Question $6(20$ marks$)$:

A falling$-$head hydraulic conductivity test is conducted on a $100$ mm in diameter and $20$ mm tall

clay soil specimen, using the apparatus shown in figure below. The standpipe had an inside

diameter of $5$ mm and the water level in the bath surrounding the soil specimen was $100$ mm

above the laboratory counter top. During the test, the water level in the standpipe fell from an

elevation of $500$ mm to $250$ mm above the counter top in $24$ hours.

a$)(10$ marks$)$ Compute the hydraulic conductivity of this soil specimen and comment if

this value seem reasonable? Why or why not?

b$)(10$ marks$)$ Compute the water level in the standpipe at $4$ and $12$ hours after the start of

the falling$-$head test.