6" SS EXHAUST STACK

[Joyce and Richard Hayden]

Kurt & David and others who might be following this discussion as I have.

When you introduced the Bernoulli's Equation into this discussion I figured it was time to ask my brother for help. He has some background with advanced math and has been helpful to another of our group in the past. I forwarded to him the messages at the bottom to give him some background and data that had already been offered. I notice now that this subject has died down somewhat so far today but here is his message to me anyway. I am not going to pretend that I understand all of it but it seems that going from 6" to 5" isn't going to be the end of the world. I know you two have Series 60 engines and I have the older 8v92 but the problem is the same and I have discovered a holds in the elbow that goes into the muffler. That elbow is probably unobtainable or if it is would be quite expensive. So, I was considering 5" as many others have.

Any, here is my brother Steve Hayden's response to me - unedited:

Brother,

You have stretched the limits of my memory on this one! The last time I thought about fluid flow and the Bernoulli Principal was probably 40 or so years ago. Not to worry; it is fun to fire up the old neurons. I'll try to answer your question below. The response isn't technically rigorous as some of your forum buddies may point out. It does seem to make sense though.

As I understand the question, it goes something like this. Does changing the diameter of the exhaust system on the bus from six inches to five inches result in any noticeable decrease in performance? I understand that the exhaust system runs from the manifolds to a turbocharger and then out through a muffler to the atmosphere. If one constricts the exhaust from the outlet of the turbocharger which results in a higher pressure at the output, then the turbocharger efficiency decreases. Have I got that about right?

If so, then the answer is changing from six inch diameter to five inch is very unlikely to result in any detectable decrease in performance. Here's the logic I used to reach this conclusion.

To make the calculation, one uses one of the forms of Bernoulli's Equation. I saw in one of the posts you sent me a reference to a nice discussion of Bernoulli's Equation. This discussion is correct in that it points out that Bernoulli's Equation is an energy conservation equation which means you can't get something for nothing. This equation only holds when no outside work is being done on the system nor is the system doing any work on the outside. Consequently, as was pointed out in the posting, the Bernoulli Equation applies to the ideal situation of, for example, non-compressible gas, laminar flow (non-turbulent), no friction with the pipe walls and so on.

Accounting for these non-ideal conditions from first principles is tedious and usually results in equations that cannot be solved in closed form. Engineers get around this by putting correction terms in the equation and then determining the coefficients of the correction terms by experimentation. This is a science within itself and not as easy as I just made it sound. Fortunately, engineers have been interested in fluid, including gas, flow in pipes for such applications as gas and oil pipelines and have derived equations for these applications. I did find an on-line calculator at http://www.pipeflowcalculations.com/ which I used to make my analysis.

Of course, I had to make some assumptions to plug into the calculator. With your help, I came up with the flowing. The amount of exhaust gas that must be expelled out the exhaust pipe per unit time was 24,000 liters/min. You estimated this from the displacement of the engine cylinders times the number of cylinders times the rpm of the engine. We also agreed that the length of pipe from the turbocharger to the exhaust outlet at 7 feet and the temperature of the exhaust at 500 F. I assumed the exhaust pipe was smooth with a roughness of lest than one thousandth of an inch. The local resistance coefficient which accounts for bends in the exhaust pipe and other local constraints was tougher. I used the calculator default value of 1 but also did a sensitivity analysis.

Since the pressure at the exhaust pipe outlet is atmospheric (14.7 psi), I calculated the pressure drop from the turbocharger outlet to atmosphere along the length of the exhaust pipe for different pipe diameters. The result is shown graphically below.

Note that the pressure drop axis is logarithmic. So the difference in pressure drop between a 5 and 6 inch diameter pipe is only about 0.15 psi. In fact, the pressure drop is less than 1 psi for exhaust pipes 3.5 inches and larger.

I did change the local resistance coefficient to see the effect. At the default value of 1 and for a 5 inch diameter pipe, the pressure drop is 0.25 psi. An order of magnitude less at 0.1 results in a pressure drop of 0.09 psi and an order of magnitude larger at 10, 1.8 psi.

I don't know what the pressure at the turbocharger input is but seems unlikely that a pressure change of 1 psi or less at the turbocharger output would result in a detectable decrease in performance. Perhaps someone on your forum has this number.

Since many systems are over designed to have a safety margin, it also seems to make sense that changing to 5 inch diameter from 6 inch should make little difference.

Hope this helps. Feel free to cut and paste onto the forum if you like. Any questions, you know where I live.

