Radius Of Influence Given Discharge In Unconfined Aquifer Calculator

Radius of Influence Formula:

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

Radius of Well (r):

Coefficient of Permeability of Soil Particle (K_soil):

m/s

Initial Aquifer Thickness (H_i):

Depth of Water (h_w):

Discharge (Q):

m³/s

Radius of Influence (R_w):

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1. What is the Radius of Influence?

The Radius of Influence is the distance measured from the center of a well to the point where the drawdown curve meets the original water table. It represents the extent of the cone of depression created by pumping from the well.

2. How Does the Calculator Work?

The calculator uses the Radius of Influence formula:

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

Where:

\( R_w \) — Radius of Influence (m)
\( r \) — Radius of well (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 3.1416)
\( \exp \) — Exponential function

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

3. Importance of Radius of Influence Calculation

Details: Determining the radius of influence is crucial for well field design, assessing interference between wells, managing groundwater resources, and preventing over-exploitation of aquifers.

4. Using the Calculator

Tips: Enter all values in appropriate units (meters for lengths, m/s for permeability, m³/s for discharge). All values must be positive numbers. Ensure consistent units throughout.

5. Frequently Asked Questions (FAQ)

Q1: What is an unconfined aquifer?
A: An unconfined aquifer is a groundwater aquifer whose upper surface is a water table that is free to rise and fall.

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

Q3: What factors can affect the accuracy of this calculation?
A: Aquifer heterogeneity, boundary conditions, time since pumping began, and well construction details can all affect the actual radius of influence.

Q4: How is this different from confined aquifer calculations?
A: Unconfined aquifer calculations account for the decreasing saturated thickness as drawdown occurs, while confined aquifer calculations assume constant aquifer thickness.

Q5: When should this equation not be used?
A: This equation may not be accurate for very large pumping rates, complex geological settings, or when aquifer boundaries are close to the well.