Centrifuge Cake Weight & G-Force Calculation
Two numbers matter most when planning a basket centrifuge batch: how hard the cake is actually being spun (G-force), and how much cake that translates to once the basket is loaded to a given thickness.
The Formula
Cake weight = Cake volume × bulk density
Where r is basket radius (cm) and N is rotational speed (rpm). Cake volume comes from the annular geometry defined by basket radius and cake thickness. In effect it is the basket's cylindrical volume minus the empty core left in the middle.
Worked Example
A basket with 40 cm radius spinning at 1,200 rpm:
= 1.118 × 10−5 × 40 × 1,440,000
≈ 644 G
If that basket carries a 10 cm-thick cake at a bulk density of 1,400 kg/m³, the cake volume comes from the annulus between the full basket radius (40 cm) and the inner radius left after the cake (40 − 10 = 30 cm) times the basket height. Multiply that volume by the bulk density to get total cake mass for the batch.
In the Plant
Bulk density of a centrifuged cake is not a fixed material property. It depends heavily on particle shape, size distribution, and how well the cake has been de-liquored during the spin. A bulk density measured from a different product, or even a different batch of the same product with different crystal habit, can give a meaningfully wrong cake weight.
Common Mistakes
Using the full basket radius instead of the cake's actual radial position when computing G-force at the cake surface versus at the basket wall (G-force varies with radius, so the value at the cake's inner surface is lower than at the basket wall); and assuming a bulk density from a handbook table rather than from an actual discharged cake of the real product.