Civil Engineering: Hydrogeology, Height of a Perched Aquifer Water Table

civilstudent2

1. The problem statement, all variables and given/known data

Heavy infiltration (due to excess irrigation) of 3 cm/d causes a perched water table to form above a low permeable, flow-restricting layer. The top of the restricting layer is at a depth of 2 m, it is 0.4 m thick, and it has a K_v of 0.01 m/day. The material above the restricting layer is a silt loam with a K_v of 0.12 m/day. Coarse sand and gravel occurs below the restricting layer. After flowing through the restricting layer, the water moves as unsaturated flow through the sand and gravel to an unconfined aquifer. What is the height of the perched water table above the top of the restricting layer?


2. Relevant equations

q= constant for all layers
q = K * I = K * (dh/dL)



3. The attempt at a solution

Because of the vertical layering and conservation of mass, the q (unit flow) through each layer should be the same. I tried the following:

q = 0.03 m/day = (0.12)(dh1/dL1) = (0.01)(dh2/0.4)

my goal, I believe is to solve for dL1 (labeled as L in the attached picture). But it appears I have too many unknowns or I am missing some fundamental concept.

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