Two monitoring wells screened in the same unconfined sand aquifer are 240 m apart along the direction of flow. The measured hydraulic heads are 96.4 m and 94.0 m. The aquifer has a hydraulic conductivity of 25 m/day, a total porosity of 0.38, and an effective porosity of 0.30. The average linear (seepage) velocity of the groundwater is most nearly:
- (A)0.075 m/day
- (B)0.25 m/day
- (C)0.66 m/day
- (D)0.83 m/day
Show worked solution
Answer: (D)
Water particles advance at about 0.83 m/day, because the Darcy flux of 0.25 m/day is carried only through the 30 percent of the cross section that is interconnected pore space.
Darcy's law supplies the specific discharge, a flux referred to the gross cross-sectional area rather than a particle speed.
Seepage velocity corrects that flux for the fraction of the section actually open to transport, which is the effective porosity and not the total porosity.
FE Reference Handbook — Water Resources and Environmental Engineering: Darcy's Law
Why the other choices appear
- (A)0.075 m/day results from multiplying the Darcy flux by the effective porosity instead of dividing, (0.25)(0.30).
- (B)0.25 m/day is the Darcy flux Ki reported directly, with the porosity correction omitted.
- (C)0.66 m/day divides the flux by the total porosity 0.38 rather than by the effective porosity 0.30.