Radius Of Well Given Discharge Due To Spherical Flow In Well Calculator

Formula Used:

\[ r' = \frac{Q_s}{2 \pi K (H - h_w)} \]

Discharge by Spherical Flow (Q_s):

m³/s

Coefficient of Permeability (K):

m/s

Thickness of Aquifer (H):

Depth of Water (h_w):

Radius of Well (r'):

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1. What is Radius of Well in Environmental Engineering?

Radius of Well in Environmental Engineering is defined as the distance from center of well to its outer boundary. It's a critical parameter in groundwater flow calculations and well design.

2. How Does the Calculator Work?

The calculator uses the formula:

\[ r' = \frac{Q_s}{2 \pi K (H - h_w)} \]

Where:

\( r' \) — Radius of Well (m)
\( Q_s \) — Discharge by Spherical Flow (m³/s)
\( K \) — Coefficient of Permeability (m/s)
\( H \) — Thickness of Aquifer (m)
\( h_w \) — Depth of Water in the well measured above the impermeable layer (m)
\( \pi \) — Archimedes' constant (≈3.1416)

Explanation: This formula calculates the radius of well based on spherical flow discharge, soil permeability characteristics, and aquifer dimensions.

3. Importance of Radius Calculation

Details: Accurate radius calculation is crucial for proper well design, determining well efficiency, and understanding the zone of influence around a well in groundwater systems.

4. Using the Calculator

Tips: Enter discharge in m³/s, coefficient of permeability in m/s, and all length measurements in meters. Ensure thickness of aquifer is greater than depth of water for valid calculation.

5. Frequently Asked Questions (FAQ)

Q1: What is spherical flow in well hydraulics?
A: Spherical flow occurs when groundwater flows radially toward a well from all directions in three-dimensional space, typically in partially penetrating wells.

Q2: How does coefficient of permeability affect well radius?
A: Higher permeability allows for smaller well radius to achieve the same discharge, as water can flow more easily through the soil.

Q3: What are typical values for well radius?
A: Well radius typically ranges from 0.1 to 1.0 meters, depending on the well type and purpose.

Q4: When is this formula most applicable?
A: This formula is particularly useful for analyzing flow in wells that partially penetrate aquifers or in cases where spherical flow dominates.

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