Miller, Frank Ltr Bee Branch Pr
deffery A. Wickenkamp, P.E.
Senior Project Manager
Camp Dresser & McKee Inc.
125 South Wacker Drive, Suite 600
Chicago, IL 60606
Dear Mr. Wickerkamp,
602 E. 22nd St.
Dubuque, IA 52~1 ~
11-18-03 ~_.~. o~
Following the Sept. 25, 2003 meeting of the Dubuque BBCAC, I visited with you briefly about an
engineering alternative for the storm water/storm sewer problems being experienced periodically
here in Dubuque. For some time I have been working with Dr. Jos. Schaefer, P. E., formerly of Loras
College's Department of Physics & Engineering, & now an Engineering Professor at Iowa State
University, Ames, Iowa. Initially Dr. Schaefer did not have specific figures on such items as storm
sewer dimensions, so I have updated his preliminary calculations to more closely reflect these
figures as now known from information you provided at the Sept. 25, 2003 meeting of the Bee
Branch Citizen Advisory Committee. Because I will be sharing this communication with members of
the BBCAC, & others, I will be including some of my initial comments to Dr. Schaefer (as quotes
from communications to him) so that you may understand the background of my proposal(s) on this
matter.
From my communication to Dr. Schaefer on 3-18-03:
"The solution to the periodic flooding problem, proposed by the city's engineering consulting firm, is
a large open ditch some 6 or more blocks in length, costing between 20 & 25 million dollars, to carry
the excess runoff which the existing storm sewers cannot handle. It would displace a considerable
number of home owners and, having experienced a similar runoff ditch system in Japan, I know it
would initiate a separate set of problems of its own. Even if the displaced people got fair market
value for their homes & property, it would be very difficult for them to locate replacement housing
here in Dubuque because their homes are generally older & quite modest by today's standards.
What follows is my alternate proposal, which I have made to two members of the city's Engineering
Division: Deron Muehring, Civil Engineer, & Gus Psihoyos, PE, Assistant City Engineer. They
indicated that they would take my idea to their engineering consulting firm but after several weeks 1
have heard nothing. If you are willing, I would ask your informal opinion of the physics of the plan,
particularly from your background in hydraulic engineering. There may be some fundamental
reason that it will not function, either theoretically or practically but as yet no one has raised such a
concern. I know that it has never been done before - (at least these two engineers have no
knowledge of such a system) - and would probably need some testing.
First, the philosophy behind my proposal. The city engineers state "we have the flooding problem
because the existing storm sewer essentially gets 'full' when we have very heavy rain in a short time
span". The storm sewer empties into the retention basin (and ultimately the river) by means of
gravity. Because it is not practical to change the gradient of the storm sewer to increase the rate of
water transport, the conventional thinking is that we need something bigger, i.e. the large open ditch
to carry the water. It seems to me that this is an example of a sort of one dimensional thinking. After
all, "bigger is better" is often a legitimate solution to many problems but if that's the only avenue of
thought, perhaps some other solution is not even considered, causing, in this case, considerable
expense, social upheaval, & the perpetuation of what caused the runoff problem in the first place.
Page 2
Proposal #1.
My contention is that there is another way to transport the runoff. Certainly one can go 'bigger' but
has anyone considered causing the water in the existinq storm sewer to flow faster? And I'm not
talking about changing the gravitational gradient of the existing storm sewer to achieve this. This
idea came to me while considering a plumbers' method (which was used in my basement) to
quickly remove a pool of standing water which had formed when we had to dig up a branch sewer
line because it had rusted through (over the past century) & plugged. The trench which resulted
from us breaking up the concrete floor & removing the soil underneath to gain access to the sewer
line soon filled with water because the line was blocked further down stream from where we dug.
However, when we cleared the blockage the water in the trench slowly began to recede as it flowed,
through gravity, into the unblocked main sewer line. At this point the plumber took a hose with a
nozzle on the end, stuck it into the defective line directing the flow towards the main sewer line & the
trench emptied in a matter of a few tens of seconds, far quicker than it had been, even through he
was actually adding water to what was already there. I knew immediately that what has causing the
increased flow rate was the use of Bernoulli's Principle. The increased speed of the water exiting
the nozzle caused a reduced pressure because of the higher velocity & subsequently the effect of
atmospheric pressure caused the water to flow at a much higher speed. Such Bernoulli devices are
often employed to create vacuums in devices designed to 'pick up' water from floors, etc. Joe, I don't
need to explain the Bernoulli Equation to you but I will write it here in case you have someone else
look at this.
