Discharge At Edge Of Zone Of Influence Calculator

Formula Used:

\[ Q_u = \pi \cdot K \cdot \frac{(H^2 - h_w^2)}{\ln(r / R_w)} \]

Coefficient of Permeability (K):

m/s

Saturated Thickness of the Aquifer (H):

Depth of Water in the Pumping Well (h_w):

Radius at the Edge of Zone of Influence (r):

Radius of the Pumping Well (R_w):

Steady Flow of an Unconfined Aquifer (Q_u):

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1. What is the Discharge at Edge of Zone of Influence?

The Discharge at Edge of Zone of Influence refers to the steady flow rate from an unconfined aquifer, calculated using the formula that considers permeability, aquifer thickness, water depth, and radial distances from the pumping well.

2. How Does the Calculator Work?

The calculator uses the formula:

\[ Q_u = \pi \cdot K \cdot \frac{(H^2 - h_w^2)}{\ln(r / R_w)} \]

Where:

\( Q_u \) — Steady Flow of an Unconfined Aquifer (m³/s)
\( K \) — Coefficient of Permeability (m/s)
\( H \) — Saturated Thickness of the Aquifer (m)
\( h_w \) — Depth of Water in the Pumping Well (m)
\( r \) — Radius at the Edge of Zone of Influence (m)
\( R_w \) — Radius of the Pumping Well (m)
\( \pi \) — Archimedes' constant (≈3.14159)
\( \ln \) — Natural logarithm function

Explanation: This formula calculates the steady-state discharge from an unconfined aquifer, accounting for the aquifer's properties and geometric configuration.

3. Importance of Discharge Calculation

Details: Accurate discharge calculation is crucial for groundwater resource management, well design, and predicting the impact of pumping on aquifer systems.

4. Using the Calculator

Tips: Enter all values in appropriate units (meters and m/s). Ensure all values are positive and that r/Rw ≠ 1 to avoid division by zero in the logarithm.

5. Frequently Asked Questions (FAQ)

Q1: What is an unconfined aquifer?
A: An unconfined aquifer is one where the water table forms the upper boundary, and it's not confined by impermeable layers above.

Q2: Why is the natural logarithm used in this formula?
A: The natural logarithm accounts for the radial flow pattern around the pumping well, which follows logarithmic distribution.

Q3: What factors affect the coefficient of permeability?
A: Soil type, grain size distribution, porosity, and degree of saturation all influence the permeability coefficient.

Q4: How does aquifer thickness affect discharge?
A: Greater aquifer thickness generally allows for higher discharge rates, as shown by the H² term in the formula.

Q5: What are typical values for these parameters?
A: Permeability varies widely (10⁻² to 10⁻⁹ m/s), aquifer thickness typically ranges from 5-100m, and well radii are usually 0.1-0.5m.