A constant$-$head permeability test was performed in the laboratory. The soil sample was $25$

$cm$ long and $6c{m}^2$ in cross sectional area. The height of the water was maintained at $61cm$

at the inflow end and $15\mathrm{.}5cm$ at the outlet end, with respect to the datum. The volume of

water flowing through the sample was $370ml(=370c{m}^3)$ in $7$ minutes. The temperature of

the water during the test was $18C.$

a$)$ Make a sketch of the described conditions $($show the dimensions$).$

b$)$ What is the coefficient of permeability at $20C(k_{20})$ of this soil in $c\frac{m}{s}?$

c$)$ What is the hydraulic gradient $($i$)$ that causes the flow?

d$)$ What is the average velocity $($or Darcy's velocity, $v)$ of the flow through this soil sample?

e$)$ If the void ratio of this soil sample is $0\mathrm{.}53,$ what is the seepage velocity?