Radius Of Well Given Discharge For Partially Penetrating Well Calculator

Formula Used:

\[ r' = \frac{r_i}{\exp\left(\frac{2\pi k b_p (H_i - h_w) G}{Q}\right)} \]

Radius of Influence in Eviron. Engin.:

Coefficient of Permeability:

m/s

Aquifer Thickness During Pumping:

Initial Aquifer Thickness:

Depth of Water:

Correction Factor:

Discharge:

m³/s

Radius of Well in Eviron. Engin.:

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1. What is the Radius of Well Formula?

The formula calculates the radius of a well for partially penetrating conditions in environmental engineering. It accounts for various hydrogeological parameters including permeability, aquifer thickness, and discharge rate to determine the well radius.

2. How Does the Calculator Work?

The calculator uses the formula:

\[ r' = \frac{r_i}{\exp\left(\frac{2\pi k b_p (H_i - h_w) G}{Q}\right)} \]

Where:

\( r' \) — Radius of Well (m)
\( r_i \) — Radius of Influence (m)
\( k \) — Coefficient of Permeability (m/s)
\( b_p \) — Aquifer Thickness During Pumping (m)
\( H_i \) — Initial Aquifer Thickness (m)
\( h_w \) — Depth of Water (m)
\( G \) — Correction Factor
\( Q \) — Discharge (m³/s)
\( \pi \) — Mathematical constant (3.14159)

Explanation: The formula calculates the well radius by considering the exponential relationship between various hydrogeological parameters and the discharge rate.

3. Importance of Radius Calculation

Details: Accurate well radius calculation is crucial for designing efficient well systems, determining optimal pumping rates, and ensuring sustainable groundwater extraction in partially penetrating well conditions.

4. Using the Calculator

Tips: Enter all required parameters with appropriate units. Ensure values are positive and physically meaningful (e.g., initial aquifer thickness should be greater than depth of water).

5. Frequently Asked Questions (FAQ)

Q1: What is the significance of the correction factor (G)?
A: The correction factor accounts for partial penetration effects and adjusts the calculation for wells that don't fully penetrate the aquifer.

Q2: How is radius of influence determined?
A: Radius of influence is typically determined through pumping tests or estimated based on aquifer properties and pumping conditions.

Q3: What are typical values for coefficient of permeability?
A: Permeability values vary widely by soil type, ranging from 10⁻² m/s for gravel to 10⁻⁹ m/s for clay.

Q4: When is this formula most applicable?
A: This formula is specifically designed for partially penetrating wells in confined or unconfined aquifers.

Q5: What are the limitations of this calculation?
A: The calculation assumes homogeneous aquifer conditions and may not account for complex geological formations or boundary effects.