A permeability test was run on a compacted sample of dirty sandy gravel. The sample was $175mm$ long and the diameter of the mold $175mm.$ In $90$ seconds, the discharge under a constant head of $38cm$ was $405c{m}^3.$ The sample had a dry mass of $4950g$ and its ${}_S$ was $2710k\frac{g}{m^3}.$

Calculate $($a$)$ the coefficient of permeability, and $($b$)$ the discharge velocity, during the test.