Coefficient of Permeability given Depth of Water in Two Wells Calculator

Formula Used:

\[ K_w = \frac{Q}{\frac{2.72 \times b_p \times (h_2 - h_1)}{\log\left(\frac{r_2}{r_1}, 10\right)}} \]

Discharge (Q):

m³/s

Aquifer Thickness During Pumping (b_p):

Depth of Water 2 (h₂):

Depth of Water 1 (h₁):

Radial Distance at Observation Well 2 (r₂):

Radial Distance at Observation Well 1 (r₁):

Coefficient of Permeability (K_w):

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1. What is the Coefficient of Permeability?

The Coefficient of Permeability (K_w) is a measure of how easily water can flow through soil or rock. It represents the velocity in meters or centimeters per second of water movement through porous materials under a hydraulic gradient.

2. How Does the Calculator Work?

The calculator uses the formula:

\[ K_w = \frac{Q}{\frac{2.72 \times b_p \times (h_2 - h_1)}{\log\left(\frac{r_2}{r_1}, 10\right)}} \]

Where:

\( K_w \) — Coefficient of Permeability (m/s)
\( Q \) — Discharge rate (m³/s)
\( b_p \) — Aquifer thickness during pumping (m)
\( h_2 \) — Depth of water in second well (m)
\( h_1 \) — Depth of water in first well (m)
\( r_2 \) — Radial distance at observation well 2 (m)
\( r_1 \) — Radial distance at observation well 1 (m)

Explanation: This formula calculates the permeability coefficient based on pumping test data from two observation wells, considering the logarithmic relationship between radial distances and water depth differences.

3. Importance of Permeability Calculation

Details: Accurate permeability calculation is crucial for groundwater flow analysis, well design, contaminant transport studies, and designing effective drainage systems in geotechnical engineering projects.

4. Using the Calculator

Tips: Enter all values in consistent units (meters and cubic meters per second). Ensure radial distances and water depths are measured accurately from the pumping well. All input values must be positive numbers.

5. Frequently Asked Questions (FAQ)

Q1: What is a typical range for permeability coefficients?
A: Permeability varies widely: gravel (10⁻¹-10⁻² m/s), sand (10⁻³-10⁻⁵ m/s), silt (10⁻⁶-10⁻⁸ m/s), clay (<10⁻⁹ m/s).

Q2: Why use logarithmic scale in the formula?
A: The logarithmic relationship accounts for the decreasing hydraulic gradient with increasing distance from the pumping well.

Q3: When is this calculation method most appropriate?
A: This method is suitable for confined aquifers with steady-state pumping conditions and homogeneous, isotropic aquifer materials.

Q4: What are the limitations of this approach?
A: The method assumes ideal conditions and may not be accurate for heterogeneous aquifers, unconfined conditions, or when well storage effects are significant.

Q5: How does aquifer thickness affect permeability?
A: Thicker aquifers generally allow more water flow, but the relationship is complex and depends on the aquifer's hydraulic properties.