Page 312 - Biosystems Engineering

Bioseparation Pr ocesses 289

FIGURE 9.3 Basket-style centrifuge.

Principle of Separation
The centrifugal force acting on a mass of w is as follows:

F = 0.000341WrN 2 (9.1)
where W = weight of basket
r = inside radius of basket
N = rpm of basket
The power required by a centrifugal machine is
hp = TN /5250 (9.2)
m
where T is the torque (ft-lb) and N is the maximum speed of basket
m
(rpm).
The torque T is equal to
T = WR N/307t (9.3)
2
where R = radius of gyration of the basket, which may be taken as
77 percent of the basket radius
N = 90 percent of the maximum running speed, rpm
T = shell thickness
The shape of the liquid surface is parabolic in nature and given by
ω 2
y = x + y (9.4)
2
2 g 0
where ω is angular velocity (rad/s) and x, y, and y are characteristics
0
of a point on the parabola.
The volume of a liquid in a basket is
⎛ ω 2 4 ⎞
b
V ′ = Π ⎜r H 0 ⎟ ⎟ (9.5)
2
⎜
⎝ 4 g ⎠