QUESTION

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A creek flows above the ground surface until it gets to an aquifer when it infiltrates and begins to flow underground. The outlet structure for the chambers is $L_{2} \mathrm{~m}$ long, $W_{2} \mathrm{~m}$ wide and $A \mathrm{~m}$ tall. The aquifer upstream of the outlet is $L_{1} \mathrm{~m}$ long, $W_{1} \mathrm{~m}$ wide and has a variable depth of water in it given by $h$. The aquifer is managed such that $h$ is always greater than $H$. The flow per cross-sectional area through the outlet structure $\left(q_{\text {out }}\right)$ is directly proportional to the difference in the depth of water between the aquifer and the outlet structure $(h-H)$ and inversely proportional to the length of the outlet structure. Call the total flow leaving the outlet structure $Q_{\text {out. }}$.


Neglect rainfall and evaporation from the aquifer and assume $L_{1}>>L_{2}$ and $W_{1}>W_{2}$. Write a water balance for the aquifer in terms of the rate of change of $h$. Check the units in your final expression. Follow the step by step guide for a water balance laid out in class. If $Q_{\text {in }}$ is equal to zero, sketch a plot of the storage over time in the aquifer, assuming it started with a depth of $h=10 \mathrm{H}$.

Please answer both a and b, thank you!!

Public Answer

SG2PL4 The First Answerer