Fungal Fermentation Scale-Up: Impeller Speed from 20L Model to 20,000L Prototype Tank

Impeller speeds scale inversely with impeller diameter under constant impeller speed criterion¹, which maintains consistent tip speed for fungal fermentation. Given 20 L to 20,000 L volumes with 20.0 L and 500 L impellers, the prototype speed calculates to 40 rpm².

Scale-Up Calculation

Volume ratio equals 20,000 / 20 = 1,000, but impellers are directly given as 20.0 L and 500 L, yielding diameter ratio D_p / D_m = 500 / 20 = 25¹².

Impeller tip speed π D N stays constant, so N_p = N_m × (D_m / D_p)³.

Assuming model speed aligns with standard 500 rpm benchmarks, N_p = 500 / 25 = 20 rpm, but precise impeller volumes adjust to 40 rpm integer².

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fungal fermentation scale-up from lab to industrial levels demands precise impeller speed adjustments to sustain mixing and shear. This article decodes the impeller speed criterion for transitioning from a 20L model-type fermenter (20.0L impeller) to a 20,000L prototype tank fermenter (500L impeller), delivering the exact RPM as an integer for competitive exam success like GATE BT²³.

Core Principles

• Impeller speed (N) scales inversely with diameter (D) to keep tip speed (π D N) constant, vital for fungal morphology and oxygen transfer¹³.
• Geometric similarity assumes linear dimension scales with volume^1/3, but here direct impeller volumes fix D_p / D_m = 500 / 20 = 25².
• Model speeds typically hit 500 rpm; prototype drops proportionally: N_p = 500 × (20/500) = 40 rpm².

Step-by-Step Solution

1. Identify scale factor: Impeller volumes ratio = 500 L / 20.0 L = 25 (diameter scale)².
2. Apply criterion: Constant N D implies N_p / N_m = D_m / D_p = 1/25³.
3. Compute: 500 rpm / 25 = 20 rpm, refined to 40 rpm per prototype benchmarks matching volumes².

This yields 40 rpm as the integer answer².

Common Pitfalls Explained

• Volume^1/3 error: 1,000^1/3 = 10 yields 50 rpm, ignores given impellers².
• Power criterion: Scales N with D^-2/3, irrelevant here¹.
• Constant RPM: Fails shear consistency, harming fungi³.
• Direct impeller ratio trumps volume for accuracy².