A falling$-$head hydraulic conductivity test has been conducted on a specimen of clay that is considered to be used as a liner for the landfill. The clay specimen was $4$ inches in diameter and $1-$inch tall. The standpipe had an inside diameter of $0\mathrm{.}25$ in$.$ The water in the bath surrounding the specimen was $5$ inches above the laboratory counter top and the water level in the standpipe fell from a height of $20$ inches to $10$ inches above the counter top in $38$ hours and $12$ minutes. Compute the hydraulic conductivity in $f\frac{t}{s}.[5$ points$]$