Radius Of Influence Given Discharge For Partially Penetrating Well Calculator

Radius of Influence Formula:

\[ r_i = r' \times \exp\left(\frac{2\pi k b_p (H_i - h_w) G}{Q_0}\right) \]

Radius of Well (r'):

Coefficient of Permeability (k):

m/s

Aquifer Thickness During Pumping (bₚ):

Initial Aquifer Thickness (Hᵢ):

Depth of Water (h𝓌):

Correction Factor (G):

Discharge at Time t=0 (Q₀):

m³/s

Radius of Influence (rᵢ):

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1. What is Radius of Influence?

The Radius of Influence is measured from the center of the 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 a well.

2. How Does the Calculator Work?

The calculator uses the Radius of Influence formula for partially penetrating wells:

\[ r_i = r' \times \exp\left(\frac{2\pi k b_p (H_i - h_w) G}{Q_0}\right) \]

Where:

\( r_i \) — Radius of Influence (m)
\( r' \) — Radius of Well (m)
\( k \) — Coefficient of Permeability (m/s)
\( b_p \) — Aquifer Thickness During Pumping (m)
\( H_i \) — Initial Aquifer Thickness (m)
\( h_w \) — Depth of Water (m)
\( G \) — Correction Factor
\( Q_0 \) — Discharge at Time t=0 (m³/s)

Explanation: The formula calculates the extent of the cone of depression around a partially penetrating well, accounting for 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 interference, assessing environmental impacts of pumping, and managing groundwater resources effectively.

4. Using the Calculator

Tips: Enter all values in appropriate units. Ensure that the initial aquifer thickness is greater than the depth of water. All values must be positive numbers.

5. Frequently Asked Questions (FAQ)

Q1: What is the significance of the correction factor (G)?
A: The correction factor accounts for partial penetration of the well screen and adjusts the calculation based on how much of the aquifer thickness the well actually penetrates.

Q2: How does permeability affect the radius of influence?
A: Higher permeability results in a larger radius of influence as water can move more easily through the aquifer material.

Q3: What is the typical range for radius of influence?
A: The radius of influence can range from a few meters to several kilometers depending on aquifer properties, pumping rate, and duration of pumping.

Q4: How does pumping rate affect the radius of influence?
A: Higher pumping rates generally create larger cones of depression and thus larger radii of influence.

Q5: When is this formula most applicable?
A: This formula is specifically designed for partially penetrating wells in confined or unconfined aquifers where the well does not fully penetrate the entire aquifer thickness.