Radius Of Well Given Confined Aquifer Discharge Calculator

Radius of Well in Environmental Engineering Formula:

\[ r' = \frac{R_w}{\exp\left(\frac{2\pi K_{WH} b_p s_t}{Q}\right)} \]

Radius of Influence (R_w):

Coefficient of Permeability (K_WH):

m/s

Aquifer Thickness During Pumping (b_p):

Total Drawdown in Well (s_t):

Discharge (Q):

m³/s

Radius of Well (r'):

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1. What is the Radius of Well Formula?

The Radius of Well in Environmental Engineering formula calculates the radius of a well in a confined aquifer based on the radius of influence, coefficient of permeability, aquifer thickness, total drawdown, and discharge rate. This calculation is essential for well design and groundwater management.

2. How Does the Calculator Work?

The calculator uses the formula:

\[ r' = \frac{R_w}{\exp\left(\frac{2\pi K_{WH} b_p s_t}{Q}\right)} \]

Where:

\( r' \) — Radius of Well (m)
\( R_w \) — Radius of Influence (m)
\( K_{WH} \) — Coefficient of Permeability (m/s)
\( b_p \) — Aquifer Thickness During Pumping (m)
\( s_t \) — Total Drawdown in Well (m)
\( Q \) — Discharge (m³/s)
\( \pi \) — Archimedes' constant (≈3.1416)
\( \exp \) — Exponential function

Explanation: The formula accounts for the relationship between well characteristics and groundwater flow parameters in confined aquifers.

3. Importance of Radius Calculation

Details: Accurate well radius calculation is crucial for proper well design, determining pumping rates, assessing aquifer characteristics, and ensuring sustainable groundwater extraction.

4. Using the Calculator

Tips: Enter all values in appropriate units (meters for length, m/s for permeability, m³/s for discharge). All values must be positive and non-zero for accurate calculation.

5. Frequently Asked Questions (FAQ)

Q1: What is the radius of influence?
A: The radius of influence is the distance from the center of the well to the point where the drawdown curve meets the original water table.

Q2: How does permeability affect the well radius?
A: Higher permeability allows water to flow more easily through the aquifer, which can affect the required well radius for a given discharge rate.

Q3: What is total drawdown in a well?
A: Total drawdown is the reduction in hydraulic head observed at a well in an aquifer, typically due to pumping during an aquifer test.

Q4: When is this formula applicable?
A: This formula is specifically designed for confined aquifers where the aquifer is bounded above and below by impermeable layers.

Q5: What are typical values for well radius?
A: Well radii typically range from 0.1 to 0.5 meters for most water supply wells, though they can vary based on specific design requirements.