Spinning gravity
A particle moving in a circle of radius r at speed v feels an outward push of v squared over r. Dividing by 9.81 expresses it in g. Using the inlet velocity as the wall speed and half the diameter as the radius gives a quick estimate of how hard the cyclone works its slurry, often tens to hundreds of times gravity.
The flow estimate assumes an inlet about one quarter of the cyclone diameter across. Both readouts are simplified; real tangential speeds vary with radius and real units are sized from vendor curves.
Try it: set the diameter to 750 mm and velocity to 3 m/s, then switch to 120 mm and 9 m/s. The spin acceleration jumps from about 2 g to well over 100 g, and the particles in the scene race around faster.
Closing a grinding circuit
In most concentrators hydrocyclones sit beside ball mills. The cyclone sends finished fines on to flotation and returns the coarse underflow to the mill for more grinding.