Anadolu University
Environmental Engineering Department
ÇEV 445 ENVIRONMENTAL MODELING
(2015 – 2016 Semester)
HOMEWORK 3
1). A substance is discharged to a lake via a stream which has the following characteristics.
Volume = 1x106 m3
Mean depth = 5 m
Residence time = 1 year
The substance has a concentration of 250 μg/L in the inflowing stream.It is a volatile
substance in dissolved form with a volatilization velocity of 10 m/year and in particulate form
it settles with a settling velocity of 50 m/year. All the forms decay by a first order reaction
with a rate constant of 2.0 1/year. The substance has a partition coefficient of 0.04 m3/g. The
suspended sediment concentration in the lake is 10 g/m3.
a) What is the steady state total concentration of the substance?
b) How much of the substance volatilizes, settles, decays and flushes out in a year?
c) It is known that the volatilization velocity varies by 12% , the settling velocity by
20% and the reaction rate constant by 15%. Find by first-order error analysis how these
uncertainties affect the concentration.
2). A lake receives a total phosphorus loading of approximately 12,500 mta (metric tons per
annum). It is known that the only losses of total phosphorus for the lake are settling and
flushing through the lake’s outlet. Assume the inflow and outflow rates are 200 km3 yr-1 and
the sediment area is 10,000 km2.
The settling velocity is known to follow a normal distribution with a mean of 20 m/yr and a
standard deviation of 5 m/yr. Generate 10000 random numbers from this distribution and
investigate the effect of the uncertainty in the settling velocity on the in-lake concentration.
Use Excel for this purpose. Report the results as histograms and as means and standard
deviations.
Due : January 15, 2016 (12:00 exact). After this the answers will be posted.
Homework format:
 Use only white A4 paper
 Head page (Name of course, Homework No., Student name, number, Name of
lecturer, Due date, Signature)
 Solution written by hand (readable and understandable, defining each step)
 Take care of the significant digits in your solutions.
Your signature tells that you have completed this homework by yourself.
50% reduction in grade will be done for homeworks not following this format.
Late homeworks will not be accepted.
Prof. Dr. Erdem Ahmet Albek
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