4/24

4/19
uploaded

4/17
 uploaded
 board
notes
on turbulent diffusion and advectiondispersion
equation

4/12

4/11
 corrected version of example problem #18 solution
is here
(the minus sign was missing in the exponent)
 HW#5 will be due at 5pm (and not at 10am) tomorrow

4/10 (2nd announcement)
 uploaded (see Contents
page):
 board notes on headloss in pipes with turbulent
flow
 example problem #
18
19 (embayment model)

4/10

4/8
 uploaded (see Contents
page):
 board notes on two lectures on turbulence
 example problem #18 (velocity profile in a
turbulent flow above a rough interface)

4/3

4/1
 board
notes for the introductory lecture on turbulence
are uploaded

3/30 
3/27
 uploaded:
 comments on problem #1 of HW#4
 hint: Monod kinetics
 there are two ways of solving this problem.
An approximate solution (when you assume that
maximum rate is indeed 7 units/day) and a more
accurate solution. Either solution is fine.
 comments on problem #4 of HW #4:
 note that dP/dx <0. Hint: look at how this
sign issue is dealt with in the Excel file with
the solution for example problem #15
 class schedule has been adjusted to reflect the
actual pace of the class. Two special topic classes
have been cancelled to have time to cover main topics.

3/25 (2nd announcement)
 comments on problem #3 of HW#4
 your task is to derive equation for density
of a compressible fluid as a function of location (rho(x,y,z))
when the fluid is
at steady state (d(rho)/dt=0) and flows
at constant
velocity in the x, y, and zdirection;
 hint: follow the algorithm we used when deriving
the continuity equation for an incompressible
fluid
 corrected
version of board notes on the topic of CarmanKozeny
equation is uploaded

3/25

3/22

3/19

3/15
 example problem #15 files are uploaded (see Contents
page)

3/14
 board
notes for lectures 22 and 23 are uploaded (see
Contents
page)
 Monday office hours are rescheduled
for Friday for the remainder of the semester (see
main ENE801
page)

2/26 (3rd announcement) 
2/26 (2nd announcement)
 unclaimed homework can be picked up from Mrs Mary
Mroz (CEE main office)

2/26
 The following materials are now uploaded and available
(also see "Contents"
page):
 Board
notes and Excel
file with example solutions (note 3 tabs/worksheets)
on the topic of StreeterPhelps model. A typo
("a sin of commission" of an odd number of sign
errors) was fixed in the board notes.
Of course, do/dt should be proportional to L
as the oxygen is *depleted* at faster rate when
BOD concentration is higher.
 To follow up on the announcement from 2/25: here
is the illustration of which typos were fixed in
the example problem #13a
 Explanation
of how we applied boundary conditions when solving
the problem of the point source discharged into
a dispersed plug flow system (see board
notes for lecture 20)

2/25
 Solutions to
HW#3 are uploaded (also see Assignments
page)
 With regard to example problem 13a:
 There were two typos in the Excel file: 1) theta
was calculated as Q/V instead of V/Q. 2) The formula
for F had lamda1 instead of lambda2 in one location.
Both typos are fixed now. Download the corrected
Excel file here.
 As you might remember shortening reactor volume
appeared to predict that the concentration should
increase with x, an obviously unphysical situation.
In fact, we forgot to adjust the limits
on the X axis (oops!). The increase we observed
was for x>L only, which was outside of the
reactor (corresponding to the range of X
values that we do not have a solution for)

2/22
 Comments on HW3:
 You do not need to solve problem #5 of HW3.
This problem will become a part of HW4.
 On volatilization (see problems 2 and 3 of HW3):
the fact that a compound is lost to volatilization
is accounted for by introducing v_v*C*A (or K_L*C*A)
term into the mass balance equation, where v_v
(or K_L) is the volatilization mass transfer coefficient.
v_v and K_L have units of m/s.
 The following materials are now uploaded and available
(also see "Contents"
page):
 Board
notes on modeling of PFR with dispersion (e.g.
mixed flow reactor)

2/20
 During our Friday class, we will cover how to
treat volatilization in a mass balance. This would
be useful for you when working on HW3.
 In the formulation of problem 1 in HW3, k_d =
k_death and k_r=k_degradation
 The following materials are now uploaded and available
(also see "Contents"
page):

2/19
 There was a typo in the formulation of problem
1 in HW3. Initial substrate concentration should
be 998 mgC/L (and not zero mgC/L)

2/18 (2nd announcement)
 Solutions to
HW#2 are uploaded (also see Assignments
page)
 HW#3 is posted. Due
by the start of the class on Monday, February 25
(also see Assignments
page)
 (in response to a question I was asked during
office hours) Here is a brief explanation  page1
and page
2  of why 3*tau (or 3*theta) is used to estimate
when steadystate will be reached in an CSTR with
a reaction of the first order

