$(10$ points$)$ A sheet pile that is driven half way $(5m)$ into the soil layer with the flownet as

shown below. Assume the hydraulic conductivity is ${10}^{-4}c\frac{m}{sec}.$ The sheet pile is $13$ m long

into the paper. The thickness of the soil layer is $10$ m $.$ A head of $5$ m of water separates

both sides of the sheet pile. Determine the following:

a$)$ Compute the amount of flow under the sheet pile for its full length in units of $\frac{m^3}{s}.$

b$)$ Compute the exit gradient.

c$)$ Compute the factor of safety with respect to a quick condition $($Assume the critical

gradient $i_c=1).$