A constant$-$head test was conducted on a cylindrical sample of soil $20cm$ long and $10cm$ in diameter. The volume of water collected in $1$ minute was $137c{m}^3.$ The head difference during this test was $30cm.$ The temperature of the water was $20C$ during the test. The porosity of this sand is $37\%$ and the specific gravity of solids is $2\mathrm{.}63.$ Calculate:

a$.$ the hydraulic conductivity at $20C($or coefficient of permeability$),k_{20}$

b$.$ the average flow velocity $($also called Darcy's velocity$),v$

c$.$ the seepage velocity

d$.$ seepage force