$(15$ pts$)$ Problem $5.$

A falling head test was performed on the setup shown below. The water reservoir connected to the top of the soil has a diameter of $6$ cm and

the elevation is maintained at $3$ cm above the sample $($see Figure $1).$ The water reservoir connected to the bottom of the soil has a diameter of

$2$ cm $.$ The soil sample has a diameter of $6$ cm $,$ a length of $55$ cm $,$ and a saturated unit weight of $20k\frac{N}{m^3}.$ When the test started, the difference

in elevation between the two reservoirs was $80cm$;$25$ minutes later, the difference in elevation decreased to $50$ cm $.$ Each porous stone is $1$ cm

thick.

a$)$ What is the hydraulic conductivity of the soil in $c\frac{m}{s}?$

b$)$ What is the difference in elevation between both reservoirs $40$ minutes after the test started?

c$)$ Would you use the constant head test for this soil? Why, or why not?