A constant$-$head permeameter has a cross$-$ sectional area of $78\mathrm{.}5$ cm$2.$ The sample is $23$ cm long. At a head of $3\mathrm{.}4$ cm$,$ the permeameter discharges $50$ cm$3$ in $38$ s$.$

a$.$ What is the hydraulic conductivity in centimeters per second and feet per day?

b$.$ What is the intrinsic permeability if the hydraulic conductivity was measured at $15\backslash$deg C$?$

c$.$ From the hydraulic conductivity value, name the type of soil.