\right)} \]

Coefficient of Permeability (K):

m/s

Width of Aquifer (H_a):

Piezometric Head at r₁ (h₁):

Piezometric Head at r₂ (h₂):

Radial Distance at Well 1 (r₁):

Radial Distance at Well 2 (r₂):

Steady Flow in Confined Aquifer (Q_sf):

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1. What is Thiem's Equilibrium Equation?

Thiem's equilibrium equation is a fundamental formula in hydrogeology that describes steady-state flow to a well in a confined aquifer. It provides a mathematical relationship between discharge rate, aquifer properties, and drawdown measurements at observation wells.

2. How Does the Calculator Work?

The calculator uses Thiem's equilibrium equation:

\[ Q_{sf} = \frac{2\pi K H_a (h_2 - h_1)}{\ln\left(\frac{r_2}{r_1}\right)} \]

Where:

\( Q_{sf} \) — Steady flow in confined aquifer (m³/s)
\( K \) — Coefficient of permeability (m/s)
\( H_a \) — Width of aquifer (m)
\( h_1 \) — Piezometric head at radial distance r₁ (m)
\( h_2 \) — Piezometric head at radial distance r₂ (m)
\( r_1 \) — Radial distance at observation well 1 (m)
\( r_2 \) — Radial distance at observation well 2 (m)
\( \pi \) — Mathematical constant pi (≈3.1416)
\( \ln \) — Natural logarithm function

Explanation: The equation calculates the steady-state discharge rate from a well in a confined aquifer based on head measurements at two observation wells located at different radial distances.

3. Importance of Steady Flow Calculation

Details: Accurate calculation of steady flow in confined aquifers is essential for groundwater resource management, well design, contamination studies, and sustainable water extraction planning.

4. Using the Calculator

Tips: Enter all values in consistent units (meters and meters/second). Ensure r₂ ≠ r₁ to avoid division by zero in the logarithmic term. All input values must be positive.

5. Frequently Asked Questions (FAQ)

Q1: What is a confined aquifer?
A: A confined aquifer is bounded above and below by impermeable layers (aquitards), with water under pressure greater than atmospheric pressure.

Q2: When is Thiem's equation applicable?
A: Thiem's equation applies to steady-state flow conditions in homogeneous, isotropic confined aquifers with fully penetrating wells.

Q3: What are typical values for coefficient of permeability?
A: Permeability coefficients range from 10⁻² m/s for gravel to 10⁻⁹ m/s for clay, with sand typically around 10⁻⁵ to 10⁻³ m/s.

Q4: How does aquifer width affect flow rate?
A: Flow rate is directly proportional to aquifer width - doubling the aquifer width doubles the flow rate, all other factors being equal.

Q5: What if I have more than two observation wells?
A: For multiple observation wells, you can calculate transmissivity (T = K×Hₐ) using different well pairs and average the results for better accuracy.