A salt solution fills the up-gradient constant head reservoir in the "ant farm" model shown below. The soil in the model has a hydraulic conductivity of 200 m/day. The concentration of salt in the injected solution is 1 gram/liter. Water flows through the model in response to a hydraulic gradient of 0.25 ft/ft. Dispersivity in the flow direction is 0.36 inches. Dispersivity in transverse directions is 1/10^th that amount. Assume that the effective porosity (ne) is 0.23 and the molecular diffusion (D*) is 1.55 x 10^-6 in²/sec.



What concentration would we expect to see if a water sample a piezometer 16 inches to the right of the reservoir after 2 1/2 minutes?

For your convenience, I include the appropriate expression here:

where:
C_o = source concentration [M/L³]
C = concentration [M/L³]
x = distance from the source in the direction of flow
= average linear velocity of ground water [L/T ]
t = time since continuous concentration release began [ T ]
D_x = dispersion coefficient in the x direction [L²/T ]
erfc = the complimentary error function ERFC


Calculate your answer, being extremely careful with respect to using consistent units and noticing how the answer is expressed (e.g. as Concentration or relative Concentration, then check yourself by deciding whether the answer is reasonable, and visiting the key. If you want to know if your answer is correct before viewing the key, click answer for the value.