Environmental Engineering FOURTH EDITION

226 ENVIRONMENTAL ENGINEERING

calculated as

(10.8)

where

w = rotational speed of bowl (rads),

g = gravitational constant (m/s2),

1-2 = radius from centerline to inside of bowl wall (m),

1-1 = radius from centerline to surface of sludge (m), and

V = liquid volume in the pool (m3).

Thus if machine 1, at C1 (calculated from machine parameters) and flow rate Ql, pro-
duces a satisfactory result, it is expected that a second, geometrically similar machine
with a larger E2 will achieve equal dewatering performance at a flow rate of Q2.
This analysis does not consider the movement of solids out of the bowl, which is a
very important component of centrifugation. The solids movement may be calculated
by the beta equatiun (Vesilind 1979) for two machines,

Qi Q2

81 82 -

-- -- (10.9)

and

8 = (Aw)SNKDZ, (10.10)

where

Q = solids per unit time (e.g., lbsh),

Ao = difference in rotational speed between the bowl and conveyor, OB - wS

(rads),

S = scroll pitch (distance between blades, m),

N = number of leads,

D = bowl diameter (m), and

z = depth of sludge in bowl (m).

The scale-up procedure involves the calculation of Q2 for liquid as well as solids

throughout, and the lowest value governs the centrifuge capacity.

EXAMPLE 10.6. A solid bowl centrifuge (machine 1) is found to perform well if fed

sludge containing 1% solids at 0.5 m3h. In order to scale-up to a larger machine

(machine 2) it is necessary to determine the flow rate at which this geometrically