Discharge In Unconfined Aquifer Calculator

Formula Used:

\[ Q = \frac{\pi \cdot K_{WH} \cdot (H^2 - h_w^2)}{\ln\left(\frac{R_w}{r}\right)} \]

Coefficient of Permeability (K_WH):

m/s

Thickness of Aquifer (H):

Depth of Water (h_w):

Radius of Influence (R_w):

Radius of Well (r):

Discharge (Q):

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1. What is the Discharge in Unconfined Aquifer Formula?

The discharge formula for unconfined aquifers calculates the rate of groundwater flow using the Dupuit-Forchheimer assumption. It provides an estimate of the discharge rate from a well in an unconfined aquifer system.

2. How Does the Calculator Work?

The calculator uses the formula:

\[ Q = \frac{\pi \cdot K_{WH} \cdot (H^2 - h_w^2)}{\ln\left(\frac{R_w}{r}\right)} \]

Where:

\( Q \) — Discharge rate (m³/s)
\( K_{WH} \) — Coefficient of permeability (m/s)
\( H \) — Thickness of unconfined aquifer (m)
\( h_w \) — Depth of water in the well (m)
\( R_w \) — Radius of influence (m)
\( r \) — Radius of well (m)
\( \pi \) — Mathematical constant pi (≈3.1416)
\( \ln \) — Natural logarithm function

Explanation: The formula accounts for the hydraulic properties of the aquifer and well geometry to estimate the discharge rate.

3. Importance of Discharge Calculation

Details: Accurate discharge calculation is crucial for well design, groundwater resource management, and determining sustainable extraction rates from unconfined aquifers.

4. Using the Calculator

Tips: Enter all values in appropriate units (meters and meters/second). Ensure that radius of influence is greater than radius of well, and aquifer thickness is greater than water depth.

5. Frequently Asked Questions (FAQ)

Q1: What is an unconfined aquifer?
A: An unconfined aquifer is a groundwater system where the water table forms the upper boundary and is free to rise and fall.

Q2: How is coefficient of permeability determined?
A: It is typically determined through pumping tests, laboratory tests, or estimated from soil properties and grain size distribution.

Q3: What is radius of influence?
A: The distance from the well center to the point where drawdown becomes negligible and the water table remains unaffected by pumping.

Q4: What are the limitations of this formula?
A: The formula assumes homogeneous isotropic aquifer, steady-state conditions, and negligible vertical flow components (Dupuit-Forchheimer assumptions).

Q5: When should this formula not be used?
A: For confined aquifers, anisotropic conditions, or when the basic assumptions of the Dupuit-Forchheimer theory are not satisfied.