Radius Of Influence Given Discharge In Confined Aquifer Calculator

Radius of Influence Formula:

\[ Radius\ of\ Influence = Radius\ of\ well \times \exp\left(\frac{2\pi \times Coefficient\ of\ Permeability \times Aquifer\ Thickness \times (Initial\ Aquifer\ Thickness - Depth\ of\ Water)}{Discharge}\right) \]

Radius of Well:

Coefficient of Permeability:

m/s

Aquifer Thickness During Pumping:

Initial Aquifer Thickness:

Depth of Water:

Discharge at Time t=0:

m³/s

Radius of Influence:

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1. What is 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 area around a pumping well that is affected by the withdrawal of groundwater.

2. How Does the Calculator Work?

The calculator uses the Radius of Influence formula:

\[ Radius\ of\ Influence = Radius\ of\ well \times \exp\left(\frac{2\pi \times K \times b_p \times (H_i - h_w)}{Q_0}\right) \]

Where:

\( Radius\ of\ well \) — Distance from center of well to its outer boundary (m)
\( K \) — Coefficient of Permeability in well hydraulics (m/s)
\( b_p \) — Aquifer Thickness During Pumping (m)
\( H_i \) — Initial Aquifer Thickness (m)
\( h_w \) — Depth of Water measured above impermeable layer (m)
\( Q_0 \) — Discharge at Time t=0 (m³/s)
\( \pi \) — Mathematical constant pi (approximately 3.1416)

Explanation: The formula calculates how far the influence of a pumping well extends into the surrounding aquifer based on the aquifer properties and pumping conditions.

3. Importance of Radius of Influence Calculation

Details: Calculating the radius of influence is crucial for well field design, determining well spacing, assessing interference between wells, and managing groundwater resources effectively. It helps in understanding the extent of the cone of depression created by pumping.

4. Using the Calculator

Tips: Enter all values in the specified units. Ensure that all input values are positive numbers. The initial aquifer thickness should be greater than the depth of water for meaningful results.

5. Frequently Asked Questions (FAQ)

Q1: What factors affect the radius of influence?
A: The radius of influence is affected by aquifer permeability, pumping rate, aquifer thickness, and the difference between initial aquifer thickness and water depth.

Q2: How does pumping rate affect the radius of influence?
A: Higher pumping rates generally result in a larger radius of influence as more water is being withdrawn from the aquifer.

Q3: What is the significance of the exponential function in the formula?
A: The exponential function accounts for the logarithmic nature of drawdown distribution in confined aquifers, where drawdown decreases logarithmically with distance from the well.

Q4: Can this formula be used for unconfined aquifers?
A: This specific formula is designed for confined aquifers. Unconfined aquifers have different equations that account for the water table being the upper boundary.

Q5: How accurate is this calculation in real-world scenarios?
A: While the formula provides a theoretical estimate, real-world conditions may vary due to aquifer heterogeneity, boundary conditions, and other factors. Field measurements are often needed for precise determination.