Aquifer Thickness Given Discharge For Partially Penetrating Well Calculator

Formula Used:

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

Discharge for Partially Penetrating Well (Qv):

m³/s

Coefficient of Permeability (k):

m/s

Initial Aquifer Thickness (Hi):

Depth of Water (hw):

Correction Factor (G):

Radius of Influence (R):

Radius of Well (r'):

Aquifer Thickness During Pumping (bp):

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1. What is Aquifer Thickness During Pumping?

Aquifer Thickness During Pumping refers to the vertical extent of the saturated aquifer material that contributes water to a pumping well. It is a critical parameter in groundwater hydrology that helps determine the well's yield and the aquifer's response to pumping.

2. How Does the Calculator Work?

The calculator uses the formula for partially penetrating wells:

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

Where:

\( b_p \) — Aquifer Thickness During Pumping (m)
\( Q_v \) — Discharge for partially penetrating well (m³/s)
\( k \) — Coefficient of permeability (m/s)
\( H_i \) — Initial aquifer thickness (m)
\( h_w \) — Depth of water above impermeable layer (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 screen into the aquifer and provides a more accurate estimation of aquifer thickness during pumping conditions.

3. Importance of Aquifer Thickness Calculation

Details: Accurate determination of aquifer thickness during pumping is crucial for well design, yield estimation, groundwater modeling, and sustainable water resource management. It helps in predicting drawdown patterns and ensuring optimal well performance.

4. Using the Calculator

Tips: Enter all values in appropriate units. Ensure that the radius of influence (R) is greater than the well radius (r') to avoid mathematical errors. The correction factor (G) depends on the degree of well penetration and aquifer characteristics.

5. Frequently Asked Questions (FAQ)

Q1: What is the difference between initial aquifer thickness and aquifer thickness during pumping?
A: Initial aquifer thickness is the saturated thickness before pumping begins, while aquifer thickness during pumping accounts for the dynamic conditions when water is being extracted from the well.

Q2: How is the correction factor (G) determined?
A: The correction factor depends on the ratio of screen length to aquifer thickness and the position of the screen within the aquifer. It is typically determined from empirical relationships or standard tables.

Q3: What is radius of influence?
A: Radius of influence is the distance from the well center to the point where drawdown becomes negligible, typically where the water table remains unaffected by pumping.

Q4: When is this formula applicable?
A: This formula is specifically designed for partially penetrating wells in confined or unconfined aquifers where the well screen does not extend through the entire aquifer thickness.

Q5: What are typical values for coefficient of permeability?
A: Permeability values vary widely: gravel (10⁻¹-10⁻³ m/s), sand (10⁻³-10⁻⁵ m/s), silt (10⁻⁵-10⁻⁷ m/s), clay (10⁻⁷-10⁻⁹ m/s).