I've made hydrocyclones, out of sheet metal, not screen.
From a fluid standpoint, they work sort of like a pump in reverse, with one important difference; there are three flows. The dirty bleed flow out of the bottom center of the cone must be continuous.
If you want to dump that concentrated effluent into a bucket and periodically wash it away, that's an option, but it's more common to just pipe it to where you need it. (Or in filtration applications, use it as the input/motive flow to a cascaded section of fewer or smaller cyclones.)
Mike Halloran
Pembroke Pines, FL, USA