Meaning and mechanism
Hydraulic head expresses the combined effects of elevation and pressure as a length. Spatial differences in hydraulic head, rather than ground-surface slope alone, determine groundwater flow.
Greater hydraulic conductivity allows more water to flow under the same hydraulic-head gradient. A pumping well changes the surrounding head and flow lines, affecting contaminant transport paths.
Relationships and conditions
Darcy flux is q=−K∇h, while mean pore-water velocity in a simple model is v=q/n. Because the latter divides by porosity n, the two velocities are generally different.
Real contaminant transport also depends on adsorption, reactions, heterogeneous strata, and dispersion. The simulation’s arrival time applies to its specified concentration threshold and hypothetical aquifer conditions.
What to observe in the simulation
The water flows toward the lower head and gathers around the well. The arrival time of contamination varies depending on the flow rate, location, diffusion, and pumping conditions.
The model uses a 40×20 grid with 5 m spacing, 1 m thickness, uniform K, porosity n=0.25, and diffusion coefficient 0.2 m²/day. Hydraulic head is fixed at 11.95/10 m on the left/right; the top and bottom boundaries are impermeable. Steady head is solved with up to 12 iterations per update, stopping after 1800 total iterations or a change below 1e-8 m. Upwind advection and conservative diffusion use stable time substeps. Arrival time is a model result for a 0.01 kg threshold in the well cell, not an observational prediction. Reactions, adsorption, and heterogeneous layers are omitted.
Key relationships and symbols
q=−K∇h · v=q/n · n=0.25
| Symbol | Meaning | Unit |
|---|---|---|
| K | Hydraulic conductivity | m/day, for example |
| h | Hydraulic head | m |
| n | Porosity | 0~1 |
Worked example
What if K=10 m/day, head gradient magnitude 0.01, and n=0.25?
The size of the flow velocity is K × slope = 0.1 m/day and the actual flow velocity is q/n = 0.4 m/day. The time for uniform straight flow is distance/speed.
Common misconceptions
- The groundwater does not always flow like a river along the large, open channel within the ground.