For the same dam and same soil conditions as in Problem $6,$ a $4-$m long vertical sheet pile was added as shown on the next page.

a$.$ Draw the flow net by using Nf $=3.$ Use solid lines to indicate flow lines and dashed lines to indicate equipotential lines.

b$.$ Calculate the flow rate under the dam in m$3/$day$.$

c$.$ Calculate the porewater pressure at the heal $($A$)$ and toe $($B$)$ sections of the dam based on the drawn flow net.

d$.$ Determine the porewater pressure distribution along the base of the dam.

e$.$ Calculate the resultant uplift force and its location. Use Equation $14\mathrm{.}19.($Hint: the location of the resultant force is along the centroid of the pressure distribution

diagram.$)$

f$.$ Suppose that the saturated unit weight of the soil is $18\mathrm{.}8$ kN$/$m$3.$ Do you expect the soil to become unstable at the base of the sheet pile? Justify your answer.Drawing not to scale.