P + 1/2j~ v2 +p g h = a constant. P is pressure, j~ is mass density, v is
velocity, g is the acceleration due to gravity, & h is the height.
The three terms in the equation are related to the pressure, kinetic energy & gravitational potential
energy, respectively. Since changes in the gravitational potential energy within the storm sewer are
relatively small, they can be ignored. Therefore, if one can increase the velocity there is a reduction
in the pressure,. The application of Bernoulli's Principle is what enables us to explain why air
planes fly, curve balls curve, & the behavior of tsunamis (tidal waves), aspirators, etc.
So, what sort of mechanism am I proposing for the storm sewer. First, I propose using the existinq
storm sewer, but converting it into a two-stage operation. The existing main storm sewer, which
causes the problems, is large enough so that a small end-loader (Bobcat) can enter it for cleaning
& debris removal purposes. (The channel is approximately a rectangle with an arched top, some
10.5 feet in height and 16 ft in width. Figures corrected from original estimate.) The idea of a two-
stage system is to place, against one wall to still allow space for cleaning equipment, a smaller
diameter storm sewer pipe, e.g. say 9 feet in diameter, which would have strategically placed
openings for water entry along its length. (These 'intakes' should probably be near the bottom of this
pipe to reduce the intake of floating debris.) See diagram on separate page. Near the retention
basin end of this pipe would be a large version of the hose nozzle described in the application
above powered by a high velocity pump. Perhaps it only needs to be something like the pumps
used by fire engines, or perhaps it needs to be something like the pump/nozzle arrangements used
in placer mining operations.
This pump/nozzle arrangement would be used only under the following conditions. When the rain is
'normal' & the storm sewer does not fill beyond the top of the 2nd interior pipe, the sewer operates
just as it does now. However, with heavy short term rain the storm sewer fills beyond the top of the
interior pipe. Then sensors would trigger the pump/nozzle arrangement, causing a higher flow rate
in the inner pipe, thus lowering the pressure, allowing atmospheric pressure along the length of the
entire system to move the water faster than is done by the gravitational gradient. Once the water
level fell below the top of the interior pipe, the pump/nozzle arrangement can be automatically shut
down. The source of the water for this pump/nozzle system could be the storm sewer system itself,
city water mains, or as one of the city engineers suggested, it could come from the 32nd St.
detention basin where they need to get rid of some water anyhow.
Page 3
These are all details that could be worked out. I also believe the cost of converting the existing
system to atwo stage system would be far cheaper than the proposed 20 to 25 million dollar price
estimate for the open trench. However, I have no expertise in estimating such costs accurately.
To summarize, the proposed two-stage storm sewer has the following advantages: It is based upon
well known scientific principles; It utilizes existing facilities; The storm sewer would continue to
operate as a gravitational drainage system as it does at present; The second stage would go into
operation only when needed; The social disruption would be minimized; Presumably the costs
would be significantly less than the proposed open ditch solution; Safety concerns of an open ditch
of rapidly running water would be eliminated."
End of my communication to Dr. Schaefer on 3-18-03
In an initial e-mail reply, on or about March 20, Dr. Schaefer commented as follows:
"1 agree with your comments about the additional problems one could expect to occur with an open
ditch, & I share your conclusion about observations made of such systems in Japan. There might be
a better way to proceed, & at least the city should try to explore alternatives.
Your comments about the socio-economic consequences for the current residents who would be
displaced are very appropriate. I wonder where those who would be displaced could find
comparable housing at affordable prices. Open ditches lead to stagnant water, no matter how well
designed, & it is easy to think of dozens of problems associated with water standing in open ditches,
e.g. mosquitoes, disease, & safety of children.
in principle your idea works very well, and we know that it works on a small scale with both air &
water .... A factor that you have not included in your analysis is the friction of the walls. Such
losses are not insignificant .... So the upshot is that I know the system you describe works, but the
question is whether it would be practical in terms of the size & cost of the equipment that it would
require & in terms of the loss of flow rate due to friction. This could be a fertile new design area for
retrofitting systems such as Dubuque where similar run off problems have developed .... If I get
some time... I will make a quick calculation to estimate the frictional losses for your geometry."
Dr. Schaefer's detailed numerical analysis appears below. This calculation
addresses the problem of frictional effects caused by the secondary pipe.
