The following questions will challenge you and help to reinforce some of the principles presented in this chapter.

1. A waste stream from a pulp mill has an average concentration of 7.2 Lbs of water/Lbs of solids. A treatment plant to be designed will have a thickening stage that concentrates the stream to 1.8 Lbs of water/Lbs of solids with the production of a relatively clear overflow. Batch settling tests were conducted on different concentration slurries to ensure that the velocity of settling exceeds the upward flow of fluid at all concentrations normally encountered in the thickening of the specified feed. Tabulated results from these tests are given below Prepare an additional column for this table showing the estimated minimum area required for clear overflow in units of 1 ton/day/ft2 of solids feed. What is the minimum area to be used for design purposes?

Mass Ratio Fluid to Solids |
Fluid Rising per Lbs Solids (Lbs/Lbs) |
Calculated Fluid Rising (ft3/hr) |
Measured Rate of Settling (ft/hr) |

7.2 |
5.9 |
7.3 |
2.9 |

6.3 |
4.1 |
4.8 |
1.5 |

4.3 |
3.2 |
3.9 |
1.1 |

3.4 |
2.6 |
3.1 |
0.85 |

2.5 |
1.7 |
2.6 |
0.59 |

Figure for Question 2. Plot of Reynolds number, and settling number (.Lyashenko number) versus Archimedes number. Use this plot for question 3. It also useful for your own design problems.

2. Determine the settling velocity of spherical quartz particles in water (d = 0.9 mm) using the dimensionless plot of the Lyachshenko and Reynolds numbers versus the Archimedes number in the figure above. The Lyashenko number is the same as the dimensionless settling number. The specific weight of the quartz is 2650 kg/m3, and the temperature of the water is 20° C.

3. Determine the maximum size of quartz particles settling in water (t = 20° C) that can be described by Stokes' law. What is this particle's settling velocity? The specific weight of quartz is 2650 kg/m3.

4. Determine the maximum diameter of spherical chalk particles entrained by an upward-moving water stream with a velocity of 0.5 m/sec. The liquid temperature is t = 10° C, and the specific weight of the chalk is 2,710 kg/10° C.

5. Determine the settling velocity in the water (t = 20° C) for lead particles having an angular shape with d„, = 1 mm. The specific weight of lead particles is 7,560 kg/10° C.

6. Calculate the sizes of elongated coal particles (ppl = 1,400 kg/m3) and plate-like particles of shale (pP2 = 2,200 kg/m3) that have the same settling velocities of 0.1 m/sec through water at 20° C.

7. Determine the settling velocity of solid spherical particles if the particle diameter is d = 25 /tm and particle density is 2,750 kg/m3. The density of the liquid phase is 1,200 kg/m3 and its viscosity is 2.4 cp.

8. Determine the velocity of hindered sedimentation of the suspension considered in question 2 if the concentration of solids in the feed is x = 30%, the density of suspension is 1,440 kg/m3, and the density of the solid phase is 2,750 kg/m3.

9. Determine the capacity, cross-sectional area and diameter of a continuous sedimentation tank for liquid suspension clarification in the amount of Qs = 20,000 kg/hr. The concentration of solids is xL = 50%, the settling velocity is Uo = 0.5 m/hr, and the density of liquid phase is 1,050 kg/m3.

10. During the spring, the mean temperature over the bottom 3 ft of the lagoon described above is 10° C, whereas the temperature at the surface is about 16° C. Would you expect good separation of solids? Substantiate your conclusions.

11. Two primary settling basins are each 100 ft in diameter with an 8-ft side water depth. The tanks are equipped with single effluent weirs located on the peripheries. For a water flow of 10 mgd, calculate the overflow rate, gpd/ft2, detention time, hr, and weir loading, gpd/ft. The overflow rate for a clarifier is defined as the surface settling rate, i.e., q0 = q/F, where q = volumetric

12. A thickener handles 80,000 gpd of sludge, increasing the solids content from 2.0 to 8.0 wt.% with 85% solids recovery. Determine the quantity of

13. Develop a list of air pollution issues and discuss possible permitting requirments you may have to face with a treatment plant that relies on both primary and secondary clarifiers for municipal sewerage treatment.

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