Coefficient of Permeability given Discharge of Two Wells under Consideration Calculator

Formula Used:

\[ KWH = \frac{Q}{\frac{\pi(h_2^2 - h_1^2)}{\ln\left(\frac{r_2}{r_1'}\right)}} \]

Discharge (Q):

m³/s

Depth of Water 1 (h₁):

Depth of Water 2 (h₂):

Observation Well 1 Radial Distance (r₁'):

Radial Distance at Observation Well 2 (r₂):

Coefficient of Permeability (KWH):

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1. What is the Coefficient of Permeability in Well Hydraulics?

The Coefficient of Permeability in Well Hydraulics describes how easily a liquid will move through the soil. It is a crucial parameter in groundwater studies and well design, indicating the soil's ability to transmit water.

2. How Does the Calculator Work?

The calculator uses the formula:

\[ KWH = \frac{Q}{\frac{\pi(h_2^2 - h_1^2)}{\ln\left(\frac{r_2}{r_1'}\right)}} \]

Where:

\( KWH \) — Coefficient of Permeability in Well Hydraulics (m/s)
\( Q \) — Discharge rate (m³/s)
\( h_1 \) — Depth of water in the 1st well (m)
\( h_2 \) — Depth of water in the 2nd well (m)
\( r_1' \) — Observation Well 1 Radial Distance (m)
\( r_2 \) — Radial Distance at Observation Well 2 (m)
\( \pi \) — Archimedes' constant (≈3.14159)
\( e \) — Napier's constant (≈2.71828)

Explanation: This formula calculates the soil's permeability coefficient based on discharge measurements and water level differences between two observation wells.

3. Importance of Permeability Calculation

Details: Accurate permeability calculation is essential for designing efficient well systems, predicting groundwater flow, and managing water resources effectively.

4. Using the Calculator

Tips: Enter all values in appropriate units (discharge in m³/s, depths and distances in meters). Ensure all values are positive and radial distances are not equal to avoid division by zero.

5. Frequently Asked Questions (FAQ)

Q1: What is the typical range of permeability coefficients?
A: Permeability coefficients vary widely from 10⁻¹² m/s for clay to 10⁻¹ m/s for gravel, depending on soil type.

Q2: Why use natural logarithm in the formula?
A: The natural logarithm (base e) is used because it provides the correct mathematical relationship for radial flow in confined aquifers.

Q3: What if the radial distances are equal?
A: If r₂ = r₁', the denominator becomes zero, making the result undefined. Ensure proper well placement to avoid this.

Q4: How accurate is this calculation method?
A: This method provides good estimates for homogeneous, isotropic aquifers under steady-state conditions.

Q5: Can this formula be used for unconfined aquifers?
A: This specific formula is designed for confined aquifers. Different equations are used for unconfined aquifer analysis.