Q$4($a$)$ Derive an expression for ${}_{\text{s}\text{a}\text{t}}$ in terms of $e,{}_{\text{a}\text{l}\text{e}\text{p}\text{h}},$ and $G_{s.}$

$($b$)$ The specific gravity of moist clay soil is $2\mathrm{.}6$ and the void ratio is $0\mathrm{.}4.$ Determine the

moist unit weight $(k\frac{N}{m^3}),$ dry unit weight $(k\frac{N}{m^3}),$ moisture content $(\%)$ and

porosity.

$($c$)$ List FIVE $(5)$ factors affecting the hydraulic conductivity of soils.

$($d$)$ A certain $20m$ thick sandy confined aquifer has a permeability of $2\mathrm{.}4{10}^{-2}c\frac{m}{s}$ and

a void ratio of $0\mathrm{.}91.$ Groundwater is flowing through this aquifer with a hydraulic

gradient of $0\mathrm{.}0065.$ Determine the time $($in hours$)$ required for water to travel $0\mathrm{.}5km$

through this aquifer