Question: (70 points) In class we discussed in some detail the case of one-dimensional steady flow in a confined aquifer bounded by two rivers. In this problem we consider the added complication where the aquifer thickness is not constant. A schematic is shown below for the case where the aquifer thickness varies from 10 meters to 20 meters along the direction of flow according to the equation:

\[

b(x)=\frac{b_{0}}{1-0.5 x / L}

\]

Where \( b_{0} \) is the aquifer thickness at \( x=0 \) and is equal to 10 meters. \( H_{0}=100 \mathrm{~m}, H_{L}=90 \mathrm{~m} \), and the steady flow. (10 points)

b) Is the flow uniform (i.e., velocity is constant over space) or nonuniform? Explain. (10 points)

c) Solve the governing equation for the head \( h(x) \) and the vertically averaged flow rate \( q \). Note: This will require you to perform a simple integration. ( 20 points)

d) Comment briefly on how your results in part (c) compare with those derived in class for the case of a constant aquifer thickness. ( 15 points)

e) Can you define an “effective” uniform transmissivity (or an “effective” uniform thickness) for this case? ( 15 points)