Flow Through Any Square Using Darcy's Law For Groundwater Flow Nets Calculator

Formula Used:

\[ Q = K \times w \times b \times \frac{dh}{dl} \]

Hydraulic Conductivity (K):

m/s

Distance Between Flow Lines (w):

Aquifer Thickness (b):

Difference in Head Between Equipotential Lines (dh):

Distance Between Equipotential Lines (dl):

Total Discharge (Q):

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1. What Is Darcy's Law For Groundwater Flow Nets?

Darcy's Law describes the flow of groundwater through porous media. For flow nets, it calculates the total discharge through any square in the flow net using hydraulic conductivity, aquifer dimensions, and head differences.

2. How Does The Calculator Work?

The calculator uses Darcy's Law formula:

\[ Q = K \times w \times b \times \frac{dh}{dl} \]

Where:

\( Q \) — Total discharge (m³/s)
\( K \) — Hydraulic conductivity (m/s)
\( w \) — Distance between flow lines (m)
\( b \) — Aquifer thickness (m)
\( dh \) — Difference in head between equipotential lines (m)
\( dl \) — Distance between equipotential lines (m)

Explanation: The formula calculates groundwater flow through a specific square in a flow net by considering the hydraulic gradient and material properties.

3. Importance Of Total Discharge Calculation

Details: Accurate discharge calculation is crucial for groundwater resource management, contaminant transport studies, and designing dewatering systems for construction projects.

4. Using The Calculator

Tips: Enter all values in consistent units (meters and m/s). Ensure all values are positive and physically reasonable for accurate results.

5. Frequently Asked Questions (FAQ)

Q1: What is a flow net in groundwater hydrology?
A: A flow net is a graphical representation of two-dimensional steady-state groundwater flow through porous media, consisting of flow lines and equipotential lines.

Q2: How does hydraulic conductivity affect discharge?
A: Higher hydraulic conductivity values result in greater discharge rates, as the material allows water to flow more easily through it.

Q3: What are typical values for hydraulic conductivity?
A: Hydraulic conductivity varies widely: gravel (10⁻²-10⁻¹ m/s), sand (10⁻⁵-10⁻³ m/s), clay (10⁻⁹-10⁻⁶ m/s).

Q4: When is this calculation most applicable?
A: This calculation is most applicable for steady-state, laminar flow through homogeneous, isotropic porous media.

Q5: What are the limitations of Darcy's Law?
A: Darcy's Law assumes laminar flow and may not be accurate for very high flow velocities, fractured rock, or non-Newtonian fluids.