Depth of Water in 1st Well given Confined Aquifer Discharge Calculator

Formula Used:

\[ h_1 = h_2 - \frac{Q \cdot \log_{10}\left(\frac{r_2}{r_1}\right)}{2.72 \cdot K_{WH} \cdot b_p} \]

Depth of Water 2 (h₂):

Discharge (Q):

m³/s

Radial Distance at Observation Well 2 (r₂):

Radial Distance at Observation Well 1 (r₁):

Coefficient of Permeability (K_WH):

m/s

Aquifer Thickness During Pumping (b_p):

Depth of Water 1 (h₁):

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1. What is the Depth of Water in 1st Well given Confined Aquifer Discharge Formula?

The formula calculates the depth of water in the first observation well for a confined aquifer system, considering the discharge rate, permeability coefficient, aquifer thickness, and radial distances from the pumping well.

2. How Does the Calculator Work?

The calculator uses the formula:

\[ h_1 = h_2 - \frac{Q \cdot \log_{10}\left(\frac{r_2}{r_1}\right)}{2.72 \cdot K_{WH} \cdot b_p} \]

Where:

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

Explanation: This formula is derived from the Thiem equation for steady-state flow to a well in a confined aquifer, accounting for the logarithmic drawdown distribution.

3. Importance of Depth of Water Calculation

Details: Accurate calculation of water depth in observation wells is crucial for determining aquifer characteristics, predicting drawdown patterns, and designing effective groundwater extraction systems.

4. Using the Calculator

Tips: Enter all values in appropriate units (meters for distances, m³/s for discharge). Ensure all input values are positive and radial distances are properly measured from the pumping well center.

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: Why use logarithmic function in the formula?
A: The logarithmic function accounts for the radial flow pattern where drawdown decreases logarithmically with distance from the pumping well.

Q3: What is the significance of the constant 2.72?
A: The constant 2.72 is approximately equal to e (Euler's number) and appears in the derivation of the Thiem equation for confined aquifers.

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

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).