$1.$ A one$-$dimensional hydraulic conductivity test is shown in the figure below. $(10$ marks$)$

a$.$ Determine the total head, elevation head, and pressure head at the points of A$,$ B$,$ C$,$ and D$.(5$ marks$)$

b$.$ If the soil has the following properties: porosity $\backslash ($ n$=0\mathrm{.}42\backslash ),$ hydraulic conductivity $\backslash ($ k$=0\mathrm{.}025\backslash )\backslash (\backslash$mathrm$\{$cm$\}/\backslash$mathrm$\{$sec$\}\backslash ),$ and sample length $\backslash ($ l$=20\backslash$mathrm$\{$~cm$\}\backslash ),$ determine the discharge velocity and the seepage velocity for the hydraulic conductivity test. $(5$ marks$)$