CEE 6550 --- HW 2
1. Consider the conservation of mass for a scalar in a well-mixed reservoir. The scalar is consumed by a first order reaction with rate coefficient, k = -0.01 d-1:
a. write a conservation of mass equation for this case.
b. Derive an analytical expression for (remaining) mass as a function of time.
c. Compute the half-life of the scalar
d. Compute the e-folding lifetime, which is when 1/e remains (where e is the irrational number forming the base of the natural log).
2. Several decades ago there was great concern about the growing ozone hole in the
atmosphere. The cause was attributed to Chloroflourocarbons (CFC-12) and this led to regulations that controlled their production and use. CFC-12 breaks down in the atmosphere (due to photolysis) with a lifetime of 100 years (i.e. k = -0.01/yr). The mean atmospheric concentration of CFC-12 at one point (before regulations) was about 400 ppt and was increasing at a rate of 4%/yr.
a. Write an integral conservation of mass expression for total CFC-12 in the atmosphere (i.e. a single control volume).
b. Estimate the rate of emissions [E, in kg/yr] to the atmosphere for a time prior to emission regulations. Be sure to state any assumptions and estimates needed along the way (such as mass or number of moles or air in the atmosphere, molecular weights, etc)
c. Now we want to look at transients.
Annual time series of CFC12 is shown in the figure. Download the annual time series of CFC concentration from the Canvas site and use the C(yr) and the mass balance equation to estimate an historical time series of annual emissions rates.
d. Give an example of another problem
where such an approach would be useful (i.e. monitoring rate of change of concentration to infer emission rate).
3. Consider the rise of liquid in a capillary tube. You want to estimate the maximum rise. You decide it must depend on the surface tension, the diameter of the tube and the specific weight o the liquid.
a. What are the significant dimensionless parameter(s) in this problem? (follow a formal approach).
4. Spend some time reading and thinking about the analysis in the attached paper and
discuss with one or more classmates. Does the result make sense? Do you understand the logic of getting to this? Can you think of analogous applications? Electric cars and batteries? See more on this at http://www.sciencebits.com/rowers