Radius Of Well Given Coefficient Of Transmissibility With Base 10 Calculator

Formula Used:

\[ r = \frac{R_w}{10^{\frac{2.72 \times T_{envi} \times (H_i - h_w)}{Q_0}}} \]

Radius of Influence (R_w):

Coefficient of Transmissibility (T_envi):

m²/s

Initial Aquifer Thickness (H_i):

Depth of Water (h_w):

Discharge at Time t=0 (Q₀):

m³/s

Radius of Well (r):

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1. What is Radius of Well Calculation?

The radius of well calculation determines the distance from the center of a well to its outer boundary based on aquifer properties and pumping conditions. This is essential for well design and groundwater resource management.

2. How Does the Calculator Work?

The calculator uses the formula:

\[ r = \frac{R_w}{10^{\frac{2.72 \times T_{envi} \times (H_i - h_w)}{Q_0}}} \]

Where:

\( r \) — Radius of well (m)
\( R_w \) — Radius of influence (m)
\( T_{envi} \) — Coefficient of transmissibility (m²/s)
\( H_i \) — Initial aquifer thickness (m)
\( h_w \) — Depth of water in the well (m)
\( Q_0 \) — Discharge at time t=0 (m³/s)

Explanation: This formula calculates the well radius based on the relationship between the radius of influence, transmissibility coefficient, aquifer thickness, water depth, and initial discharge rate.

3. Importance of Radius of Well Calculation

Details: Accurate well radius calculation is crucial for proper well design, determining optimal pumping rates, assessing aquifer yield potential, and ensuring sustainable groundwater extraction.

4. Using the Calculator

Tips: Enter all values in appropriate units (meters for lengths, m²/s for transmissibility, m³/s for discharge). Ensure all values are positive and physically meaningful (water depth should not exceed aquifer thickness).

5. Frequently Asked Questions (FAQ)

Q1: What is the coefficient of transmissibility?
A: The coefficient of transmissibility represents the rate of water flow through a vertical strip of aquifer under unit hydraulic gradient.

Q2: How is radius of influence determined?
A: Radius of influence is typically measured from pumping test data or estimated based on aquifer properties and pumping conditions.

Q3: Why is base 10 used in this formula?
A: Base 10 logarithms are commonly used in groundwater equations due to historical conventions and ease of calculation.

Q4: What are typical values for well radius?
A: Well radius typically ranges from 0.1 to 0.5 meters for most water supply wells, depending on the well construction and purpose.

Q5: When should this calculation be used?
A: This calculation is used during well design phase, aquifer testing analysis, and groundwater resource evaluation projects.