Mining operations generate large amounts of large particulate matter, which requires significant ventilation operations to ensure miner safety. At the surface, a large diameter cyclone is needed to remove particles with a massive $100$ micron diameter and $2225kg$ per cubic meter density. The ventilation system usually operates with an $8\mathrm{.}9$ cubic meter per second flowrate, which will all go through one cyclone, and a $2\mathrm{.}3$ E $-05$ Pa s viscosity.

Calculate the cut diameter $($microns$)$ needed to achieve $99\mathrm{.}5\%$ removal for the large $100$ micron particles.

Estimate the cyclone diameter needed to achieve the cut diameter under these flow conditions.