Tubular (disc-stack type) centrifugation: A typical tubular centrifuge bowl is 2–5 inches in diameter and 9–30 inches high. What is the usual maximum rotational speed range for such units?

Introduction:
Tubular and disc-stack centrifuges are workhorses in bioseparations for clarifying cell broths and harvesting biomass. Knowing the realistic operating speed range is important for estimating g-forces, capacity, shear exposure, and scale-up constraints.

Given Data / Assumptions:

• Bowl dimensions: 2–5 inch diameter; 9–30 inch height.
• Application: high-g clarification of microbial or mammalian broths.
• We refer to maximum design speed typical of commercial machines.

Concept / Approach:
G-force in a centrifuge scales with ω^2 * r. Tubular machines use high rotational speeds to reach tens of thousands of g at modest radii. Industrially, maximum speeds are commonly in the tens of thousands of rpm (not hundreds of thousands, which would exceed materials and bearing limits for such diameters).

Step-by-Step Solution:
Relate feasible surface speed to mechanical integrity limits for steel/titanium bowls.Use typical vendor specs: maximum speeds ~15–50 krpm for tubular clarifiers.Conclude the realistic range aligns with 15,000–50,000 rpm.

Verification / Alternative check:
Vendor literature and process handbooks report ~20,000–40,000 rpm for many tubular units used in biotech, confirming the selected range as representative.

Why Other Options Are Wrong:
Higher ranges (≥50,000 rpm to 200,000 rpm) are unrealistic for the stated diameters due to material stress, vibration, and bearing limits.

Common Pitfalls:

• Confusing micro-ultracentrifuges (small rotor radius) with industrial tubular centrifuges.
• Assuming diameter does not constrain maximum rpm; hoop stress scales with radius.

Final Answer:
15,000–50,000 rpm