An earthen dam is constructed on an impermeable bedrock layer that is horizontal

Question

An earthen dam is constructed on an impermeable bedrock layer that is horizontal (no slope). The distance from the water in the reservoir to the tail water below the dam is 128 meters across. The hydraulic conductivity of the material used in the dam construction is 0.22 meter per day. The water in the reservoir behind the dam is 20.1 m deep and the tailwater below the dam is 1.5 meters deep. The dam at its base on top of impermeable bedrock is 200 meters wide. What is the volumetric flow rate that seeps from the reservoir, through the dam, and into the tailwater? Report you answer in units of meters and year.

Explanation / Answer

k = 0.22 m/d , h1 = 20.1 m , h2 = 1.5 m

L = 128 m

q' = K/2 * [h12 - h22 / L]

= 0.22/2 * [20.12 - 1.52 / 128] * 200 m wide

= 69.05 m3/d

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