Steve

----- Original Message -----

From: "kguns@hughes.net"

To: "WanderlodgeForum@yahoogroups.com"

Sent: Friday, October 31, 2008 8:24 PM

Subject: [WanderlodgeForum] Re: 6" SS EXHAUST STACK

David,

A few days ago you were all for a straight pipe.

Now we have delved into the effects and merits of the, "Bernoulli
effect" it presumes that the density of the flowing gas is constant,
which will not necessarily be true in this application.

If this were a consideration and a factor in design and function
wouldn't this be a standard application on all exhausts, considering
today's drive for better performance Vs energy expended Vs
particulate
matter expelled Vs whatever else the EPA thinks we should be
ejecting from our exhaust pipes?

One factor you may have not considered are the exhaust blankets I
mentioned. They will retain the heat within the pipes thus increasing
the velocity of the exhaust creating an accelerated flow of gasses
through the tubes.

If I may present another observation, 5" exhaust systems are the
standard on all production class 8 trucks.

Furthermore and for the heck of it I don't believe that the trucker
that has 8" stacks on his rig has considered the, "Bernoulli effect"
in his choice at the Chrome Shop. Although it mat have an effect on
performance further than just looking cool. They do look good, no
doubt.

For the last four weeks I have queried Detroit Diesel, Custom Exhaust
Fabricators, Several OEM Exhaust Mfg.'s, Marine Exhaust Engineers &
Fabricators, My BB Guru, and anyone else that would lend an ear, and
no one has expressed any apprehension or regard in the respect to a
5" exhaust system. In fact all parties expressed their surprise in
respect as to why the system would change size at the muffler.

Several owners have modified their systems to 5" from end to end, and
have seen no change in performance. Positive or negative, In general
it was just a matter of convenience in acquiring parts, I won't get
into that. That has recently been beaten to death at the expense of
all parties involved

If there is someone who would like to further this debate with
Imperical evidence of the merits of, or placing a venturi somewhere
in this exhaust system I have pasted a site below where you can
formulate your calculations. I would love to see some evidence of a
positive effect, in which case I would have no problem in adding a
venturi crimp in the exhaust system.

Bernoulli Calculation

http://hyperphysics.phy-astr.gsu.edu/Hbase/pber.html#beq

The calculation of the "real world" pressure in a constriction of a
tube is difficult to do because of viscous losses, turbulence, and
the assumptions which must be made about the velocity profile (which
affect the calculated kinetic energy). The model calculation here
assumes laminar flow (no turbulence), assumes that the distance from
the larger diameter to the smaller is short enough that viscous
losses can be neglected, and assumes that the velocity profile
follows that of theoretical laminar flow. Specifically, this involves
assuming that the effective flow velocity is one half of the maximum
velocity, and that the average kinetic energy density is given by one
third of the maximum kinetic energy density.

Now if you can swallow all those assumptions, you can model* the flow
in a tube where the volume flow rate is = cm3/s and the fluid density
is ñ = gm/cm3. For an inlet tube area A1= cm2 (radius r1 =cm), the
geometry of flow leads to an effective fluid velocity of v1 =cm/s.
Since the Bernoulli equation includes the fluid potential energy as
well, the height of the inlet tube is specified as h1 = cm. If the
area of the tube is constricted to A2=cm2 (radius r1 = cm), then
without any further assumptions the effective fluid velocity in the
constriction must be v2 = cm/s. The height of the constricted tube
is specified as h2 = cm.

The kinetic energy densities at the two locations in the tube can now
be calculated, and the Bernoulli equation applied to constrain the
process to conserve energy, thus giving a value for the pressure in
the constriction. First, specify a pressure in the inlet tube:
Inlet pressure = P1 = kPa = lb/in2 = mmHg = atmos.
The energy densities can now be calculated. The energy unit for the
CGS units used is the erg.

Inlet tube energy densities
Kinetic energy density = erg/cm3
Potential energy density = erg/cm3
Pressure energy density = erg/cm3
Constricted tube energy densities
Kinetic energy density = erg/cm3
Potential energy density = erg/cm3
Pressure energy density = erg/cm3


The pressure energy density in the constricted tube can now be
finally converted into more conventional pressure units to see the
effect of the constricted flow on the fluid pressure:

Calculated pressure in constriction =
P2= kPa = lb/in2 = mmHg = atmos.

