The following data are for a falling$-$head permeability test:

Length of the soil sample $=500mm$

Area of the soil sample $=1600m{m}^2$

Area of the standpipe $=97m{m}^2$

At time $t=0,$ head difference $=410mm$

At time $t=10$min, head difference $=185mm$

If the test was conducted at $20C$

a$.$ Determine the permeability of the soil $(c\frac{m}{sec}).$

b$.$ What was the head difference at $t=7$min $?$