Depth of Water at Point 2 given Discharge from Two Wells with Base 10 Calculator

Formula Used:

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

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 the Depth of Water at Point 2 Formula?

The formula calculates the depth of water at point 2 based on the depth at point 1, discharge rate, radial distances, and coefficient of permeability. It's derived from well hydraulics principles and uses base-10 logarithm for the radial distance ratio.

2. How Does the Calculator Work?

The calculator uses the formula:

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

Where:

\( h2 \) — Depth of water at point 2 (m)
\( h1 \) — Depth of water at point 1 (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 accounts for the relationship between water depth, discharge rate, radial distances, and soil permeability characteristics.

3. Importance of Water Depth Calculation

Details: Accurate water depth calculation is crucial for groundwater modeling, well design, aquifer characterization, and environmental impact assessments in hydrogeological studies.

4. Using the Calculator

Tips: Enter all values in appropriate units (meters for distances, m³/s for discharge). Ensure all values are positive and radial distance at well 2 is greater than at well 1 for meaningful logarithmic calculation.

5. Frequently Asked Questions (FAQ)

Q1: Why use base-10 logarithm in this formula?
A: Base-10 logarithm is used because it's the standard convention in many hydrological equations and provides consistent scaling for the radial distance ratio.

Q2: What is the significance of the 1.36 constant?
A: The 1.36 constant is derived from empirical relationships and unit conversions that make the formula dimensionally consistent for the given units.

Q3: When is this formula applicable?
A: This formula is applicable for confined aquifers with steady-state flow conditions and homogeneous, isotropic soil properties.

Q4: What are the limitations of this formula?
A: The formula assumes ideal conditions and may not be accurate for unconfined aquifers, heterogeneous soils, or transient flow conditions.

Q5: How does coefficient of permeability affect the result?
A: Higher permeability values result in smaller changes in water depth between the two points, as water can move more easily through the soil.