Depth of Water at Point 1 given Discharge of Two Wells under Consideration Calculator

Formula Used:

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

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 (K_WH):

m/s

Depth of Water 1 (h₁):

Unit Converter ▲

Unit Converter ▼

From:	To:

1. What is the Depth of Water Calculation?

This calculation determines the depth of water at point 1 (h₁) based on the discharge between two wells and their radial distances. It's derived from the Thiem equation for steady-state flow to a well in a confined aquifer.

2. How Does the Calculator Work?

The calculator uses the formula:

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

Where:

\( h_1 \) — Depth of water at point 1 (m)
\( h_2 \) — Depth of water at point 2 (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)
\( \pi \) — Mathematical constant pi (≈3.1416)
\( \ln \) — Natural logarithm function

Explanation: The formula calculates the water depth at one observation point based on known parameters at another observation point, using the principles of well hydraulics.

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.

4. Using the Calculator

Tips: Enter all values in appropriate units (meters for distances, m³/s for discharge). Ensure radial distances are not equal (r₂ ≠ r₁) and all values are positive.

5. Frequently Asked Questions (FAQ)

Q1: What is the physical significance of this calculation?
A: This calculation helps determine the drawdown effect and water table elevation at different distances from a pumping well.

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

Q3: What are the limitations of this approach?
A: This approach assumes ideal aquifer conditions and may not accurately represent complex geological settings or transient flow conditions.

Q4: How does permeability affect the result?
A: Higher permeability values result in smaller differences between h₁ and h₂, as water moves more easily through the aquifer material.

Q5: Can this be used for unconfined aquifers?
A: For unconfined aquifers, a modified approach using the Dupuit-Forchheimer assumption is typically employed.