Coefficient Of Permeability When Interference Among Three Well Is Present Calculator

Formula Used:

\[ K = \frac{Q}{\frac{2\pi b_p (b_w - h_w)}{\ln\left(\frac{R^3}{r' B^2}\right)}} \]

Discharge (Q):

m³/s

Aquifer Thickness During Pumping (bₚ):

Aquifer Thickness (b_w):

Depth of Water (h_w):

Radius of Influence (R):

Radius of Well (r'):

Distance Between Well (B):

Coefficient of Permeability (K):

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1. What is Coefficient of Permeability?

The coefficient of permeability (K) of soil describes how easily a liquid will move through the soil. It is a crucial parameter in environmental engineering for groundwater flow analysis and well interference studies.

2. How Does the Calculator Work?

The calculator uses the formula for permeability when interference among three wells is present:

\[ K = \frac{Q}{\frac{2\pi b_p (b_w - h_w)}{\ln\left(\frac{R^3}{r' B^2}\right)}} \]

Where:

\( K \) — Coefficient of permeability (m/s)
\( Q \) — Discharge rate (m³/s)
\( b_p \) — Aquifer thickness during pumping (m)
\( b_w \) — Aquifer thickness (m)
\( h_w \) — Depth of water (m)
\( R \) — Radius of influence (m)
\( r' \) — Radius of well (m)
\( B \) — Distance between wells (m)
\( \pi \) — Mathematical constant pi (≈3.1416)
\( e \) — Mathematical constant e (≈2.7183)

Explanation: This formula accounts for the interference effects between three wells in an aquifer system, providing accurate permeability calculations for complex groundwater flow scenarios.

3. Importance of Permeability Calculation

Details: Accurate permeability calculation is essential for designing effective groundwater extraction systems, predicting contaminant transport, and managing aquifer resources sustainably.

4. Using the Calculator

Tips: Enter all values in meters and cubic meters per second. Ensure all input values are positive and physically meaningful. The depth of water should be less than the aquifer thickness.

5. Frequently Asked Questions (FAQ)

Q1: What is well interference?
A: Well interference occurs when multiple wells are close enough that their individual cones of depression overlap, affecting each other's performance and water extraction rates.

Q2: Why is the natural logarithm used in the formula?
A: The natural logarithm (base e) is used because it provides the most mathematically convenient form for solving the groundwater flow equations that describe radial flow to wells.

Q3: What are typical values for coefficient of permeability?
A: Permeability values range from 10⁻¹² m/s for clay to 10⁻¹ m/s for gravel. The specific value depends on soil type and composition.

Q4: How does aquifer thickness affect permeability calculations?
A: Thicker aquifers generally allow for greater water storage and transmission, but the relationship is complex and depends on the aquifer's material properties.

Q5: When is this specific formula applicable?
A: This formula is specifically designed for situations where three wells are interacting and interfering with each other's flow patterns in a confined or unconfined aquifer.