Coefficient Of Permeability Given Discharge For Partially Penetrating Well Calculator

Formula Used:

\[ k = \frac{Q_v}{\frac{2\pi b_p (H_i - h_w) G}{\ln\left(\frac{R}{r'}\right)}} \]

Discharge for Partially Penetrating Well (Qv):

m³/s

Aquifer Thickness During Pumping (bp):

Initial Aquifer Thickness (Hi):

Depth of Water (hw):

Correction Factor (G):

Radius of Influence (R):

Radius of Well (r'):

Coefficient of Permeability (k):

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1. What is the Coefficient of Permeability?

The Coefficient of Permeability (k) of soil describes how easily a liquid will move through the soil. It's a crucial parameter in hydrogeology and environmental engineering for analyzing groundwater flow and well performance.

2. How Does the Calculator Work?

The calculator uses the formula for partially penetrating wells:

\[ k = \frac{Q_v}{\frac{2\pi b_p (H_i - h_w) G}{\ln\left(\frac{R}{r'}\right)}} \]

Where:

\( k \) — Coefficient of Permeability (m/s)
\( Q_v \) — Discharge for partially penetrating well (m³/s)
\( b_p \) — Aquifer thickness during pumping (m)
\( H_i \) — Initial aquifer thickness (m)
\( h_w \) — Depth of water in the well (m)
\( G \) — Correction factor for partial penetration
\( R \) — Radius of influence (m)
\( r' \) — Radius of well (m)
\( \pi \) — Mathematical constant pi (≈3.1416)
\( \ln \) — Natural logarithm function

Explanation: This formula accounts for the partial penetration of the well into the aquifer and provides a more accurate estimation of permeability for such conditions.

3. Importance of Coefficient of Permeability Calculation

Details: Accurate determination of permeability is essential for designing efficient well systems, predicting groundwater flow rates, assessing contaminant transport, and managing water resources effectively.

4. Using the Calculator

Tips: Enter all values in appropriate units (meters for lengths, m³/s for discharge). Ensure that R > r' to avoid mathematical errors. All input values must be positive numbers.

5. Frequently Asked Questions (FAQ)

Q1: What is the difference between fully and partially penetrating wells?
A: A fully penetrating well extends through the entire aquifer thickness, while a partially penetrating well only extends through part of the aquifer thickness.

Q2: How is the correction factor G determined?
A: The correction factor depends on the degree of penetration and aquifer characteristics, typically obtained from empirical charts or tables.

Q3: What are typical values of coefficient of permeability?
A: Permeability values range from 10⁻¹² m/s for clay to 10⁻¹ m/s for gravel, with most soils falling between 10⁻⁹ to 10⁻⁴ m/s.

Q4: When should this formula be used instead of fully penetrating well formulas?
A: This formula should be used when the well screen doesn't extend through the entire aquifer thickness, which is common in practice.

Q5: What are the limitations of this calculation method?
A: The method assumes homogeneous, isotropic aquifer conditions and may not account for complex geological features or transient flow conditions.