Chemical-plant equipment costs rarely vary in proportion to size. In the simples

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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 18 Chemical Engineering Thermodynamics C = ?S? The size exponent?is typically between 0 and 1. For a wide varity of equipment types it is approximately 0.6. (a) For 0 <?< 1, show that cost per unit size decreases with increasing size. ("Econ-omy of scale") (b) Consider the case of a spherical storage tank. The size is commonly measured by internal volume Vit. Show that?= 2/3. On what parameters or properties would you expect quantity ? to depend?

Explanation / Answer

www.chemengr.ucsb.edu/~ceweb/.../che110a/pdf/w08-110a-hw2.pdf

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