Given a flow net under a $400m$ long $40m$ wide concrete dam and the hydraulic conductivity of soil

below the dam is $k=0\mathrm{.}1$ m$/$day$.$

a$)$ Calculate the quantity of water seeping under the dam in $1$ day

b$)$ Calculate the uplift force for the dam. Hint: Assume a linear pressure distribution from $A$ to $F$

c$)$ Calculate the actual seepage velocity of water at point $P$ if the porosity of soil is $n=0\mathrm{.}3$

d$)$ Calculate the factor of safety against piping at point $P$ if the soil parameters are $Gs=2\mathrm{.}7$ and $e_0=0\mathrm{.}4$