Radius of Influence of Unconfined Aquifer With Known Discharge Calculator

Radius of Influence Formula:

\[ r_i = r' \times \exp\left(\frac{0.434 \times \pi \times k \times (h^2 - h_p)}{Q}\right) \]

Radius of Well (r'):

Coefficient of Permeability (k):

m/s

Original Piezometric Head (h):

Piezometric Head at Well (hₚ):

Discharge (Q):

m³/s

Radius of Influence (rᵢ):

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1. What is Radius of Influence?

The radius of influence is the distance from the center of a well to the point where the drawdown curve meets the original water table. It represents the area around a well that is affected by pumping and is crucial for determining well spacing and managing groundwater resources.

2. How Does the Calculator Work?

The calculator uses the radius of influence formula:

\[ r_i = r' \times \exp\left(\frac{0.434 \times \pi \times k \times (h^2 - h_p)}{Q}\right) \]

Where:

\( r_i \) — Radius of influence (m)
\( r' \) — Radius of well (m)
\( k \) — Coefficient of permeability (m/s)
\( h \) — Original piezometric head (m)
\( h_p \) — Piezometric head at well (m)
\( Q \) — Discharge rate (m³/s)
\( \pi \) — Mathematical constant pi (≈3.1416)

Explanation: This formula calculates how far the influence of a pumping well extends into an unconfined aquifer based on the well characteristics, aquifer properties, and pumping rate.

3. Importance of Radius of Influence Calculation

Details: Calculating the radius of influence is essential for proper well field design, preventing interference between wells, managing groundwater resources sustainably, and assessing the environmental impact of groundwater extraction.

4. Using the Calculator

Tips: Enter all values in consistent units (meters and meters per second). Ensure the piezometric head at the well is less than the original piezometric head. All values must be positive numbers.

5. Frequently Asked Questions (FAQ)

Q1: What is an unconfined aquifer?
A: An unconfined aquifer has a water table that serves as its upper boundary and is exposed to the atmosphere through pore spaces in the overlying material.

Q2: How does permeability affect the radius of influence?
A: Higher permeability allows water to move more easily through the soil, resulting in a larger radius of influence for the same pumping rate.

Q3: What is the difference between confined and unconfined aquifers?
A: Confined aquifers are bounded above and below by impermeable layers, while unconfined aquifers have a water table as their upper boundary.

Q4: Why is the radius of influence important for well spacing?
A: Proper well spacing based on radius of influence prevents interference between wells, ensuring each well can extract water without affecting neighboring wells' performance.

Q5: How does discharge rate affect the radius of influence?
A: Higher discharge rates typically increase the radius of influence as more water is being extracted from a larger area of the aquifer.