Discharge Through Each Well When Interference Among Three Well Is Present Calculator

Formula Used:

\[ Q = \frac{2\pi K b_p (b_w - h_w)}{\ln\left(\frac{R^3}{r' B^2}\right)} \]

Coefficient of Permeability (K):

m/s

Aquifer Thickness During Pumping (bₚ):

Aquifer Thickness (b_w):

Depth of Water (h_w):

Radius of Influence (R):

Radius of Well (r'):

Distance Between Well (B):

Discharge (Q):

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1. What Is Discharge Through Each Well When Interference Among Three Well Is Present?

This calculation determines the discharge rate from each well when three wells are operating simultaneously and interfering with each other's flow patterns. The interference effect reduces the individual well's discharge capacity compared to when operating alone.

2. How Does The Calculator Work?

The calculator uses the formula:

\[ Q = \frac{2\pi K b_p (b_w - h_w)}{\ln\left(\frac{R^3}{r' B^2}\right)} \]

Where:

\( Q \) — Discharge from each well (m³/s)
\( K \) — Coefficient of permeability (m/s)
\( b_p \) — Aquifer thickness during pumping (m)
\( b_w \) — Aquifer thickness (m)
\( h_w \) — Depth of water in the well (m)
\( R \) — Radius of influence (m)
\( r' \) — Radius of well (m)
\( B \) — Distance between wells (m)
\( \pi \) — Mathematical constant pi (≈3.1416)
\( \ln \) — Natural logarithm function

Explanation: This formula accounts for the interference effects between three wells by incorporating the distance between wells and their combined influence on the aquifer's flow characteristics.

3. Importance Of Discharge Calculation

Details: Accurate discharge calculation is crucial for designing well fields, optimizing water extraction systems, and preventing over-pumping that could lead to aquifer depletion or land subsidence.

4. Using The Calculator

Tips: Enter all parameters in consistent units (meters and m/s). Ensure that aquifer thickness values are positive and that the depth of water does not exceed the aquifer thickness. All distance measurements should be positive values.

5. Frequently Asked Questions (FAQ)

Q1: What Causes Interference Between Wells?
A: Interference occurs when multiple wells draw water from the same aquifer, creating overlapping cones of depression that reduce each well's effective drawdown and discharge capacity.

Q2: How Does Well Spacing Affect Discharge?
A: Closer well spacing increases interference effects, reducing individual well discharge. Optimal spacing minimizes interference while maximizing total water extraction.

Q3: What Is The Radius Of Influence?
A: The distance from the well center to where drawdown becomes negligible, typically where the water table returns to its pre-pumping level.

Q4: When Is This Formula Most Applicable?
A: This formula applies to confined aquifers with three equally spaced wells where the interference pattern is symmetrical and steady-state conditions prevail.

Q5: What Are The Limitations Of This Calculation?
A: The formula assumes homogeneous aquifer properties, steady-state flow, and perfect well construction. Real-world conditions with heterogeneous aquifers or varying well efficiencies may require adjustments.