Soil Mechanics / Water in soil and Darcy's law

Heads and hydraulic gradient

Water flows from high total head to low — not from high pressure to low.

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Why this matters

A common mistake is to think water flows from high pressure to low pressure. It does not — it flows from high total head to low total head. Getting heads right is the foundation of every seepage, effective-stress and consolidation calculation that follows.

What you should already know

Porewater pressure and the idea of hydrostatic pressure from the effective-stress module

The energy of water at a point is measured as a head — an equivalent height of water. Two parts matter in soils (the velocity head is negligible):

Elevation head $z$ — the height of the point above a chosen datum.
Pressure head $h_p = u/\gamma_w$ — the height the porewater would rise in a standpipe (piezometer) at that point.

Their sum is the total head:

Total head

h = z + \dfrac{u}{\gamma_w}

What it calculates: the total energy of the porewater as an equivalent height

h: total head (m)
z: elevation head above datum (m)
$u/\gamma_w$: pressure head (m)

In plain terms: Water flows from high total head to low total head. Two points can have the same pressure but different total head (different elevations) and water will still flow between them.

Hydraulic gradient

i = \dfrac{\Delta h}{L}

What it calculates: the driving force for flow — head loss per unit flow length

i: hydraulic gradient (dimensionless)
$\Delta h$: total-head loss along the path (m)
L: length of the flow path (m)

In plain terms: A steeper gradient drives faster flow. When Δh = 0 (equal total heads) there is no flow, whatever the pressures.

Predict first

Two piezometers in a soil show the SAME porewater pressure, but one tip is 1 m higher than the other. Between the two points, which way does water flow?

Summary

Total head h = elevation head z + pressure head u/γw.
Water flows from high total head to low total head, never from pressure alone.
Hydraulic gradient i = Δh/L drives the flow; i = 0 means no flow.