In a constant$-$head permeability test, a sample of soil $12$ cm long and $6$ cm in diameter discharged $1\mathrm{.}5\backslash$times $103$ m$3$ of water in $10$ minutes. The head difference in two manometers A and B located at $1$ cm and $11$ cm$,$ respectively, from the bottom of the sample is $2$ cm$.$a$)$ Determine the hydraulic conductivity of the soil.

b$)$ What is the soil type tested?