Radius of Well of Unconfined Aquifer with Known Discharge Calculator

Formula Used:

\[ r' = \frac{r_i}{\exp\left(\frac{0.434 \cdot \pi \cdot k \cdot (h^2 - h_p)}{Q}\right)} \]

Radius of Influence in Environ. Engin. (r_i):

Coefficient of Permeability (k):

m/s

Original Piezometric Head of the Well (h):

Piezometric Head at Well (h_p):

Discharge (Q):

m³/s

Radius of Well in Environ. Engin. (r'):

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1. What is the Radius of Well Formula?

The formula calculates the radius of a well in an unconfined aquifer when the discharge is known. It's derived from the relationship between the radius of influence, permeability coefficient, piezometric heads, and discharge rate in environmental engineering applications.

2. How Does the Calculator Work?

The calculator uses the formula:

\[ r' = \frac{r_i}{\exp\left(\frac{0.434 \cdot \pi \cdot k \cdot (h^2 - h_p)}{Q}\right)} \]

Where:

\( r' \) — Radius of Well in Environ. Engin. (m)
\( r_i \) — Radius of Influence in Environ. Engin. (m)
\( k \) — Coefficient of Permeability (m/s)
\( h \) — Original Piezometric Head of the Well (m)
\( h_p \) — Piezometric Head at Well (m)
\( Q \) — Discharge (m³/s)
\( \pi \) — Archimedes' constant (≈3.1416)

Explanation: The formula accounts for the exponential relationship between well radius and the hydraulic parameters of the aquifer system.

3. Importance of Well Radius Calculation

Details: Accurate well radius calculation is crucial for designing efficient well systems, determining optimal pumping rates, and assessing the environmental impact of groundwater extraction in unconfined aquifers.

4. Using the Calculator

Tips: Enter all values in appropriate units (meters for lengths, m/s for permeability, m³/s for discharge). Ensure all values are positive and piezometric head at well is less than or equal to original piezometric head.

5. Frequently Asked Questions (FAQ)

Q1: What is an unconfined aquifer?
A: An unconfined aquifer is a groundwater aquifer where the water table is the upper boundary and is free to rise and fall.

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

Q3: What factors affect coefficient of permeability?
A: Soil type, grain size distribution, porosity, and degree of saturation all influence the coefficient of permeability.

Q4: When is this formula most accurate?
A: This formula works best for steady-state flow conditions in homogeneous, isotropic unconfined aquifers.

Q5: What are typical values for well radius?
A: Well radii typically range from 0.1 to 1.0 meters, depending on the well construction and aquifer characteristics.