Correction Factor For Partial Penetration Given Discharge For Partially Penetrating Well Calculator

Formula Used:

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

Discharge for Partially Penetrating Well (Q_v):

m³/s

Coefficient of Permeability (k):

m/s

Aquifer Thickness During Pumping (b_p):

Initial Aquifer Thickness (H_i):

Depth of Water (h_w):

Radius of Influence (R):

Radius of Well (r'):

Correction Factor (G):

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1. What is Correction Factor for Partial Penetration?

The Correction Factor for Partial Penetration accounts for the reduced efficiency of a partially penetrating well compared to a fully penetrating one. It is applied to correct the discharge calculation when the well does not fully penetrate the aquifer.

2. How Does the Calculator Work?

The calculator uses the formula:

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

Where:

\( G \) — Correction Factor
\( Q_v \) — 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 (m)
\( R \) — Radius of influence (m)
\( r' \) — Radius of well (m)
\( \pi \) — Mathematical constant pi (≈3.1416)
\( \ln \) — Natural logarithm function

Explanation: The formula calculates the correction factor by comparing the actual discharge from a partially penetrating well with the theoretical discharge that would occur under ideal conditions.

3. Importance of Correction Factor Calculation

Details: Accurate calculation of the correction factor is essential for proper well design, groundwater resource assessment, and predicting well performance in partially penetrating conditions.

4. Using the Calculator

Tips: Enter all values in the specified units. Ensure that radius of influence is greater than radius of well, and all numerical values are positive.

5. Frequently Asked Questions (FAQ)

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

Q2: When is the correction factor needed?
A: The correction factor is needed when calculating discharge from partially penetrating wells to account for the reduced efficiency compared to fully penetrating wells.

Q3: What values indicate a good correction factor?
A: Correction factors typically range between 0 and 1, with values closer to 1 indicating better well performance.

Q4: What are the limitations of this calculation?
A: This calculation assumes homogeneous aquifer conditions and may not accurately represent complex geological settings or anisotropic aquifers.

Q5: How does well radius affect the correction factor?
A: Larger well radii generally result in higher correction factors as they allow for better water entry into the well.