For laminar flow through saturated soil, the discharge velocity ($v$) is proportional to the hydraulic gradient ($i$). $v = ki$ Flow Rate ($q$): $q = vA = kiA$

• $k$: Coefficient of permeability (hydraulic conductivity).
• $i$: Hydraulic gradient ($\Delta h / L$).
• $A$: Cross-sectional area perpendicular to flow.

The actual velocity of water moving through the voids is higher than the discharge velocity. $v_s = \frac{v}{n} = \frac{v(1+e)}{e}$ Where $n$ is porosity.

Used for coarse-grained soils (high permeability). $k = \frac{QL}{A h t}$

• $Q$: Volume of water collected.
• $L$: Length of specimen.
• $h$: Constant head difference.
• $t$: Time.

Used for fine-grained soils (low permeability). $k = 2.303 \frac{aL}{At} \log_{10} \left( \frac{h_1}{h_2} \right)$

• $a$: Area of standpipe.
• $A$: Area of soil specimen.
• $h_1, h_2$: Initial and final heads.

A graphical representation of 2D flow.

• Flow Lines: Paths followed by water particles.
• Equipotential Lines: Lines of constant total head. Seepage Quantity ($q$): $q = k H \frac{N_f}{N_d}$
• $H$: Total head loss.
• $N_f$: Number of flow channels.
• $N_d$: Number of potential drops.