Seawater intrusion in coastal aquifers is a widespread and serious problem in many parts of the world. Groundwater degradation due to seawater intrusion is often accentuated in small island aquifers due to overpumping or limited replenishing amounts of precipitation. Solve the following problem analytically and using MAGNET, assuming that a sharp interface exists between the fresh water and salt water.

An unconfined aquifer shown in the vertical section below receives recharge at a constant rate E. Find the steady state water table elevation h(x) and the depth to the sea water interface H(x). The aquifer is homogeneous with hydraulic conductivity K.

Hint: H(x) = α h(x),  where α depends on the density difference. Derive this factor based on the hydrostatic force balance in the vertical direction at fresh-saline groundwater interface.