In your geotech lab, you perform a constant head test on a sample from an aquifer with the setup shown below, where the diameter of the sample is $8$ in and the length is $16$ in $.$

a$.$ Following the test, you calculate from the graduated cylinder and the stopwatch that the volumetric flow rate was $4\mathrm{.}55{10}^{-2}i\frac{n^3}{s}$ for a hydraulic head of $20$ in at the top of the specimen and a hydraulic head of $0$ at the outlet. Determine the hydraulic conductivity of the soil

b$.$ You also measure that the effective flow area through the pores is $20i{n}^2,$ Determine the effective porosity.

c$.$ If the confined aquifer is between EL$.528\mathrm{.}5$ ft MSL and EL$.278\mathrm{.}5$ ft MSL$,$ for a unit crosssectional width of $1$ ft and a hydraulic gradient of $0\mathrm{.}5,$ determine the volumetric flow rate of the groundwater in $f\frac{t^3}{s}.$

d$.$ Determine the time it takes to travel from proposed observation well $1$ to the drinking wate well at the middle school near TSU if the total distance between them would be $0\mathrm{.}5$ miles.