Equilibrium Equation for Flow in Confined Aquifer at Observation Well Calculator

Equilibrium Equation for Flow in Confined Aquifer:

\[ Q = \frac{2\pi\tau(h_2 - h_1)}{\ln\left(\frac{r_2}{r_1}\right)} \]

Transmissivity (τ):

m²/s

Piezometric Head at Radial Distance r2 (h₂):

Piezometric Head at Radial Distance r1 (h₁):

Radial Distance at Observation Well 2 (r₂):

Radial Distance at Observation Well 1 (r₁):

Discharge Entering Cylindrical Surface into Well (Q):

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1. What is the Equilibrium Equation for Flow in Confined Aquifer?

The Equilibrium Equation for Flow in Confined Aquifer estimates the discharge entering a cylindrical surface into a well based on transmissivity, piezometric heads at different radial distances, and the radial distances themselves. It provides a fundamental approach to understanding groundwater flow in confined aquifers.

2. How Does the Calculator Work?

The calculator uses the equilibrium equation:

\[ Q = \frac{2\pi\tau(h_2 - h_1)}{\ln\left(\frac{r_2}{r_1}\right)} \]

Where:

\( Q \) — Discharge entering cylindrical surface into well (m³/s)
\( \tau \) — Transmissivity (m²/s)
\( h_2 \) — Piezometric head at radial distance r₂ (m)
\( h_1 \) — Piezometric head at radial distance r₁ (m)
\( r_2 \) — Radial distance at observation well 2 (m)
\( r_1 \) — Radial distance at observation well 1 (m)
\( \pi \) — Archimedes' constant (≈3.14159)

Explanation: The equation calculates the flow rate of groundwater entering a cylindrical well based on the hydraulic gradient and aquifer properties.

3. Importance of Discharge Calculation

Details: Accurate discharge calculation is crucial for well design, groundwater management, and understanding aquifer behavior under pumping conditions.

4. Using the Calculator

Tips: Enter all values in appropriate units. Transmissivity and radial distances must be positive values. Radial distances r₂ and r₁ must be different (r₂ ≠ r₁).

5. Frequently Asked Questions (FAQ)

Q1: What is transmissivity in groundwater hydrology?
A: Transmissivity is the measure of how much water can be transmitted horizontally through a unit width of the entire thickness of an aquifer under a unit hydraulic gradient.

Q2: Why is the natural logarithm used in this equation?
A: The natural logarithm accounts for the radial flow pattern around the well, where flow converges toward the well in a cylindrical pattern.

Q3: What are typical transmissivity values for confined aquifers?
A: Transmissivity values can range from 0.001 to 1000 m²/day, depending on aquifer material and thickness.

Q4: When is this equation applicable?
A: This equation applies to steady-state flow in homogeneous, isotropic confined aquifers with fully penetrating wells.

Q5: What are the limitations of this equation?
A: The equation assumes ideal conditions and may not accurately represent complex aquifer systems with heterogeneity, anisotropy, or boundary effects.