Radius Of Influence Given Discharge In Confined Aquifer With Base 10 Calculator

Formula Used:

\[ Radius\ of\ Influence = Radius\ of\ well \times 10^{\frac{2.72 \times Coefficient\ of\ Permeability \times Aquifer\ Thickness\ During\ Pumping \times (Initial\ Aquifer\ Thickness - Depth\ of\ Water)}{Discharge\ at\ Time\ t=0}} \] \[ R_w = r \times 10^{\frac{2.72 \times KWH \times b_p \times (H_i - h_w)}{Q_0}} \]

Radius of Well (r):

Coefficient of Permeability (KWH):

m/s

Aquifer Thickness During Pumping (bₚ):

Initial Aquifer Thickness (Hᵢ):

Depth of Water (h_w):

Discharge at Time t=0 (Q₀):

m³/s

Radius of Influence (R_w):

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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 to which pumping from a well affects the surrounding groundwater levels in a confined aquifer.

2. How Does the Calculator Work?

The calculator uses the formula:

\[ R_w = r \times 10^{\frac{2.72 \times KWH \times b_p \times (H_i - h_w)}{Q_0}} \]

Where:

\( R_w \) — Radius of Influence (m)
\( r \) — Radius of well (m)
\( KWH \) — 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 in the well measured above the impermeable layer (m)
\( Q_0 \) — Discharge at Time t=0 (m³/s)

Explanation: This formula calculates the radius of influence for a confined aquifer using base 10 logarithm, accounting for aquifer properties and pumping conditions.

3. Importance of Radius of Influence Calculation

Details: Determining the radius of influence is crucial for well field design, assessing interference between wells, and managing groundwater resources effectively. It helps in understanding how far the cone of depression extends during pumping operations.

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 a confined aquifer?
A: A confined aquifer is an aquifer bounded above and below by impermeable layers, with water under pressure.

Q2: How does permeability affect the radius of influence?
A: Higher permeability allows water to move more easily through the aquifer, typically resulting in a larger radius of influence.

Q3: What is the significance of the 2.72 constant?
A: The constant 2.72 is derived from mathematical relationships in groundwater flow equations and represents a conversion factor in the formula.

Q4: How does discharge rate affect the radius of influence?
A: Higher discharge rates generally create a larger cone of depression and thus a larger radius of influence.

Q5: Are there limitations to this equation?
A: This equation assumes ideal conditions and homogeneous aquifer properties. Real-world conditions with heterogeneous aquifers may require more complex modeling approaches.