Chemical plant equipment costs rarely vary in proportion to size In the simplest case, cost C varies with size S according to the allometric equation The size exponent is typically between 0 and 1 For a wide variety of equipment types it is approximately 0 6 (a) For 0 1, show that cost per unit siz...

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Chemical-plant equipment costs rarely vary in proportion to size. In the simplest case, cost C varies with

Question:

Chemical-plant equipment costs rarely vary in proportion to size. In the simplest case, cost C varies with size S according to the allometric equation

The size exponent β is typically between 0 and 1. For a wide variety of equipment types it is approximately 0.6.
(a) For 0 < β < 1, show that cost per unit size decreases with increasing size. (“Economy of scale.”)
(b) Consider the case of a spherical storage tank. The size is commonly measured by internal volume V ⁱ_t . Show why one might expect that β = 2/3. On what parameters or properties would you expect quantity α to depend?

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