14.3-4. Settling Velocity of Quartz Particles in Water. Solid quartz particles having a diameter of 1000 µm are settling from water 294.3 K. The density of the spherical particles is 2650 kg/m3. Calculate the terminal settling velocity of these particles.

14.3-5. Hindered Settling of Solid Particles. Solid spherical particles having adiameter of 0.09 mm and a solid density of 2002 kg/m3 are settling in a solution of water at 26.7°C. The volume fraction of the solids in the water is 0.45. Calculate the settling velocity and the Reynolds number.

14.3-9. Separation by Settling. A mixture of galena and silica particles has a size range 0.075 – 0.5 mm and is to separated by a rising stream of water at 293.2 K. Use specific gravities from Example 14.3-3.

a. To obtain an uncontaminated product of galena, what velocity of water flow is needed and what is the size range of the pure product?

b. If another liquid, such as benzene, having a specific gravity of 0.85 and a viscosity of 6.50 × 10-4 Pa·s is used, what celocity is needed and what is the size range of the pure product?

14.4-1. 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 r1 = 76.2 mm and the second r2 = 305 mm. Calculate the rev/min and the centrifugal forces developed in each bowl.

14.4-2. Forces in a Centrifuge. A centrifuge bowl is spinning at a constant 2000 rev/min. What radius bowl is needed for the following?

a. A force of 455 g’s.

b. A force four times that in part a.

14.4-3. Effect of varying Centrifuge Dimensions and Speed. Repeat example 14.4-2 but with the following changes:

a. Reduce the rev/min to 10 000 and double the center-bowl radius r2 to 0.0445 m, keeping r1 = 0.00716 m.

b. Keep all variables as in Example 14.4-2 but double the throughput.

14.4-4. 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/m3. 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 = 100.1 mm, r1 = 5.00 mm, and r2 = 30.0 mm. Calculate the expected flow rate in m3/s just to remove these particles.