Aquifer Thickness From Impermeable Layer Given Coefficient Of Transmissibility With Base 10 Calculator

Formula Used:

\[ H_i = h_w + \frac{Q \cdot \log_{10}\left(\frac{R_w}{r}\right)}{2.72 \cdot T_w} \]

Depth of Water (h_w):

Discharge (Q):

m³/s

Radius of Influence (R_w):

Radius of Well (r):

Coefficient of Transmissibility (T_w):

m²/s

Initial Aquifer Thickness (H_i):

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1. What is Aquifer Thickness Calculation?

The calculation of aquifer thickness from an impermeable layer is a fundamental concept in hydrogeology and environmental engineering. It determines the vertical extent of a water-bearing formation above an impermeable layer, which is crucial for understanding groundwater resources and well performance.

2. How Does the Calculator Work?

The calculator uses the following formula:

\[ H_i = h_w + \frac{Q \cdot \log_{10}\left(\frac{R_w}{r}\right)}{2.72 \cdot T_w} \]

Where:

\( H_i \) — Initial Aquifer Thickness (m)
\( h_w \) — Depth of Water in the well measured above the impermeable layer (m)
\( Q \) — Discharge rate (m³/s)
\( R_w \) — Radius of Influence (m)
\( r \) — Radius of Well (m)
\( T_w \) — Coefficient of Transmissibility (m²/s)

Explanation: This formula calculates the initial aquifer thickness by considering the water depth, pumping rate, well characteristics, and the aquifer's transmissibility properties.

3. Importance of Aquifer Thickness Calculation

Details: Accurate determination of aquifer thickness is essential for groundwater resource assessment, well design, pumping test analysis, and sustainable water management. It helps in understanding the storage capacity and yield potential of aquifers.

4. Using the Calculator

Tips: Enter all values in appropriate units (meters for distances, m³/s for discharge, m²/s for transmissibility). Ensure all values are positive and physically meaningful for accurate results.

5. Frequently Asked Questions (FAQ)

Q1: What is the significance of the coefficient 2.72 in the formula?
A: The coefficient 2.72 is derived from the conversion between natural logarithms and base-10 logarithms, specifically 2.302585 (ln(10)) which is approximately 2.72 when rounded for practical calculations.

Q2: How is radius of influence determined?
A: Radius of influence is typically determined through pumping tests where drawdown is measured at various distances from the pumping well until it becomes negligible.

Q3: What factors affect the coefficient of transmissibility?
A: The coefficient depends on the hydraulic conductivity of the aquifer material and the saturated thickness of the aquifer.

Q4: When is this calculation most applicable?
A: This calculation is particularly useful for confined aquifers or unconfined aquifers with small drawdown relative to aquifer thickness.

Q5: What are typical values for coefficient of transmissibility?
A: Values can range from less than 10 m²/day for fine-grained aquifers to over 1000 m²/day for highly productive coarse-grained aquifers.