2/18
 The following materials are now uploaded and available
(also see "Contents"
page):

2/13
 the due date for the HW#2 is moved to 10:20am
on Monday, Feb 18

2/9

2/8
 HW#2 is posted. Due
by the start of the class on Friday, February 15
(also see Assignments
page)

2/6 (2nd announcement)
 Comments on today's lecture
 Question: "In Eg # 9, formulation pdf, could
you please edit the 'C' as 'BOD'?"
 Answer: " One can quantify both substrate
and bacterial mass in terms of organic carbon.
So let's leave units for substrate S to be "mg(C)/L"

2/6
 The following materials are now uploaded and available
(also see "Contents"
page):

2/2
 Comments on HW#1
 problem #7
 Question: "The reaction dopes not look
like a first order reaction. Is it firstorder?"
 Answer: "settling is assumed to follow
the firstorder process". Thus you do not need
to guess the order of the "reaction" that describes
settling of particulate phosphorus. Assume that
the scatter in data is due to experimental error
 problem #3
 Question: " ... the first method is related
to the times emptying the glass, while the second
one is related to the time of the flow rate
of the tap water, so I do not know how to compare
the efficiency of these two methods."
 Answer: Try comparing concentrations of soap
in the glass after you've used V0 (the volume
of the glass itself), m3 of clean water for
rinsing.
 problem #3
 Question: "Its said the initial soap concentration
of wash water is Co. Does wash water refer to
the water used for washing the glass or is it
the soapy water contained in the glass? "
 Answer: C0 is the concentration of the soapy
water contained in the glass initially. Note
that C0 would also be the concentration
of soap in the film (volume of the film = 0.01*V0)
that remains on the wall of the glass after
the first rinse with soapfree water.

1/30 (3rd announcement)
 there were two typos in the board notes from the
lecture on adsorption. The original file has been
corrected (see Jan 28 entry on the "Contents"
page or download the corrected file, with changes
tracked, by clicking here)

1/30 (2nd announcement)
 On the request from the Engineering Dean's office,
the class on Friday, Apr 26 is canceled. The reason
is the Engineering Design Day, which will take place
in the Engineering Building on that day. See "Contents"
page for corresponding changes in the class schedule.

1/30
 The following materials are now uploaded and available
(also see "Contents"
page):
 Before our class on Friday (Feb 1):
 Go over the solution of the example
problem #6 to:
 explore how the solution changes as a
function of various parameters (lake volume,
flow rate, reaction constant, initial concentration);
 see how the discrepancy between analytical
and numerical solutions depends on the time
step delta(t).
 Go over the solution of the example
problem #7 to:
 recall the procedure
for solving ordinary nonhomogeneous differential
equations;
 understand contributions of each of the
two terms in the analytical solution  see
sheet 1 in this
file;
 explore how the solution changes as a
function of various parameters (lake volume,
flow rate, reaction constant, initial concentration,
concentration in the influent) 
see sheet 1 in the
same file;
 confirm what you learned (when going over
the numerical solution to example problem
#6) about solving differential equations
in Excel  see sheet
2 in the
same file;
 see how the discrepancy between analytical
and numerical solutions depends on the time
step delta(t)  see
sheet 3 in the
same file.

1/28
 Materials for Lecture #8:
 Assumptions made in the derivation of
 Langmuir isotherm (all three of them were
actually mentioned in the class):
 Monolayer coverage of the adsorbent (i.e.
"no double parking")
 Homogeneous surface; all adsorption sites
are the same
 Filled adsorption sites do not affect
adsorption of subsequent molecules. No interaction
between solutes
 Freundlich isotherm
 Each adsorption site is “Langmurian”
 (But) the adsorption sites exhibit a distribution
of adsorption energies
 Midterm
exam preparation guide
 Paper "The
constitution and fundamental properties of solids
and liquids. Part I. Solids" By Irving Langmuir.
Received September 5, 1916
 Miscellaneous: to pry out is to remove
something from something with or as if with a lever.
To peel out is to speed off in a car with
a screeching of tires.

1/25
 HW#1 is posted. Due
by the start of the class on Friday, February 8
(see Assignments
page)

1/15

1/14
 The following files are now uploaded (see "Contents"
page):
 addendum to example problem #2 (algebraic
derivation for 2c part of the problem)
 example problem #5 (with solution)

1/12
 The following files are now uploaded (see "Contents"
page):
 board notes for lecture 3
 example problem #3: "flow rate of a meandering
brook" problem
 PPT file with the derivation of the continuity
equation
 example problem #4: application of the continuity
equation

1/9
 PDF files with example problems #1 and #2 are
uploaded (see "Contents"
page)

1/7
 A PPT file with course overview slides is uploaded
(see "Contents"
page)

11/9
