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Discharge velocity vs seepage velocity

Short answer

Discharge velocity is Q divided by total cross-sectional area, a fictitious average velocity; seepage velocity is Q divided by void area, the actual pore velocity. Seepage velocity equals discharge velocity divided by porosity and is always larger.

Differentiate between discharge velocity and seepage velocity when water flows through the soil.

Discharge velocity $v$ is the quantity of water flowing per unit time through a unit gross cross-sectional area of the soil (solids plus voids). Seepage velocity $v_s$ is the actual velocity of water through the void space, which is only a part of the area.

v = \frac{Q}{A}, \qquad v_s = \frac{Q}{A_v} = \frac{v}{n}

where $A_v = nA$ is the area of voids and $n$ is porosity.

Point	Discharge velocity	Seepage velocity
Area used	Gross area $A$	Void area $A_v$
Formula	$v = ki$	$v_s = v/n = ki/n$
Nature	Fictitious (average) velocity	Actual velocity in pores
Magnitude	Smaller	Larger, since $n<1$
Use	Computing discharge $Q = vA$	Time of travel of water or contaminant

✓ Answer checked by Claude Opus 5.5 (high effort)

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