In the design of an agitator vessel with model volume V₁ and prototype volume V₂, the scale-up ratio is given by
Options:
(A) V₂/V₁
(B) (V₂/V₁)^(1/2)
(C) (V₂/V₁)^(1/4)
(D) (V₂/V₁)^(1/3)
Official Answer Key:
D
Step-by-Step Solution & Explanation
For geometrically similar vessels, volume scales with the cube of the characteristic linear dimension (V ∝ L³). The scale-up (linear dimension) ratio between prototype and model is therefore the cube root of the volume ratio: Scale-up ratio = (V₂/V₁)^(1/3). Options (B) and (C) use incorrect powers (square-root and fourth-root scaling do not correspond to 3-D geometric similarity), and (A) uses the volume ratio directly without any root, which would represent the volume scale-up, not the linear dimension scale-up ratio. Hence (D) is correct.
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