a$.)$ Consider a $100$ cm long one$-$dimensional vertical column undergoing steady$-$state saturated flow. The datum elevation is located at the base of the column. The water table is located at the top of the column. The medium is homogeneous and has a hydraulic conductivity of $1$ cm$/$day$.$ The column is initially under hydrostatic conditions. At time t$=0,$ the top boundary is changed to cause a downward flux of $1\mathrm{.}5$ cm$/$day$.$ Plot the hydrostatic head $($x$-$axis$)$ as a function of height above the base of the column $($y$-$axis$)$ for the initial conditions, the eventual steady state, and two times when flow is transient. Explain any significant characteristics of the profiles.

b$.)$ Repeat part a$,$ replacing the constant flux top boundary condition with a constant head boundary condition. The head value at the top boundary is changed to form the same final steady state flow conditions described in part a$.$