Mean Velocity Using Darcy's Law Calculator

Darcy's Law Formula:

\[ V_{mean} = k \times H \]

Mean Velocity (V_mean):

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1. What is Darcy's Law?

Darcy's Law is a fundamental equation in hydrogeology that describes the flow of water through porous media. It states that the flow rate is proportional to the hydraulic gradient and the permeability of the medium.

2. How Does the Calculator Work?

The calculator uses Darcy's Law formula:

\[ V_{mean} = k \times H \]

Where:

\( V_{mean} \) — Mean velocity (m/s)
\( k \) — Coefficient of permeability (m/s)
\( H \) — Hydraulic gradient (dimensionless)

Explanation: The equation calculates the average velocity of groundwater flow through porous media based on the medium's permeability and the hydraulic gradient.

3. Importance of Mean Velocity Calculation

Details: Calculating mean velocity is crucial for understanding groundwater flow patterns, contaminant transport, and designing effective groundwater remediation systems.

4. Using the Calculator

Tips: Enter coefficient of permeability in m/s and hydraulic gradient (dimensionless). Both values must be positive numbers.

5. Frequently Asked Questions (FAQ)

Q1: What is the coefficient of permeability?
A: The coefficient of permeability (k) is a measure of how easily water can flow through a porous medium. It depends on the properties of both the fluid and the porous material.

Q2: How is hydraulic gradient defined?
A: Hydraulic gradient is the change in hydraulic head per unit distance in the direction of flow. It's a dimensionless quantity that drives groundwater flow.

Q3: What are typical values for permeability coefficients?
A: Permeability coefficients vary widely: gravel (10^-1-10^-2 m/s), sand (10^-3-10^-5 m/s), clay (10^-7-10^-9 m/s).

Q4: What are the limitations of Darcy's Law?
A: Darcy's Law applies to laminar flow in saturated porous media. It may not be accurate for very high flow velocities, unsaturated conditions, or in fractured media.

Q5: How does mean velocity relate to actual groundwater velocity?
A: Mean velocity represents the average linear velocity. Actual groundwater velocity is higher due to the tortuous path water takes through pore spaces.