Depth of Water in Well given Discharge in Unconfined Aquifer Calculator

Formula Used:

\[ hw = \sqrt{H^2 - \frac{Q \cdot \ln\left(\frac{R_w}{r}\right)}{\pi \cdot K_{WH}}} \]

Thickness of Unconfined Aquifer (H):

Discharge (Q):

m³/s

Radius of Influence (R_w):

Radius of well (r):

Coefficient of Permeability (K_WH):

m/s

Depth of Water (hw):

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1. What is the Depth of Water in Well Formula?

The formula calculates the depth of water in a well above the impermeable layer in an unconfined aquifer. It considers aquifer thickness, discharge rate, radius of influence, well radius, and soil permeability coefficient to determine water depth.

2. How Does the Calculator Work?

The calculator uses the formula:

\[ hw = \sqrt{H^2 - \frac{Q \cdot \ln\left(\frac{R_w}{r}\right)}{\pi \cdot K_{WH}}} \]

Where:

\( hw \) — Depth of water in well (m)
\( H \) — Thickness of unconfined aquifer (m)
\( Q \) — Discharge rate (m³/s)
\( R_w \) — Radius of influence (m)
\( r \) — Radius of well (m)
\( K_{WH} \) — Coefficient of permeability (m/s)
\( \pi \) — Archimedes' constant (3.14159)
\( \ln \) — Natural logarithm function

Explanation: The formula accounts for the relationship between water depth, aquifer properties, and flow characteristics in unconfined aquifers.

3. Importance of Depth Calculation

Details: Accurate depth calculation is crucial for well design, groundwater management, and determining sustainable extraction rates from unconfined aquifers.

4. Using the Calculator

Tips: Enter all values in appropriate units (meters for lengths, m³/s for discharge). Ensure all values are positive and physically meaningful for accurate results.

5. Frequently Asked Questions (FAQ)

Q1: What is an unconfined aquifer?
A: An unconfined aquifer has a water table that serves as its upper boundary and is free to rise and fall based on water levels.

Q2: How is radius of influence determined?
A: Radius of influence is the distance from the well center to where drawdown becomes negligible, typically determined through pumping tests.

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

Q4: When is this formula applicable?
A: This formula applies to steady-state flow conditions in homogeneous, isotropic unconfined aquifers with fully penetrating wells.

Q5: What are typical permeability values?
A: Permeability ranges from 10⁻² m/s for gravel to 10⁻⁹ m/s for clay, with sand typically around 10⁻⁵ to 10⁻³ m/s.