$(30$ points$)$ A constant$-$head permeability test is performed in a laboratory where the soil sample is $25cm$ in length and $6c{m}^2$ in cross section. The height of water is maintained at $2ft$ at the inflow end and $6$ in$.$ at the end. The quantity of water flowing through the sample is $200mL$ in $2$ minutes.

a$.$ Compute the coefficient of permeability of the soil.

b$.$ Find the seepage loss in cubic meter per day per meter of width of the dam.

c$.$ Find the uplift force per meter of the width of the dam.