In Example 19.10, a laboratory test was conducted with a small, tubular-bowl centrifuge on a fermentation broth. At the operating conditions, a sigma value of 7,400 ft² was computed, with a measured volumetric flow rate of 0.11 gpm. For the commercial plant that will process the same broth, the largest tubular bowl centrifuge available has the following characteristics: bowl speed = 15,000 rpm, R₀ = 5 cm, R₁ = 2 cm, and bowl length = L = 10 cm. Using the sigma scale-up theory, calculate how many gpm this unit can process.

Example 19.10

A laboratory tubular-bowl centrifuge has the following dimensions, with respect to Figure 19.28, and operating conditions: bowl speed 800 rps, R₀ =  0.875 inch, R₁ = 0.65 in., and bowl length = L = 4.5 inches. When used to remove E. coli cells from the following fermentation broth, a satisfactory volumetric feed capacity of the centrifuge, Q, of 0.11 gpm is achieved.

Broth: ρ_f = 1.01 g/cm³ and μ = 1.02x10^–3 kg/m-s

E. coli: smallest diameter = d_pmin = 0.7 μm and ρ_p = 1.04 g/cm³

Assuming the applicability of Stokes’ law, estimate the feed capacity of the centrifuge.

Liquid- interface Exit Ro {R Feed Figure 19.28 Tubular-bowl centrifuge. Ring weir