Rotational speed practice:\nIn small propeller-driven laboratory fermenters and mixers, typical direct-drive motor speeds are closest to which of the following pairs?

Introduction / Context:
Small propeller mixers are often powered by standard synchronous or induction motors. Knowledge of common base speeds helps with selecting gear ratios, estimating tip speed, and assessing shear environments for sensitive cultures. This question targets the recall of typical nominal motor speeds used for small propellers.

Given Data / Assumptions:

• Direct-drive (no gearbox) operation.
• Line frequency values around 50–60 Hz.
• Common small propeller impeller diameters (few centimeters) in lab-scale vessels.

Concept / Approach:
Standard electric motors run near discrete synchronous speeds. For 60 Hz power, common unloaded speeds are approximately 1800 rpm and 1200 rpm (1750 and 1150 rpm under load for 4- and 6-pole motors). These map well to typical small propeller operations. Lower speeds like 20–300 rpm are more typical of large, geared agitators; very high speeds (6000–12000 rpm) correspond to high-shear rotor–stator devices, not standard propellers.

Step-by-Step Solution:

Verification / Alternative check:
Equipment catalogs list direct-drive lab mixers at nominal 1150/1750 rpm with optional VFDs to adjust speed; tip speed is then calculated as π * D * N.

Why Other Options Are Wrong:

• 20–150 rpm: characteristic of large, geared paddles or anchors.
• 150–300 rpm and 400–800 rpm: feasible with gear reduction; not typical direct-drive bases.
• 6000–12000 rpm: rotor–stator homogenizers, not propellers.

Common Pitfalls:
Confusing motor base speed with impeller tip speed; tip speed depends on diameter as well as rpm.

Final Answer:
1150 rpm or 1750 rpm