Earth dams essentially behave as unconfined aquifers. The earthen dam depicted below is constructed to hold back contaminated water from downstream habitat(s). H₁ CLAY It is made of a homogeneous clay material with a low saturated hydraulic conductivity of K=106 m s¹ and high porosity of 0 = 0.5[-]. A cap on top of the dam prevents any vertical recharge into the dam. The steady water levels Hi and H2 are kept at 4 [m] and 1 [m], respectively, across the entire length of the dam L=5 [m], where L is the length of the clay portion of the dam shown above. a) Write down the differential equation governing the (steady-state) water table profile (piezometric head) within the clay dam. b) Integrate this equation using the boundary conditions provided to find an expression for the head profile, h(x). c) Estimate the flux Q, per unit width (i.e., w = 1(m)) of the dam using: =- dh Q=qA = q(wh) -Kh d) What is the pore-velocity of the contaminated water through the earthen dam? e) What is the travel time for contaminated water from the holding through the distance L of the earth dam? (Hint: Travel time, t distance velocity