The rule behind the numbers
Keep geometric similarity and hold power per volume constant, and impeller speed has to fall as the vessel grows, with N ∝ D-2/3. Tip speed, π·N·D, still rises with D1/3. You cannot hold both constant at once.
A thousandfold increase in volume is a tenfold increase in diameter. Under this rule the impeller turns at about a fifth of its bench speed, and its tip moves about twice as fast.
| Stage | Volume | Diameter | Impeller speed | Tip speed |
|---|---|---|---|---|
| Bench | 2 L | ×1.0 | ×1.00 | ×1.00 |
| Pilot | 50 L | ×2.9 | ×0.49 | ×1.43 |
| Clinical | 500 L | ×6.3 | ×0.29 | ×1.85 |
| Commercial | 2,000 L | ×10.0 | ×0.22 | ×2.15 |
Constant power per volume is one scale-up rule among several. Holding tip speed, mixing time or oxygen transfer constant instead fixes a different parameter and lets the others move.