Radius Of Well Given Coefficient Of Transmissibility Calculator

Formula Used:

\[ r = \frac{R_w}{\exp\left(\frac{2\pi T_{envi}(H_i - h_w)}{Q_0}\right)} \]

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 (Q_0):

m³/s

Radius of Well (r):

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1. What is the Radius of Well Calculation?

The radius of well calculation determines the distance from the center of a well to its outer boundary using the relationship between radius of influence, coefficient of transmissibility, aquifer thickness, water depth, and discharge rate.

2. How Does the Calculator Work?

The calculator uses the formula:

\[ r = \frac{R_w}{\exp\left(\frac{2\pi T_{envi}(H_i - h_w)}{Q_0}\right)} \]

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 (m)
\( Q_0 \) — Discharge at time t=0 (m³/s)
\( \pi \) — Mathematical constant pi (approximately 3.14159)
\( \exp \) — Exponential function

Explanation: This formula calculates the well radius based on the exponential relationship between the radius of influence and various hydrogeological parameters.

3. Importance of Well Radius Calculation

Details: Accurate well radius calculation is crucial for well design, determining pumping rates, assessing aquifer characteristics, and planning groundwater extraction projects.

4. Using the Calculator

Tips: Enter all values in appropriate units. Ensure that initial aquifer thickness is greater than depth of water, and all values are positive. The calculator provides results in meters.

5. Frequently Asked Questions (FAQ)

Q1: What is the coefficient of transmissibility?
A: Coefficient of transmissibility represents the rate of water flow through a vertical strip of aquifer and is a measure of the aquifer's ability to transmit water.

Q2: How is radius of influence determined?
A: Radius of influence is measured from the well center to the point where the drawdown curve meets the original water table, typically determined through pumping tests.

Q3: Why is the exponential function used in this formula?
A: The exponential function models the logarithmic relationship between drawdown and distance from the well, which is characteristic of groundwater flow equations.

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

Q5: When should this calculation be used?
A: This calculation is used in hydrogeological studies, well design, groundwater resource assessment, and environmental impact assessments involving groundwater extraction.