Discharge in Unconfined Aquifer with Base 10 Calculator

Formula Used:

\[ Q = \frac{1.36 \times K_{WH} \times (b_w^2 - h_w^2)}{\log_{10}\left(\frac{R_w}{r}\right)} \]

Coefficient of Permeability (K_WH):

m/s

Aquifer Thickness (b_w):

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 flow rate of groundwater using the coefficient of permeability, aquifer thickness, water depth, and well geometry. This equation is fundamental in well hydraulics for determining pumping rates and aquifer characteristics.

2. How Does the Calculator Work?

The calculator uses the formula:

\[ Q = \frac{1.36 \times K_{WH} \times (b_w^2 - h_w^2)}{\log_{10}\left(\frac{R_w}{r}\right)} \]

Where:

\( Q \) — Discharge rate (m³/s)
\( K_{WH} \) — Coefficient of permeability (m/s)
\( b_w \) — Aquifer thickness (m)
\( h_w \) — Depth of water in well (m)
\( R_w \) — Radius of influence (m)
\( r \) — Radius of well (m)

Explanation: The formula accounts for the hydraulic properties of the aquifer and the geometric configuration of the well system to estimate groundwater discharge.

3. Importance of Discharge Calculation

Details: Accurate discharge calculation is crucial for well design, groundwater resource management, contamination studies, and determining sustainable pumping rates for water supply systems.

4. Using the Calculator

Tips: Enter all values in consistent units (meters and meters/second). Ensure the radius of influence is greater than the well radius, and water depth is less than aquifer thickness for valid results.

5. Frequently Asked Questions (FAQ)

Q1: What is an unconfined aquifer?
A: An unconfined aquifer has a water table that serves as its upper boundary and is in direct contact with the atmosphere through pore spaces.

Q2: Why use base 10 logarithm in this formula?
A: The base 10 logarithm is used in this specific formulation of the discharge equation, which is derived from empirical relationships in groundwater hydrology.

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

Q4: How does aquifer thickness affect discharge?
A: Greater aquifer thickness generally allows for higher discharge rates as there is more water-bearing material available for extraction.

Q5: What are typical values for coefficient of permeability?
A: Permeability coefficients vary widely: gravel (10⁻¹-10⁻² m/s), sand (10⁻³-10⁻⁵ m/s), silt (10⁻⁶-10⁻⁸ m/s), clay (10⁻⁹-10⁻¹² m/s).