Equilibrium Equation for Well in Unconfined Aquifer Calculator

Equilibrium Equation:

\[ Q_u = \frac{\pi \times K \times (H_2^2 - H_1^2)}{\ln\left(\frac{r_2}{r_1}\right)} \]

Coefficient of Permeability (K):

m/s

Water Table Depth 2 (H₂):

Water Table Depth (H₁):

Radial Distance at Observation Well 2 (r₂):

Radial Distance at Observation Well 1 (r₁):

Steady Flow of an Unconfined Aquifer (Q_u):

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1. What is the Equilibrium Equation for Well in Unconfined Aquifer?

The Equilibrium Equation for Well in Unconfined Aquifer, also known as the Dupuit-Forchheimer equation, calculates the steady-state discharge from a well in an unconfined aquifer. It's based on the assumption of horizontal flow and constant hydraulic conductivity.

2. How Does the Calculator Work?

The calculator uses the equilibrium equation:

\[ Q_u = \frac{\pi \times K \times (H_2^2 - H_1^2)}{\ln\left(\frac{r_2}{r_1}\right)} \]

Where:

\( Q_u \) — Steady flow of an unconfined aquifer (m³/s)
\( \pi \) — Archimedes' constant (≈3.1416)
\( K \) — Coefficient of permeability (m/s)
\( H_2 \) — Water table depth at observation well 2 (m)
\( H_1 \) — Water table depth at observation well 1 (m)
\( r_2 \) — Radial distance at observation well 2 (m)
\( r_1 \) — Radial distance at observation well 1 (m)
\( \ln \) — Natural logarithm function

Explanation: The equation calculates the discharge rate based on the difference in water table elevations between two observation wells and their distances from the pumping well.

3. Importance of Steady Flow Calculation

Details: Accurate calculation of steady flow in unconfined aquifers is crucial for groundwater resource management, well design, and predicting the impact of pumping on water table levels.

4. Using the Calculator

Tips: Enter all values in appropriate units (meters and meters per second). Ensure radial distances are different (r₂ ≠ r₁) and all values are positive. Water table depths should be measured from the same reference level.

5. Frequently Asked Questions (FAQ)

Q1: What is an unconfined aquifer?
A: An unconfined aquifer has a water table that serves as its upper boundary and is in direct contact with the atmosphere through the unsaturated zone.

Q2: What assumptions does this equation make?
A: The equation assumes homogeneous and isotropic aquifer, horizontal flow, steady-state conditions, and that the Dupuit-Forchheimer assumptions apply.

Q3: How does this differ from confined aquifer equations?
A: Unconfined aquifer equations account for the decreasing saturated thickness with drawdown, while confined aquifer equations assume constant aquifer thickness.

Q4: What are typical values for coefficient of permeability?
A: Permeability values range from 10⁻² m/s for gravel to 10⁻⁹ m/s for clay. Sand typically ranges from 10⁻³ to 10⁻⁵ m/s.

Q5: When is this equation not applicable?
A: The equation may not be accurate near the well where flow lines are not horizontal, in heterogeneous aquifers, or when the drawdown is large relative to the aquifer thickness.