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

[civilstudent2]

Homework Statement

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?

Homework Equations

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

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.

 

[KataKoniK]

Dear fellow scientist,

Thank you for sharing your attempt at solving this problem. I agree with your approach of using the equation q=K*I to solve for the height of the perched water table.

However, I believe you have made a small mistake in your calculation. The equation should be:

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

This is because the permeability values (K) are given in units of m/day, so they should be multiplied by the units of flow (m/day) to get the actual flow rate (q).

Using this corrected equation, you should be able to solve for the height of the perched water table (dh1). Let me know if you have any further questions or if this solution does not work for you.