Depth Of Water In 2nd Well Given Confined Aquifer Discharge Calculator

Formula Used:

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

Depth of Water 1 (h₁):

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 2 (h₂):

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1. What is the Depth Of Water In 2nd Well Given Confined Aquifer Discharge Formula?

The formula calculates the depth of water in the second well based on the confined aquifer discharge and various hydraulic parameters. It is derived from the Thiem equation for steady-state flow to a well in a confined aquifer.

2. How Does the Calculator Work?

The calculator uses the formula:

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

Where:

\( h_2 \) — Depth of water in 2nd well (m)
\( h_1 \) — Depth of water in 1st 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: The formula accounts for the logarithmic distribution of drawdown in a confined aquifer under steady-state conditions.

3. Importance of Depth Calculation

Details: Accurate calculation of water depth in observation wells is crucial for determining aquifer characteristics, designing well fields, and managing groundwater resources effectively.

4. Using the Calculator

Tips: Enter all parameters in consistent units (meters and m³/s). Ensure radial distances are measured from the pumping well center, and all values are positive.

5. Frequently Asked Questions (FAQ)

Q1: What is the significance of the 2.72 constant?
A: The constant 2.72 represents 2π/ln(10), which converts natural logarithms to base-10 logarithms in the formula derivation.

Q2: When is this formula applicable?
A: This formula applies to confined aquifers under steady-state conditions with fully penetrating wells and homogeneous, isotropic aquifer properties.

Q3: What are typical ranges for coefficient of permeability?
A: Permeability coefficients range from 10⁻² m/s for gravel to 10⁻⁹ m/s for clay, with most aquifers falling between 10⁻⁴ to 10⁻⁶ m/s.

Q4: How does radial distance affect the calculation?
A: Water depth increases logarithmically with distance from the pumping well due to decreasing drawdown effects.

Q5: What are the limitations of this approach?
A: The formula assumes ideal conditions and may not account for aquifer heterogeneity, partial penetration, or transient effects.