Suppose that a reactor used to pretreat a hot gas is a cylinder of diameter D = 20 cm and length L = 2 m that is filled with spherical catalyst particles of diameter d = 5 mm. The void fraction is ε = 0.35, the gas properties are ρ = 0.705 kg/m3 and μ = 2.71 × 10−5 Pa · s, and the superficial velocity is vs = 0.5 m/s.

(a) Calculate for the packed bed.

(b) Suppose now that a change in the composition of the feed gas has made the pretreatment unnecessary and that it has been decided to bypass the packed bed with a pipe of the same length. If it were desired to keep

the same, so as not to affect other units in the plant, what pipe diameter D_p would be needed? (Re for the equivalent pipe is in the Blasius range, which makes it possible to derive an explicit expression for x = D_p/D.)

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