THE UNIVERSITY OF ZAMBIA
SCHOOL OF ENGINEERING
DEPARTMENT OF AGRICULTURAL ENGINEERING
FOOD PROCESS ENGINEERING
AEN 4512 ASSIGNMENT 1
1. A sample of maize seeds weighs 9.38 g per 16 seeds. Assume each seed is equivalent to a sphere
with 9.8 mm diameter. Estimate the flotation air velocity. Assume the density and viscosity of air are
1.2 kg/m3 and 1.71*10-5 kg/m.s respectively.
2. Determine the diameter of a cylinder separator which if it rotates at 62.4 rpm, all the material is held
in the indents by centrifugal force.
3. If in question 2 the cylinder separator was rotating at 62.4 rpm and the material was discharged at
120 from the bottom, what would be its diameter?
4. Full cream milk is contained in a 15 cm long milk bottle. If the average particle or globule of butter
fat has diameter 6 microns and weighs 866 kg/m3, and skim milk weighs 1033 kg/m3, calculate the
time it would take a globule of butter fat to rise from the bottom to the top of the bottle. Skim milk
has a viscosity of 1.4*10-3 Ns/m.
5. A cream separator has a bowl 15 cm in diameter and operating at 8600 rpm. If the butter fat has
average diameter of 6 microns and weigh 866 kg per m3, skim milk weighs 1033 kg per m3, calculate
the rate of movement of a fat particle assuming that the average reaction is 5 cm from bowl axis.
Skim milk has viscosity 1.4 * 10-3 Ns/m2.
6. Show that the number of "g’s" that can be obtained in a centrifuge which spins a liquid at N rpm at a
maximum radius R is given as 1.12 * 10-3 RN2.
7. How many "g’s" can be obtained in a centrifuge which can spin a liquid at 2000 rev/min at a
maximum radius of 10 cm. Compare this force to that for a bowl with a radius of 20 cm rotating at
the same rev/min.
8. A dispersion of oil in water is to be separated using a centrifuge. Assume that the oil is dispersed in
the form of spherical globules 5.1 * 10-5 m diameter and that its density is 894 kg/m3. If the
centrifuge rotates at 1500 rpm and the effective radius at which the separation occurs is 3.8 cm
calculate the velocity of the oil through the water. Take the density of water to be 1000 kg/m3 and its
viscosity to be 7 * 10-4 Ns/m2.
9. In a centrifuge separating oil (of density 900 kg/m 3) from brine (of density 1070 kg/m3) the discharge
radius for the oil is 5 cm. Calculate the suitable radius for the brine discharge and for the feed intake
so that the machine will work smoothly assuming that the volumes of oil and of brine are
approximately equal.
10. If an olive-oil emulsion of 5 m droplets is to be separated in a centrifuge, from water, what speed
would be necessary if the radial travel of the particles is 3 cm and the effective radius of the
centrifuge is 5 cm.
11. In sedimentation, particles fall from rest under the force of gravity. The settling velocity of the
particles is given by Stokes’ Law:
vm = D2 g (ρp – ρf )/18μ
where: D = diameter of the particles
ρp = density of the particle
ρf = density of the fluid
μ = viscosity of the fluid
In a continuous thickener type of sedimentation tank (figure 1), settling proceeds as material flows
through the tank and clarified liquid is taken from the top and sludge from the bottom. The
minimum area necessary for a continuous thickener can be calculated by equating the rate of
sedimentation to the counter flow velocity of the rising fluid. Show that the counter flow velocity of
the rising liquid is given by:
vu = (F – L) (dw/dt)/Aρ
where: vu = upward velocity of the flow of the liquid
F = mass ratio of liquid to solid in the feed
L = mass ratio of liquid to solid in the underflow liquid
dw/dt = mass rate of feed of the solids
ρ = density of the liquid
A = settling area in the tank
Figure 1: Continuous sedimentation plant
12. A continuous sedimentation tank is to be designed to follow after a water washing plant for a liquid
oil. Estimate the necessary area for the tank if the oil, on leaving the washer, is in the form of
globules 5.1 * 10-5 m diameter, the feed concentration is 4 kg water to 1 kg oil, and the leaving water
is effectively oil free. The underflow is water free. The feed rate is 1000 kg/h, the density of the oil is
894 kg/m3, and the density and viscosity of water are 1000 kg/m3 and 7.0 * 10-4 Ns/m2 respectively.
