Discharge when Two Observation Well is Taken Calculator

Formula Used:

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

Coefficient of Permeability (K_WH):

m/s

Depth of Water 1 (h₁):

Depth of Water 2 (h₂):

Radial Distance at Well 1 (r₁):

Radial Distance at Well 2 (r₂):

Discharge (Q):

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1. What is the Discharge Calculation Formula?

The discharge calculation formula estimates the flow rate of groundwater between two observation wells based on the coefficient of permeability, water depths, and radial distances. This formula is essential in well hydraulics for determining aquifer characteristics.

2. How Does the Calculator Work?

The calculator uses the discharge formula:

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

Where:

\( Q \) — Discharge (m³/s)
\( \pi \) — Archimedes' constant (3.141592653589793)
\( K_{WH} \) — Coefficient of permeability (m/s)
\( h_1 \) — Depth of water in well 1 (m)
\( h_2 \) — Depth of water in well 2 (m)
\( r_1 \) — Radial distance at observation well 1 (m)
\( r_2 \) — Radial distance at observation well 2 (m)
\( \ln \) — Natural logarithm function

Explanation: The formula calculates groundwater discharge based on the difference in water levels and distances between two observation wells, considering the soil's permeability characteristics.

3. Importance of Discharge Calculation

Details: Accurate discharge calculation is crucial for groundwater resource management, well design, aquifer testing, and environmental impact assessments of water extraction projects.

4. Using the Calculator

Tips: Enter all values in appropriate units (meters and meters/second). Ensure radial distances are positive and not equal, and water depths are non-negative. All values must be valid for accurate calculation.

5. Frequently Asked Questions (FAQ)

Q1: What is the coefficient of permeability?
A: The coefficient of permeability (K_WH) describes how easily water moves through soil or rock. Higher values indicate more permeable materials.

Q2: Why use natural logarithm in the formula?
A: The natural logarithm accounts for the logarithmic distribution of drawdown around a pumping well, which is characteristic of radial flow in confined aquifers.

Q3: What are typical values for permeability coefficients?
A: Permeability varies widely: gravel (10^-1-10^-2 m/s), sand (10^-3-10^-5 m/s), clay (10^-7-10^-9 m/s).

Q4: When is this formula applicable?
A: This formula applies to steady-state radial flow to a well in a confined aquifer with homogeneous, isotropic properties and fully penetrating wells.

Q5: What are the limitations of this approach?
A: The formula assumes ideal conditions and may not account for aquifer heterogeneity, partial penetration, or transient flow conditions.