Discharge from Two Wells with Base 10 Calculator

Formula Used:

\[ Q = \frac{1.36 \times K_{WH} \times (h_2^2 - h_1^2)}{\log_{10}\left(\frac{r_2}{r_1}\right)} \]

Coefficient of Permeability (K_WH):

m/s

Depth of Water 2 (h₂):

Depth of Water 1 (h₁):

Radial Distance at Well 2 (r₂):

Radial Distance at Well 1 (r₁):

Discharge (Q):

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1. What is the Discharge from Two Wells Formula?

The discharge from two wells formula calculates the rate of flow between two wells in an aquifer system. It's based on the principle of radial flow to wells and uses logarithmic relationships to determine the discharge rate.

2. How Does the Calculator Work?

The calculator uses the formula:

\[ Q = \frac{1.36 \times K_{WH} \times (h_2^2 - h_1^2)}{\log_{10}\left(\frac{r_2}{r_1}\right)} \]

Where:

\( Q \) — Discharge rate (m³/s)
\( K_{WH} \) — Coefficient of permeability (m/s)
\( h_2 \) — Depth of water in well 2 (m)
\( h_1 \) — Depth of water in well 1 (m)
\( r_2 \) — Radial distance at observation well 2 (m)
\( r_1 \) — Radial distance at well 1 (m)

Explanation: The formula accounts for the difference in water depths and the logarithmic distribution of drawdown between two observation points.

3. Importance of Discharge Calculation

Details: Accurate discharge calculation is crucial for groundwater resource management, well field design, contamination studies, and sustainable water extraction planning.

4. Using the Calculator

Tips: Enter all values in consistent units (meters and m/s). Ensure radial distances are measured from the pumping well center, and water depths are measured from a common datum.

5. Frequently Asked Questions (FAQ)

Q1: What is the significance of the 1.36 constant?
A: The constant 1.36 is derived from the integration of the flow equation and conversion factors for base-10 logarithms in the well hydraulics formulation.

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

Q3: What are typical values for coefficient of permeability?
A: Permeability values range from 10⁻² m/s for gravel to 10⁻⁹ m/s for clay. The specific value depends on the aquifer material.

Q4: What if r2 equals r1?
A: The formula becomes undefined when r2 equals r1 because log₁₀(1) = 0, causing division by zero. Radial distances must be different.

Q5: How does water depth affect discharge?
A: Discharge is proportional to the difference of squares of water depths (h₂² - h₁²), making it sensitive to changes in water table levels.