Darcy's Law Calculator
Calculate groundwater flow, permeability, and hydraulic parameters using Darcy's law
Calculate Using Darcy's Law
Pressure Gradient
Water at 20°C: 0.001 Pa·s
Length of flow path through material
Material and Flow Parameters
Hydraulic conductivity of the material
Results
Darcy's Law: Q = k × i × A
Hydraulic Gradient: i = Δp / (μ × L)
Pressure Difference: 0 Pa
Example Calculation
Groundwater Flow Through Sand
Problem: Water flows through a sand layer
Inlet pressure: 150,000 Pa
Outlet pressure: 100,000 Pa
Flow distance: 10 m
Cross-sectional area: 2 m²
Sand permeability: 1×10⁻⁴ m/s
Water viscosity (20°C): 0.001 Pa·s
Solution
1. Hydraulic gradient: i = (150,000 - 100,000) / (0.001 × 10) = 5×10⁶ m⁻¹
2. Flow rate: Q = k × i × A = 1×10⁻⁴ × 5×10⁶ × 2
Q = 1.0 m³/s
3. Darcy velocity: v = Q/A = 1.0/2 = 0.5 m/s
Typical Soil Permeabilities
Note: Permeability values can vary significantly within each soil type
Key Concepts
Darcy's law applies to laminar flow through porous media
Higher permeability = easier fluid flow
Hydraulic gradient drives the flow
Temperature affects fluid viscosity
Understanding Darcy's Law
What is Darcy's Law?
Darcy's law describes the flow of fluids through porous media. It states that the flow rate is proportional to the hydraulic gradient and the cross-sectional area, and inversely proportional to the material's resistance to flow.
Applications
- •Groundwater flow analysis and well design
- •Soil permeability testing and characterization
- •Filtration system design and optimization
- •Environmental remediation and contaminant transport
Formula Explanation
Q = k × i × A
i = Δp / (μ × L)
- Q: Flow rate (m³/s)
- k: Permeability coefficient (m/s)
- i: Hydraulic gradient (dimensionless)
- A: Cross-sectional area (m²)
- Δp: Pressure difference (Pa)
- μ: Dynamic viscosity (Pa·s)
- L: Flow path length (m)
Note: Darcy's law assumes steady, laminar flow through a homogeneous, isotropic porous medium.
Flow Types in Porous Media
Laminar Flow
Slow, ordered flow where Darcy's law applies directly
Turbulent Flow
High-velocity flow with non-linear behavior
Mixed Flow
Combination of laminar and turbulent characteristics