Assigned: Monday $02/12/24$Due: Monday $5$ pm$,02/26/24$

$(20pt)$ Three productive aquifers overlie each other separated by thin aquitards. Extensive pumping in the upper fresh water aquifer by the municipality of Thirsty City, TX$,$ has lowered the average hydraulic head throughout the region. This has created concerns that the pumping may have reversed the natural downward vertical gradient $($favoring flow downwards$)$ to upward. Water level measurements indicated that there is still a strong downward gradient however some private well owners are complaining of brackish water in their shallow wells. a$)$ Determine the orientation $($up or down$)$ and magnitude of the vertical hydraulic gradient between the fresh and brackish aquifers, and between the brackish and brine aquifers. b$)$ With the current state of hydraulic heads, how long would it take for brackish water to cross the aquitard separating the fresh and brackish aquifers? c$)$ given the information provided here, if the urban pumping only began $30$ years ago and has been relative constant since, can the urban pumping be responsible for people's wells turning brackish? The thickness of the upper and lower

a$)$

$\frac{dh}{dz}=\frac{92-91}{60-20}=\frac{1}{40}=0\mathrm{.}025$

$\frac{dh}{?}$