8/11/2019 Environmental Engineering Problems

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Fall 2014

CEE 2502

Physical Chemical Principles of Environmental Engineering

Homework No. 1

1. What is the settling velocity of a particle having a diameter of 10-5 cm and a density of

2.0 g/cm3in air at 27 oC and 2 atm of pressure? Assume that air is dry and has 21% O2

and 79% N2by volume.

2. A particle has a settling velocity of 1x10-7and 1x10-4cm/sec in water and air at 20 oCand 1 atmosphere, respectively. Compute the particle diameter and its density. The

density and viscosity of water at 20 oC are 0.99823 g/cm3and 1.0087 cp, respectively.

The viscosity of air at 1 atm and 20 oC is 0.000178 g/cm-sec. Assume that air is dry and

has 21% O2

and 79% N2

by volume.

3. Fluidized bed biological reactors are often used for denitrification and the treatment oftoxic wastes. In such reactors, granular activated carbon (GAC) particles can be used as

a support media for the growth of microbial biofilm and are kept in suspension (fluidized)

by an upflow fluid velocity. As the particles become coated with a bacterial films, theirsettling characteristics are altered. Assuming that a bacterial film with a specific density

of 1.04 grows on a GAC particle (specific density = 1.4) to a thickness kD where D is the

diameter of a GAC particle, develop a general mathematical relationship for the settling

velocity in terms of k and D. Plot the variation of settling velocity with bacterial filmthickness for a GAC particle with a diameter of 0.077 cm and for 0.0 < k < 1.0. Explain

the effect of bacterial growth on the settling properties of GAC particles.

4. In an ideal settling tank, a particle is completely removed if its terminal settling velocity

is greater or equal to the depth/detention time ratio.

a. Calculate the diameter of the smallest particle with a specific gravity 1.6 that would

be removed in a rectangulat basin that is 45m long, 6m wide, and 2m deep with aretention time of 30 min.

b. To improve removal efficiency, a consultant has proposed to install plates 6m wide

and 2m high inclined at 60oto the horizontal and placed 10 cm apart (perpendiculardistance between the plates) along the whole length of the tank. Find the new area

available for settling and hence, compute the diameter of the smallest particle that

will be removed. Comment on the results.