Aquifer Thickness From Impermeable Layer Given Discharge In Confined Aquifer Calculator

Formula Used:

\[ Initial\ Aquifer\ Thickness = Depth\ of\ Water + \frac{Discharge \times \ln\left(\frac{Radius\ of\ Influence}{Radius\ of\ well}\right)}{2\pi \times Coefficient\ of\ Permeability \times Aquifer\ Thickness} \]

\[ H_i = h_w + \frac{Q \times \ln\left(\frac{R_w}{r}\right)}{2\pi \times K_w \times b_w} \]

Depth of Water (h_w):

Discharge (Q):

m³/s

Radius of Influence (R_w):

Radius of Well (r):

Coefficient of Permeability (K_w):

m/s

Aquifer Thickness (b_w):

Initial Aquifer Thickness (H_i):

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1. What is the Aquifer Thickness Formula?

This formula calculates the initial aquifer thickness from the impermeable layer based on discharge in a confined aquifer. It considers factors like water depth, discharge rate, radius of influence, well radius, permeability coefficient, and aquifer thickness.

2. How Does the Calculator Work?

The calculator uses the formula:

\[ H_i = h_w + \frac{Q \times \ln\left(\frac{R_w}{r}\right)}{2\pi \times K_w \times b_w} \]

Where:

\( H_i \) — Initial Aquifer Thickness (m)
\( h_w \) — Depth of Water in the well (m)
\( Q \) — Discharge rate (m³/s)
\( R_w \) — Radius of Influence (m)
\( r \) — Radius of well (m)
\( K_w \) — Coefficient of Permeability (m/s)
\( b_w \) — Aquifer Thickness (m)
\( \pi \) — Mathematical constant pi (≈3.1416)
\( \ln \) — Natural logarithm function

Explanation: The formula calculates the initial aquifer thickness by adding the water depth to a term that accounts for the discharge and aquifer properties.

3. Importance of Aquifer Thickness Calculation

Details: Accurate calculation of aquifer thickness is crucial for groundwater resource assessment, well design, pumping test analysis, and sustainable water management in confined aquifers.

4. Using the Calculator

Tips: Enter all values in appropriate units (meters for length, m³/s for discharge). Ensure all values are positive and the radius of influence is greater than the well radius for valid results.

5. Frequently Asked Questions (FAQ)

Q1: What is a confined aquifer?
A: A confined aquifer is bounded above and below by impermeable layers, with water under pressure.

Q2: How is radius of influence determined?
A: Radius of influence is typically determined through pumping tests or estimated based on aquifer properties and pumping rate.

Q3: What is the coefficient of permeability?
A: The coefficient of permeability (hydraulic conductivity) measures how easily water can move through porous materials.

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

Q5: What are typical values for these parameters?
A: Permeability coefficients range from 10⁻² to 10⁻⁹ m/s, discharge rates vary by well capacity, and aquifer thickness can range from a few meters to hundreds of meters.