Radius Of Well Based On Discharge In Unconfined Aquifer Calculator

Formula Used:

\[ r = \frac{R_w}{\exp\left(\frac{\pi \cdot K_{soil} \cdot (H_i^2 - h_w^2)}{Q}\right)} \]

Radius of Influence (R_w):

Coefficient of Permeability (K_soil):

m/s

Initial Aquifer Thickness (H_i):

Depth of Water (h_w):

Discharge (Q):

m³/s

Radius of Well (r):

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1. What is the Radius of Well Calculation?

The radius of well calculation determines the distance from the center of a well to its outer boundary in an unconfined aquifer. This calculation is essential for understanding the well's influence zone and designing effective groundwater extraction systems.

2. How Does the Calculator Work?

The calculator uses the following formula:

\[ r = \frac{R_w}{\exp\left(\frac{\pi \cdot K_{soil} \cdot (H_i^2 - h_w^2)}{Q}\right)} \]

Where:

\( r \) — Radius of well (m)
\( R_w \) — Radius of influence (m)
\( K_{soil} \) — Coefficient of permeability of soil particle (m/s)
\( H_i \) — Initial aquifer thickness (m)
\( h_w \) — Depth of water in the well (m)
\( Q \) — Discharge rate (m³/s)
\( \pi \) — Mathematical constant (approximately 3.14159)
\( \exp \) — Exponential function

Explanation: The formula calculates the well radius based on the relationship between discharge rate, soil permeability, aquifer characteristics, and the radius of influence.

3. Importance of Well Radius Calculation

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

4. Using the Calculator

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

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 level.

Q2: How does soil permeability affect well radius?
A: Higher permeability soils typically require smaller well radii for the same discharge rate, as water flows more easily through the soil.

Q3: What is the significance of initial aquifer thickness?
A: Initial aquifer thickness affects the available water storage and influences the relationship between discharge rate and well radius.

Q4: When is this calculation most applicable?
A: This calculation is specifically designed for unconfined aquifers where the water table represents the upper boundary of the saturated zone.

Q5: Are there limitations to this equation?
A: The equation assumes homogeneous and isotropic aquifer conditions, steady-state flow, and may not account for complex geological features or transient conditions.