From Dr. Schaefer's March 22, 2003 communication (with updated numeric
values & appropriate supporting editorial changes):
This is a calculation comparing the flow in a channd with a secondary pipe in it to the
flow with no such pipe present. For simplicity I treated it as open channel flow, even
though the storm sewer is enclosed. The situation shown in the diagrams would
approximate open charmel flow if the storm sewer is not completely full, e.g. the water
level was within, say, an inch of the top so that the water did not make contact with
the top. The same assumption is made for the pipe, i.e. there is a small area at the top
of the pipe that does not have contact with the water. Obviously, that is not the case
because for the given conditions the secondary pipe would, indeed be full. A more
complete calculation could be made for closed channel flow, but I do not want to go
through all of that today.
Page 4
I assume that the original storm sewer and the Secondary pipe are made of the same
material so that they have the same frictional effect. Perhaps the original storm sewer
is rough concrete or even brick so that in reality it would have a different friction
coefficient than new, smooth concrete that would be presumably used for the
secondary pipe, but my intent is not to get an exact answer. More about that later.
Using the dimensions from the diagram, assuming the depth of the charred to be 10.$
ft., the width to be 16 ft., the diameter of the secondary pipe to be 9 ft., and assuming
the channel to be rectangular in shape (the July 6, 1899 diagrams from city records
show the shape of a good portion of the Bee Branch line to approximate a rectangle
with an arched top), one can calculate certain mathematical properties of the storm
sewer charmel & secondary pipe which will be needed in further calculations, e.g.
areas, perimeters, etc. Because these calculations do not need to be extremely precise,
small variations in dimensions, certain estimates & assumptions, etc., do not
significantly effect the final result which may be off by a few percent due to these
variations.
If you wish to skip the mathematical portion of what follows, proceed to the results at
the asterisk, *, on page 6.
With the assumptions regarding open channel flow, the flowrate is given by the
Mamning Equation, which is:
Q= (k/n) A (Rh)2/3 So1/2
where OAs the flowrate in either m3/s or ft3/s, k is a conversion factor that is equal to
1.00 for S Iunits and is equal to 1.49 for British units (Manning was a Civil Engineer,
sohe did not express the equation in dimensionless parameters the way most such
equations in fluid mechanics are expressed). I will compare the two cases, so if both
calculations are conducted in the same units, the factor k will cancel out anyway.
n isthe Manning coefficient that represents the friction effect of the fluid on a
particular surface. For finished concrete n = 0.012, for unfinished concrete n = 0.013,
and for brickwork n = 0.015 so the assumption that the surfaces have the same
Manning coefficient is justified. If you prefer you could make a calculation with one
value for the original channel and another for the pipe, but as you will see that
difference will produce a small effect compared to the change in the wetted perimeter.
A is the cross sectional area of the channel, in either square feet or square meters, Rh
is the hydraulic radius of the channel. It is calculated by dividing the cross sectional
area of the channel by the wetted perimeter of the channel carrying the fluid. The
hydratd~c radius has the dimension of length. You have to be careful to not confuse
the hydraulic radius used in the Manning equation with the hydraulic diameter used
in calculations for the closed pipe. It does not necessarily follow that hydraulic radius
is one half the hydraulic diameter.
So is the slope of the channel, which I will assume is the same for both cases.
Page 5
Case 1 The original storm sewer in the present condition
Area: A = (10.5 ft) (16 ft) = 168 ft2 (Due to the irregular & changing shape of
the Bee Branch channel, I believe an area of 140 ft2 is a more
representative value of the actual average area, and this value, i.e. A =
140 ft2, will be used in the calculations which follow.)
Wetted Perimeter, "P": Under the assumptions listed above water is in contact with
both sides of the channel a_nd with the bottom of the channel so that P = 10.5 ft + 10.5
ft+ 16 ft = 37 ft
Hydraulic Radius: Rh= A / P = 140 ft2 / 37 ft= 3.78 ft
Thus we have the flowrate for the original condition, Qo as:
Cb = (k/n) (A) (Rh)2/3 So1/2 = (k/n) (3140) (6.3.78)2/3 So1/2 = 340 (k/n) So1/2
Case 2. Pipe with circular cross section ofdiameter 9 ft placed inside the original
storln sewer.
Area: I assume that there, s no reduction in the area for flow produced by the
insertion of the pipe, i.e. the wall thickness for the pipe is negligible. This is an
assumption in your favor, the effect of which can be calculated in a more precise
mathematical analysis.
