Tutorial #5 on Centrifugal Settling and Cyclones

SCHOOL OF CIVIL, ENVIRONMENTAL AND CHEMICAL ENGINEERING

PROC2079 Fluid Flow and Particle Tutorial

5 –

Mechanics

Centrifu Cen trifugal gal sedimentation and cyclones

Question 1 Comparison of forces in centrifuges. Two centrifuges rotate at the same peripheral velocity of 53.34 m/s. The first bowl has a radius of r 1 = 76.2 mm and the second r 2 = 305 mm. Calculate the rev/min and the centrifugal forces developed in each bowl. Ans : N1 = 6684 rev/min , N 2 = 1670 rev/min , 3806g’s in bowl 1 and 1951g’s in bowl 2

Question 2 3

Settling in a centrifuge. A viscous solution containing particles with density 1461 kg/m is to be clarified by centrifugation. The solution density ! = 801 kg/m3 and its viscosity is 100 cp. The centrifuge has a bowl with r 2 = 0.02225 m, r 1 = 0.00716 m and height b = 0.1970 m. Calculate the critical particle diameter of the largest particles in the exit stream if N = 23,000 3 rev/min and the flow rate q = 0.002832 m /h. Ans: D pc = 0.746 µm

Question 3 Repeat the above question but with the following changes: a) Reduce the rev/min rev/min to 10000 10000 and and double double the outer outer bowl bowl radius radius r 2 to 0.0445 m keeping r 1 = 0.00716 m  b) Keep all variables as in Question 3 but double the throughput. throughput. -6 Ans : (b) D p = 1.747 x 10 m

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Question 4 Centrifuging to remove food particles. A dilute slurry contains small solid food particles having a diameter of 5 ! 10-2 mm which are to be removed by centrifuging. The particle density is 1050 kg/m3 and the solution density is 1000 kg/m 3. The viscosity of the liquid is 1.2 ! 10-3 Pa.s. A centrifuge at 3000 rev/min is to be used. The bowl dimensions are b = 3 100.1 mm, r 1= 5.00 mm and r 2 = 30.0 mm. Calculate the expected flow rate in m /s just to remove these particles.

Question 5  S cale up and ! values in centrifuges. For the conditions given in Question 2 do as follows:

(a) Calculate the ! value (b) A new centrifuge having the following dimensions is to be used: r 2 = 0.0445 m, r 1 = 0.01432 m, b = 0.394 m, and N = 26000 rev/min. Calculate the new ! value and scale up the flow rate using the same solution. Ans: ! = 196.3 m2

Question 6 3

Cyclone. Air carrying particles of density 1800 kg/m and an average diameter of 20 micrometres enters a cyclone at a linear velocity of 18 m/s. The diameter of the cyclone is 600 mm. (a) What is the approximate separation factor for this cyclone? (b) What fraction of the particles will be removed from the gas stream?

Question 7 Cyclone. What is the capacity in cubic meters per hour of a clarifying centrifuge operating under the following conditions?

Diameter of bowl 600 mm Thickness of liquid layer, 75 mm Depth of bowl, 400 mm Speed, 1200 rpm Specific gravity of liquid, 1.2 Specific gravity of solid, 1.6 Viscosity of liquid, 2 cp Cut size of particles, 30 µm Ans: q = 210 m 3/h or 0.0584 m 3/s

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