Confined Aquifer Discharge Given Coefficient of Transmissibility Calculator

Formula Used:

\[ Q = \frac{2\pi T s_t}{\ln\left(\frac{R_w}{r}\right)} \]

Coefficient of Transmissibility (T):

m²/s

Total Drawdown in Well (s_t):

Radius of Influence (R_w):

Radius of Well (r):

Discharge (Q):

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1. What is the Confined Aquifer Discharge Formula?

The confined aquifer discharge formula calculates the rate of groundwater flow from a well in a confined aquifer. It's based on the Thiem equation and considers the transmissibility properties of the aquifer and geometric factors of the well system.

2. How Does the Calculator Work?

The calculator uses the formula:

\[ Q = \frac{2\pi T s_t}{\ln\left(\frac{R_w}{r}\right)} \]

Where:

\( Q \) — Discharge (m³/s)
\( T \) — Coefficient of transmissibility (m²/s)
\( s_t \) — Total drawdown in well (m)
\( R_w \) — Radius of influence (m)
\( r \) — Radius of well (m)
\( \pi \) — Mathematical constant pi (≈3.14159)
\( \ln \) — Natural logarithm function

Explanation: The formula calculates groundwater discharge based on aquifer properties and well geometry, assuming steady-state radial flow to a fully penetrating well in a confined aquifer.

3. Importance of Discharge Calculation

Details: Accurate discharge calculation is crucial for well design, groundwater resource management, contamination studies, and sustainable water extraction planning in confined aquifer systems.

4. Using the Calculator

Tips: Enter all values in consistent units (meters and m²/s). Ensure radius of influence is greater than radius of well to avoid mathematical errors. All input values must be positive numbers.

5. Frequently Asked Questions (FAQ)

Q1: What is coefficient of transmissibility?
A: The coefficient of transmissibility represents the rate at which water is transmitted through a unit width of aquifer under a unit hydraulic gradient.

Q2: How is radius of influence determined?
A: Radius of influence is typically determined through pumping tests and represents the distance from the well where drawdown becomes negligible.

Q3: When is this formula applicable?
A: This formula applies to confined aquifers with steady-state conditions, homogeneous isotropic properties, and fully penetrating wells.

Q4: What are the limitations of this equation?
A: The formula assumes ideal conditions and may not account for aquifer heterogeneity, partial penetration, or transient flow conditions.

Q5: How does drawdown affect discharge?
A: Discharge is directly proportional to drawdown - greater drawdown results in higher discharge rates, but excessive drawdown may cause aquifer dewatering.