Discharge For Partially Penetrating Well Calculator

Formula Used:

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

Coefficient of Permeability (k):

m/s

Aquifer Thickness During Pumping (b_p):

Initial Aquifer Thickness (H_i):

Depth of Water (h_w):

Correction Factor (G):

Radius of Influence (R):

Radius of Well (r'):

Discharge for Partially Penetrating Well (Q_v):

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1. What is Discharge for Partially Penetrating Well?

Discharge for Partially Penetrating Well refers to the volumetric flow rate of water extracted from an aquifer when the well does not fully penetrate the entire thickness of the aquifer. This calculation is essential in environmental engineering for designing efficient groundwater extraction systems.

2. How Does the Calculator Work?

The calculator uses the following formula:

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

Where:

\( Q_v \) — Discharge for partially penetrating well (m³/s)
\( k \) — Coefficient of permeability (m/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)
\( \pi \) — Archimedes' constant (3.14159)
\( \ln \) — Natural logarithm function

Explanation: The formula accounts for the geometry of partial penetration and the hydraulic properties of the aquifer to calculate the discharge rate.

3. Importance of Discharge Calculation

Details: Accurate discharge calculation is crucial for designing efficient well systems, managing groundwater resources, and preventing over-extraction that could lead to aquifer depletion or land subsidence.

4. Using the Calculator

Tips: Enter all values in appropriate units. Ensure that the radius of influence is greater than the well radius, and that initial aquifer thickness is greater than depth of water. All values must be positive numbers.

5. Frequently Asked Questions (FAQ)

Q1: What is partial penetration in wells?
A: Partial penetration occurs when a well does not extend through the full thickness of the aquifer, which affects the flow pattern and discharge rate.

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 relationships or 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.

Q4: When should this formula be used?
A: This formula is specifically for partially penetrating wells in confined or unconfined aquifers where the well does not fully penetrate the aquifer.

Q5: What are the limitations of this calculation?
A: The formula assumes homogeneous aquifer properties and may not account for complex geological conditions or time-dependent effects.