Example 12.3: When an aqueous slurry is filtered in a plate and frame press, fitted with two 50 mm thick frames each 150 mm square, at 450 kN/m² pressure, the frames are filled in 3500 seconds. How long will it take to produce the same volume of filtrate as is obtained from a single cycle when using a centrifuge with a perforated basket, 300 mm diameter and 200 mm deep? The radius of the inner surface of the slurry is maintained constant at 75 mm and the speed of rotation is 65 Hz. Assume that the filter cake is incompressible and the resistance of the cloth is equivalent to 3 mm of cake in both cases.

Solution: Plate and Frame Press

Pressure drop across the filter is 450 minus 101.3 or 384.4 kilo newton per m² or 3.487 time 105 newton per m². Thickness of the cake is 25 mm or 0.025 meter. Resistance of cloth is 3 mm or 0.003 meter. Slurry properties group r mu over nu is given by 2 delta P t over (l² plus 2 L l) and is equal to 3.15 time 10¹².

The volume of the cake obtained in plate and frame presses is n L_PW_P delta or 2.225 time 10^-3 m³. The same amount of cake will be generated by centrifugal separation. So inner radius of cake in the basket is square root of (b² minus V_cake/pi H) or 0.138 meter. Angular velocity of centrifuge, omega, is 2 pi f or 408.4 radians per second. Note that frequency is 65 Hertz.

Radius of the centrifuge, b, is given as 0.15 meter, inner radius of slurry, x, is 0.075 meter, and density of filtrate is 1000 kilogram per cubic meter. Centrifuge depth is 200 mm, or 0.2 meter. From these data, time required to obtain same level of filtration is found to be 249 seconds.