Module 14 · Lesson 14.2

Using a flow net

The seepage flow rate and pore pressure from the net.

Why this matters

A flow net answers the two questions a designer of a dam or an excavation must ask: how much water seeps through (for pumping and stability), and what is the pore pressure at any point (for effective stress and uplift). Both come straight from the counts $N_{f}$ and $N_{d}$ .

From first principles

The flow-net flow rate

We want to show: Get the total seepage per unit width from the geometry of the net alone.

Every square in the net carries the same little bit of flow, because it has the same head drop across it and the same shape. Add up the squares and the flow rate falls out in terms of just Nf, Nd and k.

Pore pressure at a point follows from counting drops. If a point lies $n_{d}$ drops down from the upstream boundary, its total head is $h_{u p} - n_{d} Δ h$ . Subtract the elevation head to get the pressure head, and multiply by $γ_{w}$ for the pore pressure — which then feeds straight into effective stress (Module 8) and uplift on the structure.

Try it

Flow-net explorer

Seepage beneath a sheet-pile cutoff. Set the head, soil and net, and read the flow rate and the margin against piping.

Total head loss h6.0 m

Permeability k1e-6 m/s

Flow channels Nf4

Equipotential drops Nd12

Exit-square length l1.5 m

Flow rate q = k·h·Nf/Nd: 2.00e-6 m³/s/m
Head per drop Δh = h/Nd: 0.50 m
Exit gradient i_exit: 0.33
Critical gradient i_cr: 1.00
FoS piping F = i_cr/i_exit: 3.0

Flow 2.0e-6 m³/s per m; exit gradient 0.33 against a critical 1.00 gives a factor of safety of 3.0 — safe against piping.

Worked example

Seepage beneath a sheet-pile wall

Given

Total head loss across the wall h = 6 m
Soil permeability k = 1 × 10⁻⁶ m/s
Flow net: Nf = 4 flow channels, Nd = 12 equipotential drops

Find

The seepage flow rate per metre width, and the head loss per drop.

Assumptions

Homogeneous, isotropic soil; a properly drawn square flow net; steady state.

Practice

A flow net beneath a dam has Nf = 5 and Nd = 15, with a head loss h = 9 m and k = 2 × 10⁻⁶ m/s. What is the seepage flow rate per metre width, in m³/s/m?

Summary

Seepage flow rate from a flow net: q = k·h·(Nf/Nd) — derived from Darcy's law on one square.
The square side cancels, so only the counts Nf and Nd and the permeability and head matter.
Total head at a point = upstream head − (drops passed)·Δh; subtract elevation head for pore pressure.
Pore pressure from the net feeds directly into effective stress and uplift.

Progress is kept in this browser only.

This is educational material. It uses simplified examples to teach principles, and must not be relied on for real design or safety-critical decisions. Module overview and checkpoint