Depth Of Water In Well Given Discharge Due To Spherical Flow In Well Calculator

Formula Used:

\[ h_w = H - \left( \frac{Q_s}{2 \pi K r'} \right) \]

Thickness of Aquifer (H):

Discharge by Spherical Flow (Qs):

m³/s

Coefficient of Permeability (K):

m/s

Radius of Well (r'):

Depth of Water (h_w):

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1. What is Depth of Water in Well?

Depth of Water in the well measured above the impermeable layer. It is an important parameter in hydrogeology and environmental engineering for analyzing groundwater flow and well performance.

2. How Does the Calculator Work?

The calculator uses the formula:

\[ h_w = H - \left( \frac{Q_s}{2 \pi K r'} \right) \]

Where:

\( h_w \) — Depth of Water (m)
\( H \) — Thickness of Aquifer (m)
\( Q_s \) — Discharge by Spherical Flow (m³/s)
\( K \) — Coefficient of Permeability (m/s)
\( r' \) — Radius of Well (m)
\( \pi \) — Archimedes' constant (≈3.1416)

Explanation: This formula calculates the depth of water in a well considering spherical flow conditions, accounting for aquifer thickness, discharge rate, soil permeability, and well radius.

3. Importance of Depth of Water Calculation

Details: Accurate calculation of water depth in wells is crucial for groundwater resource management, well design, pumping test analysis, and environmental impact assessments.

4. Using the Calculator

Tips: Enter all values in appropriate units (meters for length, m³/s for discharge). Ensure all values are positive and within reasonable ranges for accurate results.

5. Frequently Asked Questions (FAQ)

Q1: What is spherical flow in well hydraulics?
A: Spherical flow refers to the three-dimensional radial flow pattern that occurs around a well screen in confined or unconfined aquifers.

Q2: How does coefficient of permeability affect water depth?
A: Higher permeability allows water to flow more easily into the well, resulting in shallower drawdown and greater water depth for a given discharge rate.

Q3: What are typical values for coefficient of permeability?
A: Permeability values range from 10⁻² m/s for gravel to 10⁻⁹ m/s for clay, with most soils falling between 10⁻⁴ to 10⁻⁷ m/s.

Q4: When is this formula most applicable?
A: This formula is particularly useful for analyzing well performance in confined aquifers or situations where spherical flow conditions dominate.

Q5: What limitations does this calculation have?
A: The formula assumes homogeneous isotropic aquifer conditions, steady-state flow, and may not account for well losses or boundary effects.