Spring 2013
ENE 801: Dynamics of Environmental Systems






  • uploaded
    • board notes on turbulent diffusion and advection-dispersion equation



  • 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)



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



  • board notes for the introductory lecture on turbulence are uploaded


  • 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 z-direction;
    • hint: follow the algorithm we used when deriving the continuity equation for an  incompressible fluid
  • corrected version of board notes on the topic of Carman-Kozeny equation is uploaded





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


  • 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 Streeter-Phelps 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)
  • 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)
  • 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.


  • 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):
  • 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 steady-state will be reached in an CSTR with a reaction of the first order


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



  • 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"


  • Comments on HW#1
    • problem #7
      • Question:  "The reaction dopes not look like a first order reaction. Is it first-order?"
      • Answer:  "settling is assumed to follow the first-order 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 soap-free 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.



  • Materials for Lecture #8:
  • Assumptions made in the derivation of
    • Langmuir isotherm (all three of them were actually mentioned in the class):
      1. Monolayer coverage of the adsorbent (i.e. "no double parking")
      2. Homogeneous surface; all adsorption sites are the same
      3. Filled adsorption sites do not affect adsorption of subsequent molecules. No interaction between solutes
    • Freundlich isotherm
      1. Each adsorption site is “Langmurian”
      2. (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.


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



  • 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)


  • 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


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


  • A PPT file with course overview slides is uploaded (see "Contents" page)