Depth of Water at Point 1 given Discharge from Two Wells with Base 10 Calculator

Formula Used:

\[ h1 = \sqrt{h2^2 - \frac{Q \cdot \log_{10}(\frac{r2}{r1})}{1.36 \cdot KWH}} \]

Depth of Water 2 (h2):

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 1 (h1):

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1. What is the Depth of Water at Point 1 Calculation?

The Depth of Water at Point 1 calculation determines the water depth at a specific observation well using the relationship between two wells, discharge rate, radial distances, and soil permeability coefficient. This is essential in well hydraulics for understanding groundwater flow patterns.

2. How Does the Calculator Work?

The calculator uses the formula:

\[ h1 = \sqrt{h2^2 - \frac{Q \cdot \log_{10}(\frac{r2}{r1})}{1.36 \cdot KWH}} \]

Where:

\( h1 \) — Depth of water at point 1 (m)
\( h2 \) — Depth of water at point 2 (m)
\( Q \) — Discharge rate (m³/s)
\( r2 \) — Radial distance at observation well 2 (m)
\( r1 \) — Radial distance at observation well 1 (m)
\( KWH \) — Coefficient of permeability in well hydraulics (m/s)

Explanation: The formula calculates the water depth at the first observation point based on the known depth at the second point, discharge rate, distance ratio, and soil permeability.

3. Importance of Water Depth Calculation

Details: Accurate water depth calculation is crucial for groundwater resource management, well design, contaminant transport studies, and understanding aquifer characteristics in hydrogeological investigations.

4. Using the Calculator

Tips: Enter all values in appropriate units (meters for distances, m³/s for discharge, m/s for permeability). Ensure all values are positive and radial distances are properly measured from the well center.

5. Frequently Asked Questions (FAQ)

Q1: What is the significance of the 1.36 constant in the formula?
A: The constant 1.36 is derived from the conversion factors and empirical relationships in well hydraulics that account for the specific conditions of groundwater flow between observation wells.

Q2: Why use base-10 logarithm in this calculation?
A: Base-10 logarithm is used because it simplifies the mathematical relationships in well hydraulics and aligns with conventional practices in groundwater engineering calculations.

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: When is this calculation most applicable?
A: This calculation is most applicable for steady-state flow conditions in confined or unconfined aquifers with homogeneous isotropic properties.

Q5: What are the limitations of this formula?
A: The formula assumes ideal conditions and may not account for aquifer heterogeneity, transient flow conditions, or complex boundary conditions that affect real-world groundwater systems.