Wetted Perimeter, "P": The water touches one 10.5 ft wall of the original channel. The
pipe makes contact with the other 10.5 ft wall and with the 16 ft base of the original
channel. In an ideal world the pipe would be tangent to those surfaces with an
infinites~ region of contact, but in reality there will be a greater length of the
original channel not in contact with the water. While this gives a wetted perimeter of
37 ft, for this calculation I reduced the wetted perimeter ofthe original channel to 35
ft, again an assumption probably still in your favor. The pipe is wetted on both sides
(inside & outside) so its wetted perimeter is 2 (,r) (D) = 2 (,r) (9 ft) = 56.5 ft. The
portion of the outside wall of the pipe touching the two wails will not be wetted, but I
believe that the 2 ft reduction in P for the channel covers that. It also covers the fact
that for open channel flow the pipe will not be completely full. This gives a total
wetted perimeter of P = 35 + 56.5 = 91.5 ft. Compare this to the 37 ft calculated for
the original condition. You could reduce this number if you believe that the
assumptions regarding contact between the pipe and the wails is not generous enough.
Hydraulic Radius: Rh = A / P = 140 ft2 / 91.5ft = 1.53 ft
Note the significant reduction in the hydraulic radius because the water is in contact
with more surface. The real culprit here is the fact that the secondary pipe makes
contact with the water on both sides, inside & out.
Page 6
The flowrate for the condition with the secondary pipe, Qp is:
Qp = (k/n) (A) (Rh)2/35ol/2 =
(k/n)(36140) (2.1.53)2/3 So1/2 = 186(k/n) So1/2
When we calculate the ratio ofthe two flowrates with the assumption that both
materials have the same Manning coefficient and both channels have the same slope,
the (k/n) So1/2 te~ms cancel out and the ratio of the flowrates is:
Qp / Qo = 186 / 340 = 0.547
*This means the flowrate with the secondary pipe in place is only 54.7% of the original
flowrate because of the greater loss to friction. I suspect that you will have difficulty
accepting that the frictional effect is so great, because I know that I had some
difficulty in accepting it when I D_rst encountered it in teaching Fluid Mechanics from
an engineering approach. You see, we both are accustomed to a Physics approach that
assumes ideal, inviscid fluids.
Stating this in another way, the reduction in flow that occurs because of the added
friction due to inserting the pipe in the original storm sewer is 100% - 54.7% = 45.3%.
That means that your system using the Bernoulli effect would have to bring about at
least a 45.3% increase in flowrate inside the secondary pipe to break even without
considering the cost of purchasing, installing, and operating the system.
One might think that substitution a smooth steel pipe would help reduce the losses,
but it turns out that the Manning coefficient for smooth steel is the same 0.012 as for
finished concrete. Interestingly enough, for painted steel n = 0.014, although there
may be some special epoxy paint that is slicker and might give a smaller value.
I believe that all of the assumptions that I made in these calculations favor your
system in any roundoffs, the neglecting of contact length, etc.
This calculation leads me to believe that it would be difficult to implement your
suggestion in a practical way because of all the losses incurred.
End of Dr. Schaefer's communication of March 22, 2003
From Dr. Schaefer's analysis above, one would need to increase the flow rate in the
secondary pipe at least a factor of 2 to have any meaningful gain with the two-pipe
system. While I believe it is possible to achieve that type of gain on a small scale, I am
not qualified to judge whether or not it can be achieved on the larger scale needed.
Now having gone through ali of this it struck me that a simpler modification of this
idea might be much more promising.
Page 7
Proposal #2.
books make the point that pipes are not really necessary for the Bernoulli
effect to work. Therefore, what would happen if one discarded the idea of the second
pipe & simply put the water injection nozzles near the end of the Bee Branch channel
near 16th Street? This works on the smaller scale plumbing example mentioned
above. Costs would be far cheaper, ff one could get a flow rate twice as fast due to the
Bernoulli effect, it would be like having two identical Bee Branch chmmels for far less
than building a large open ditch. ~
From another communication from Prof. Schaefer:
"Perhaps you could convince the city staff to have the Iowa Institute of Hydraulic
Research (rlHR) conduct some experiments with models to test the idea(s). The costs of
such a study would depend upon how much of a complete analysis would be required,
but I would think that $10,000 to $20,000 would finance an investigation that would
give some reasonable answers.
If the city wants to pursue that (i.e. this secondary pipe idea, Proposal #1), or if you
simply want to ask some questions, I suggest contacting Rob Ettema. He is Chairman of
Civil Engineering at the State University of Iowa, Iowa City. (Dr. Schaefer worked with
him for 7 summers at l/HR. He can be reached at: 319-384-0596 or e-mail at robert-
ettema@uiowa.edu"
hoankyou for your time in examining these proposals. It is personal belief that
posal #2 should be considered first, my
Sincerely,
Frank Miller, Member of BBCAC