Depth Of Water In Well Given Discharge In Confined Aquifer Calculator

Formula Used:

\[ h_{well} = b_w - \frac{Q \cdot \ln\left(\frac{R_w}{r}\right)}{2\pi \cdot K_{WH} \cdot b_p} \]

Aquifer Thickness (b_w):

Discharge (Q):

m³/s

Radius of Influence (R_w):

Radius of Well (r):

Coefficient of Permeability (K_WH):

m/s

Aquifer Thickness During Pumping (b_p):

Depth of Water in Well (h_well):

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1. What is the Depth of Water in Well Formula?

The formula calculates the depth of water in a well in a confined aquifer system. It's derived from the Thiem equation and accounts for aquifer properties, pumping rate, and well geometry to determine the water level in the well during pumping.

2. How Does the Calculator Work?

The calculator uses the formula:

\[ h_{well} = b_w - \frac{Q \cdot \ln\left(\frac{R_w}{r}\right)}{2\pi \cdot K_{WH} \cdot b_p} \]

Where:

\( h_{well} \) — Depth of water in well (m)
\( b_w \) — Aquifer thickness (m)
\( Q \) — Discharge rate (m³/s)
\( R_w \) — Radius of influence (m)
\( r \) — Radius of well (m)
\( K_{WH} \) — Coefficient of permeability (m/s)
\( b_p \) — Aquifer thickness during pumping (m)
\( \ln \) — Natural logarithm function

Explanation: The formula calculates the drawdown in a confined aquifer well by considering the logarithmic distribution of drawdown around the well.

3. Importance of Depth of Water Calculation

Details: Accurate calculation of water depth in wells is crucial for designing well systems, determining sustainable pumping rates, and managing groundwater resources in confined aquifers.

4. Using the Calculator

Tips: Enter all values in consistent units (meters for length, m³/s for discharge). Ensure all values are positive and physically reasonable (e.g., radius of influence should be greater than well radius).

5. Frequently Asked Questions (FAQ)

Q1: What is a confined aquifer?
A: A confined aquifer is bounded above and below by impermeable layers, with water under pressure greater than atmospheric pressure.

Q2: How is radius of influence determined?
A: Radius of influence is typically determined through pump tests or estimated based on aquifer properties and pumping duration.

Q3: What is the difference between b_w and b_p?
A: b_w is the original aquifer thickness, while b_p is the effective thickness during pumping, which may be reduced due to compression in some cases.

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

Q5: 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, with sand typically around 10⁻⁴ to 10⁻⁵ m/s.