Radius Of Well Based On Discharge In Unconfined Aquifer With Base 10 Calculator

Formula Used:

\[ r = \frac{R_w}{10^{\frac{1.36 \times K_{soil} \times (H_i^2 - h_w^2)}{Q}}} \]

Radius of Influence (Rw):

Coefficient of Permeability of Soil Particle (Ksoil):

m/s

Initial Aquifer Thickness (Hi):

Depth of Water (hw):

Discharge (Q):

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 based on the discharge rate and aquifer properties in an unconfined aquifer system using base 10 logarithm.

2. How Does the Calculator Work?

The calculator uses the formula:

\[ r = \frac{R_w}{10^{\frac{1.36 \times K_{soil} \times (H_i^2 - h_w^2)}{Q}}} \]

Where:

\( r \) — Radius of well (m)
\( R_w \) — Radius of influence (m)
\( K_{soil} \) — Coefficient of permeability of soil particle (m/s)
\( H_i \) — Initial aquifer thickness (m)
\( h_w \) — Depth of water in the well (m)
\( Q \) — Discharge rate (m³/s)

Explanation: The formula calculates the well radius by considering the ratio of radius of influence to the exponential function of the hydraulic parameters and discharge rate.

3. Importance of Radius of Well Calculation

Details: Accurate determination of well radius is crucial for well design, pumping test analysis, and understanding the hydraulic behavior of unconfined aquifers during groundwater extraction.

4. Using the Calculator

Tips: Enter all values in appropriate units (meters for lengths, m/s for permeability, m³/s for discharge). All values must be positive and valid for accurate calculation.

5. Frequently Asked Questions (FAQ)

Q1: What is the significance of base 10 in this formula?
A: The base 10 logarithm is used to simplify calculations and provide results that are easier to interpret in practical engineering applications.

Q2: How does soil permeability affect the well radius?
A: Higher permeability soils typically result in larger calculated well radii as water can flow more easily through the soil particles.

Q3: What is the relationship between discharge rate and well radius?
A: Higher discharge rates generally lead to smaller calculated well radii, as more water is being extracted from a concentrated area.

Q4: When is this calculation most applicable?
A: This calculation is specifically designed for unconfined aquifers where the water table forms the upper boundary of the aquifer.

Q5: Are there limitations to this equation?
A: The equation assumes homogeneous aquifer conditions and may be less accurate in complex geological settings or where aquifer properties vary significantly.