Problem Set- Particle Fluid Separation2012

PROBLEM SET: Particle-Fluid Separation Group 1

Group 2 Group 3

Group 4

Group 5

Group 6

Group 7 Group 8

Group 9

Group 10

Part 1 7.7 MSH (for Galena and Quartz) instead of water, change to suspension of 25% solids by weight; 22.11F Find the diameter of spherical mica beads settling in water at 40oC at a rate of 0.005 m/s 22.5 Foust

Find the diameter of spherical mica beads settling in air at 25oC at a rate of 0.0005 m/s Calculate the diameter of an industrial centrifuge operating at 1000 rpm if the same slurry was tested in a laboratory centriuge, 30 cm in diameter and rotating at 250 rpm 22.8 Foust 22.5 F Instead of settling in water consider settling in air at 1 atm and 25oC Disc shaped (1mm diameter by 0.25 mm thick) basalt settle in a suspension of porosity 40% in water. Find its terminal velocity What is the diameter of coral spheres settling through a suspension of water at 0.002 m/s. Assume a porosity of 0.5

Part 2 29.13 MSH

22.13F 22.7 Foust

Using the following height vs time for a laboratory sedimentation test: t, min z, inches 0 5 5 3.9 15 1.9 30 1.1 45 0.95 60 0.8 70 0.8 find the diameter of a batch tank needed to handle 2 m3 of slurry if it takes 1 day for the solids to settle to a height of 30% of the original height. 22.21 Foust (Kynch Method- obtain underflow velocity from last 2points of test data)

22.19 Foust (Talmadge and Fitch)

22.9 Foust 22.8 but replace 0.1 m/s to 0.15 m/s

29.13 MSH (assume negligible liquid thickness)

22.19 Foust (Kynch Method- obtain underflow velocity from last 2points of test data)

1.

(22.5F) Glass beads 50 microns in diameter settle in water at 25oC. Specific Gravity of glass is 2.6. a. If unhindered settling occurs, what is the maximum velocity attained? b. If hindered settling occurs such that the mass ratio of water to glass is 2, what is the maximum velocity 2. (22.7F) A mixture of galena and silica is to be elutriated by a water stream flowing at a velocity of 0.1 m/s and a temperature of 25oC. The solid feed analyzes 30 weight percent galena and a screen analysis is in the ff table: Dp (microns) 20 30 40 50 60 70 80 90 100 Wt % (undersize) 33 53 67 77 83 88 91 93 94.5 If the size distribution given applies for both component in the feed, what Wt. fraction of the galena fed is in the overhead and bottom product and what is the wt. fraction (dry basis) of galena in these products. 3. (22.8) A mixture of Galena & Silica is to be elutriated by Carbon Tetrachloride stream flowing at a velocity of 0.1 m/s and a temperature of 25 C. The solid feed analyses 30 weight % galena and a screen analysis is indicated in the table. Find the weights and analysis of the overhead and bottoms product.

4.

Particle diameter, microns

20

30

40

50

60

70

80

90

100

Weight % of undersize

33

53

67

77

83

88

91

93

94.5

(22.9F) A gravity settling tank is to be used to clean wastewater from an oil refinery. The waste stream contains 1% oil by volume (sp = 0.87) as small drops ranging in size between 10 to 500 microns. The tank is rectangular and measures 3m and 2m deep. Provision is made at the discharge end for the clean water to be continuously removed from the bottom of the tank. Periodic skimming of the liquid surface at the discharge end removes the accumulated oil. If 6.3 m3/s of the wastewater is to be processed, how long must the settling tank be? 5. (22.11F) Quartz and pyrites (FeS2) are separated by continuous hydraulic classifications. The feed to the classifier ranges in size between 10 microns and 300 microns. Three fractions are obtained: a pure quartz product, a pure pyrites product and a mixture of quartz and pyrites. The specific gravity of quartz is 2.65 and that of pyrites is 5.1. What are the sizes of the 2 materials in the mixed fraction for each of the following cases : a. the bottoms product to contain the maximum amount of pure pyrites b. the overhead product to contain the maximum amount of quartz 6. (22.13F) A tubular bowl centrifuge is to be used to separate water from a fish oil. This centrifuge has a bowl 4 in. in diameter by 40 in. long and rotates at 1500 rpm. The fish oil has a density of 0.94 g/cm3 and a viscosity of 50 cP at 25ºC. The radii of the inner and outer overflow dams are 1.246 in. and 1.250 in. respectively. Determine the critical diameter of droplets of water suspended in oil and the critical diameter of oil in water if the feed rate is 300 gal/hr of a suspension containing 20 wt.% fish oil. 7. (22.19) A 3 wt% CaCO3 slurry was subjected to batch sedimentation test. The density of the solids in the slurry is 2.63 g/mL and that of the liquid is 1 g/mL. The results are indicated below: Time, 0 20 40 60 80 100 120 140

min Z, m 176 100 74 57 42 34 26 22 Determine the area and depth of a continuous thickener that will handle 40000 solids per day from 3% to 40% solids. 8. (22.21F) 40 tons/hr of a metallurgical pulp are to be thickened fro, 186 gmol/l to 1200 gmol/l in a Dorr Thickener. Batch-settling data on the feed material gave the following information: time (hr) pulp height (ft)

0 3

0.1 2

0.25 1.4

0.5 0.9

0.75 0.68

1 0.48

2 0.25

4 0.1

Specific gravity of solids = 4.44 Concentration = 186 gmol/L What depth and diameter thickener is required to accomplish the specified assignment? Use the Talmadge and Finch Method. 9. (29.13MSH) What is the capacity in cubic meters per hour of a clarifying centrifuge operating under the following condition Diameter of the bowl = 600mm Spg Liquid = 1.2 Thickness of the liquid layer = 75mm Spg Solid = 1.6 Depth of the bowl = 400mm Viscosity of the liquid = 2 cP Speed = 1200 rev/min Cut size particle = 30 microns