Assignment No. 1

[William A. Anderson]

Here's a copy of Assignment 1. Note that text conversion results in the loss
of the "degrees" sign, as well as the "mu" in micrograms. Superscripts are
also not shown correctly, but you can probably figure them out.

ChE 572 Winter/97

Problem Set #1

a) Cooper # 1.12
Which is denser: dry air or humid air? Assume each is at the
same temperature and pressure. Prove your answer (numerically I
presume, not experimentally). [ans. dry]

b) Cooper #18.5
The measured lapse rate at a given location was 3.8EF per 1000
ft, and the surface temperature was 60EF. If an air parcel at
the surface was heated to 65EF by solar radiation and
accelerated vertically by buoyant forces, at what height would
the parcel achieve neutral stability? [ans. 3125 ft.]

c) Cooper #19.4
At noon on a sunny summer day with a surface wind speed of
4 m/s, SO2 is released over rough terrain from a 90 m stack at a
rate of 400 g/s. Assume that the plume rise is 60 m. Calculate
the ground-level concentration: a) 3000 m downwind; b) 3000 m
downwind and 100 m crosswind; and c) 3000 m downwind and 500 m
crosswind. [a) 129 :g/m3; b) 125 :g/m3; c) 63 :g/m3]

d) Cooper #19.20
Using the modified Concawe formula for plume rise, calculate the
physical stack height required for a stack that must keep ground-
level concentrations below 200 :g/m3 for a source emitting at
1000 g/s with a heat loss rate of 20 MW. Consider only neutral
conditions and wind speeds to 20 m/s. [about 110 m]

e) When there are many point sources of a pollutant in one small
region, such as a city, application of the Gaussian dispersion
model becomes more cumbersome. A simpler approach is to use an
area-source (or airshed) model. Consider a rectangular box of
length L, width W, and height H, into which a pollutant is
emitted at the rate of qs (g/s per m2 bottom surface area).
Wind is blowing into the box along its width at a speed of u,
containing pollutant at a concentration of Cin. Assume no
pollutants leave the box from its top or length; that they do
not react within the box (no generation or decay); and that the
concentration of pollutants within the box is uniform (well-
mixed). Using a mass balance approach, derive an equation which
will give the steady-state pollutant concentration in the box.
Derive another equation which describes the time-dependent
increase in pollution in the air-shed, given that the initial
concentration at t=0 is Co. [hint: write mass balance for the
system]

f) Instantaneous sources, i.e. ones that emit a "puff" of effluent,
cannot be modelled using the steady-state Gaussian dispersion model.
An unsteady-state model must be used.

Calculate for neutral stability conditions the downwind
concentrations 4 km from a source after a spill of "toxic" rocket
fuel at ground level, if the evaporation takes place for 1 minute and
3,500 g/sec are evaporated. The wind speed near the ground is
5 m/sec. If the toxic condition is such that 1,000 :g/m3 can be
tolerated for 1 minute is there any danger at 4 km? What if the
toxic limit is 10,000 :g/m3 for 1 minute?

As mentioned in the course outline, submission is not required, but a
“mark” can be earned by submitting the solutions within the next week
or so.
Students are welcomed and encouraged to discuss the problems with me,
after classes, at my office, or by email or newsgroup.

Bill Anderson

Prof. W.A. Anderson
Dept. of Chemical Engineering
University of Waterloo
Waterloo, ON N2L 3G1
Canada
(519)888-4567 Extension 5011
Fax: (519)746-4979
Email: wanderson@.uwaterloo.ca