Radius Of Well Given Drawdown At Well Calculator

Radius of Well in Well Hydraulics Formula:

\[ r'' = \frac{R_w}{\exp\left(\frac{2\pi T_{envi} s_t}{Q}\right)} \]

Radius of Influence (R_w):

Coefficient of Transmissibility (T_envi):

m²/s

Total Drawdown in Well (s_t):

Discharge (Q):

m³/s

Radius of Well (r''):

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1. What is Radius of Well in Well Hydraulics?

The radius of well in well hydraulics is defined as the distance from the center of the well to its outer boundary. It's a critical parameter in groundwater flow equations and well design calculations.

2. How Does the Calculator Work?

The calculator uses the well hydraulics formula:

\[ r'' = \frac{R_w}{\exp\left(\frac{2\pi T_{envi} s_t}{Q}\right)} \]

Where:

\( r'' \) — Radius of well (m)
\( R_w \) — Radius of influence (m)
\( T_{envi} \) — Coefficient of transmissibility (m²/s)
\( s_t \) — Total drawdown in well (m)
\( Q \) — Discharge rate (m³/s)
\( \pi \) — Mathematical constant pi (≈3.1416)
\( \exp \) — Exponential function

Explanation: This formula calculates the radius of a well based on the radius of influence, transmissibility coefficient, total drawdown, and discharge rate using exponential relationships.

3. Importance of Well Radius Calculation

Details: Accurate well radius calculation is crucial for proper well design, determining pumping rates, assessing aquifer characteristics, and predicting drawdown effects in groundwater systems.

4. Using the Calculator

Tips: Enter all values in appropriate units (meters for lengths, m²/s for transmissibility, m³/s for discharge). All values must be positive and non-zero for accurate calculation.

5. Frequently Asked Questions (FAQ)

Q1: What is the radius of influence?
A: Radius of influence is the distance from the center of the well to the point where the drawdown curve meets the original water table level.

Q2: How is coefficient of transmissibility measured?
A: Coefficient of transmissibility is typically determined through aquifer pumping tests and represents the aquifer's ability to transmit water.

Q3: What factors affect total drawdown in a well?
A: Total drawdown is influenced by pumping rate, aquifer properties, well construction, and duration of pumping.

Q4: Why is the exponential function used in this formula?
A: The exponential function models the logarithmic relationship between drawdown and distance from the well in confined aquifers.

Q5: What are typical well radius values?
A: Well radius typically ranges from 0.1 to 1.0 meters, depending on the well type and construction method.