Darcy's Law Calculator

Calculate groundwater flow, permeability, and hydraulic parameters using Darcy's law

Calculate Using Darcy's Law

Pressure Gradient

Pa·s

Water at 20°C: 0.001 Pa·s

Length of flow path through material

Material and Flow Parameters

m/s

Hydraulic conductivity of the material

Results

0.000e+0
Hydraulic Gradient (i)
0.000e+0
Flow Rate (m³/s)
0.000e+0
Darcy Velocity (m/s)

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

Gravel (coarse)1e-2 m/s
Sand (coarse)1e-3 m/s
Sand (medium)1e-4 m/s
Sand (fine)1e-5 m/s
Silt1e-7 m/s
Clay1e-9 m/s
Fractured rock1e-12 m/s

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