Depth Of Water At Point 2 Given Discharge Of Two Wells Under Consideration Calculator

Formula Used:

\[ h_2 = \sqrt{h_1^2 + \frac{Q \cdot \ln\left(\frac{r_2}{r_1}\right)}{\pi \cdot K_{WH}}} \]

Depth Of Water 1 (h1):

Discharge (Q):

m³/s

Radial Distance at Observation Well 2 (r2):

Radial Distance at Observation Well 1 (r1):

Coefficient of Permeability (KWH):

m/s

Depth Of Water 2 (h2):

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1. What is Depth Of Water At Point 2 Given Discharge Of Two Wells Under Consideration?

This calculation determines the depth of water at a second observation point based on the discharge rate, permeability coefficient, and radial distances from two wells. It's essential in groundwater hydrology for understanding aquifer behavior and well interactions.

2. How Does the Calculator Work?

The calculator uses the formula:

\[ h_2 = \sqrt{h_1^2 + \frac{Q \cdot \ln\left(\frac{r_2}{r_1}\right)}{\pi \cdot K_{WH}}} \]

Where:

\( h_2 \) — Depth of water at point 2 (m)
\( h_1 \) — Depth of water at point 1 (m)
\( Q \) — Discharge rate (m³/s)
\( r_2 \) — Radial distance at observation well 2 (m)
\( r_1 \) — Radial distance at observation well 1 (m)
\( K_{WH} \) — Coefficient of permeability (m/s)
\( \pi \) — Archimedes' constant (≈3.1416)
\( \ln \) — Natural logarithm function

Explanation: The formula calculates the water depth at a second observation point based on the logarithmic relationship between radial distances and the discharge-permeability ratio.

3. Importance of Depth Calculation

Details: Accurate depth calculation is crucial for groundwater modeling, well field design, contamination studies, and sustainable water resource management. It helps predict drawdown effects and optimize well spacing.

4. Using the Calculator

Tips: Enter all values in consistent units (meters and m³/s). Ensure radial distances are measured from the pumping well center. All input values must be positive numbers.

5. Frequently Asked Questions (FAQ)

Q1: What is the significance of the natural logarithm in this formula?
A: The natural logarithm accounts for the radial flow pattern in confined aquifers, where drawdown decreases logarithmically with distance from the pumping well.

Q2: When is this formula applicable?
A: This formula applies to steady-state radial flow in confined aquifers with homogeneous, isotropic properties and fully penetrating wells.

Q3: What are typical values for coefficient of permeability?
A: Permeability coefficients vary widely: gravel (10⁻¹-10⁻² m/s), sand (10⁻³-10⁻⁵ m/s), silt (10⁻⁶-10⁻⁸ m/s), clay (10⁻⁹-10⁻¹² m/s).

Q4: How does well discharge affect water depth?
A: Higher discharge rates cause greater drawdown, resulting in deeper water depths at observation points, particularly closer to the pumping well.

Q5: What are the limitations of this approach?
A: This method assumes ideal aquifer conditions and may not account for boundary effects, partial penetration, or heterogeneous aquifer properties.