For a falling$-$head permeability test, the following are given.

Length of the soil specimen $=670mm$

Area of the soil specimen $=15c{m}^2$

Area of the standpipe $=1\mathrm{.}05c{m}^2$

Head difference at time $t=0$ is $800mm$

Head difference at time $t=8$min is $400mm$

Assume that the test was conducted at $20C,$ and at $20C,{}_w=9\mathrm{.}789k\frac{N}{m^3},$ and $=1\mathrm{.}005{10}^{-3}N*\frac{s}{m^2}.$

$($a$)$ Determine the absolute permeability of the soil $($in $c{m}^2).$

Your response differs significantly from the correct answer. Rework your solution from the beginning and check each step carefully. $c{m}^2$

$($b$)$ What is the head difference $($in $mm)$ at time $t=6$min $?$

Your response differs from the correct answer by more than $10\%.$ Double check your calculations. $mm$