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Home/Biophysics, Fluids & Geoscience/Darcy Flow & Penetration Depth

Darcy Flow & Penetration Depth

1D head h(z,t): ∂h/∂t = K ∂²h/∂z²; recharge at surface, fixed head at depth — relaxation time and diffusion length.

Aquifer diffusion

0.08
1
1
0

Transient 1D diffusion of hydraulic head ∂h/∂t = K ∂²h/∂z² (porous medium storativity set to 1 in these units). Fixed head at top and bottom relaxes the column; √(K t) is a rough penetration scale for disturbances.

Measured values

Steps0
√(K·t) scale0.000

Live graphs

About this model

In a saturated porous medium, hydraulic head obeys a diffusion-like equation ∂h/∂t = K∇²h when storativity is normalized. Fixed-head boundaries relax the profile; the readout √(K t) hints how disturbances penetrate over time.

Who it's for: Introductory hydrogeology or transport lectures.

Key terms

  • Darcy law
  • Hydraulic conductivity
  • Groundwater
  • Diffusion

How it works

Darcy-scale groundwater relaxation: head obeys a diffusion equation in a confined column; compare hydraulic conductivity K to how quickly the profile flattens.

Frequently asked questions

Where is specific storativity?
It is absorbed into the time scaling of this toy model; focus is on shape relaxation rather than field-scale parameter identification.