This calculation can give some perspective on the energy involved in
fluid flow, but it's accuracy is always suspect because of the
assumption of laminar flow. For typical inlet conditions, the energy
density associated with the pressure will be dominant on the input
side; after all, we live at the bottom of an atmospheric sea which
contributes a large amount of pressure energy. If a drastic enough
reduction in radius is used to yield a pressure in the constriction
which is less than atmospheric pressure, there is almost certainly
some turbulence involved in the flow into that constriction.
Nevertheless, the calculation can show why we can get a significant
amount of suction (pressure less than atmospheric) with
an "aspirator" on a high pressure faucet. These devices consist of a
metal tube of reducing radius with a side tube into the region of
constricted radius for suction.

*Note: Some default values will be entered for some of the values as
you start exploring the calculation. All of them can be changed as a
part of your calculation.

Kurt Horvath
95 PT 42
10AC

> > > >
> > > > --- In "WanderlodgeForum%40yahoogroups.com"
> > Forum%40yahoogroups.com>
> > > > Forum%40yahoogroups.com>, David Brady

> > > > wrote:
> > > > >
> > > > > Hi Kurt,
> > > > >
> > > > > No thanks, I already have a stock muffler. Thanks for the
links,
> > > > > there's some pretty nifty items there. Be careful with
those fancy
> > > > > braided stainless steel pieces. They look sharp, but
they've always
> > > > > leaked on my turbocharged subaru wrx. Kurt, you've been
around
> > > > > a few over-the-road coaches, Prevost' and what not, what do
they
> > > > > run on their exhaust systems; i.e., expansion pipes, flex
pipe, etc.
> > > > >
> > > > > David Brady
> > > > > '02 LXi, NC
> > > > >
> > > > > Kurt Horvath wrote:
> > > > > >
> > > > > > David, Would you like to take that brand new muffler off
my
> > > > hands???
> > > > > >
> > > > > > According to DD straight pipe & ECU will not have any
issues in
> > > > the
> > > > > > 95 vintage S 60.
> > > > > >
> > > > > > OEM built that pipe for BB ACAP - As Cheep As Possible -
> > > > > >
> > > > > > The original routing of the pipe leaves the turbo, source
of the
> > > > > > first failure, cracked the 1st 90 degree turn a short
straight run
> > > > > > 2nd. 90 degree turn, then into a double ball connector
that also
> > > > > > telescopes in and out. You can check out that piece of S--
-, sorry
> > > > > > engineering wonder here.
> > > > > >
> > > > > >
http://www.dynaflexproducts.com/downloads/DP_Catalog_03_pg70-
> > <http://www.dynaflexproducts.com/downloads/DP_Catalog_03_pg70->
> > > > <http://www.dynaflexproducts.com/downloads/DP_Catalog_03_pg70-

> > <http://www.dynaflexproducts.com/downloads/DP_Catalog_03_pg70->>
> > > > 89.pdf
> > > > > >
<http://www.dynaflexproducts.com/downloads/DP_Catalog_03_pg70-
> > <http://www.dynaflexproducts.com/downloads/DP_Catalog_03_pg70->
> > > > <http://www.dynaflexproducts.com/downloads/DP_Catalog_03_pg70-

> > <http://www.dynaflexproducts.com/downloads/DP_Catalog_03_pg70->>
> > > > 89.pdf>
> > > > > >
> > > > > > Page 76 Double Ball Joint with Slip Joint Feature
Allowing Lateral
> > > > > > Movement length 16 to 18 inches mine measures 14 .55
inches at
> > > > > > present. This marvel allows for 10 degrees of angularity
360
> > > > degree
> > > > > > rotation 2" of offset 2" axial movement,. Hell the u
joints can't
> > > > > > move around that much. Besides it was hard clamped to the
mount
> > > > from
> > > > > > the engine in front of this connection not to mention
rusted to
> > > > the
> > > > > > point that it took an pneumatic impact chisel to get it
apart.. So
> > > > > > what's the point. You need flex in between the turbo and
the first
> > > > > > mount.
> > > > > >
> > > > > > The Flex Connector with liner I choose is here at
> > > > > >
> > > > > > http://vibrantperformance.com/catalog/product_info.php?
> > <http://vibrantperformance.com/catalog/product_info.php?>
> > > > <http://vibrantperformance.com/catalog/product_info.php?
> > <http://vibrantperformance.com/catalog/product_info.php?>>
> > > > > > <http://vibrantperformance.com/catalog/product_info.php?
> > <http://vibrantperformance.com/catalog/product_info.php?>
> > > > <http://vibrantperformance.com/catalog/product_info.php?
> > <http://vibrantperformance.com/catalog/product_info.php?>>>
> > > > > >
> > > >
cPath=1022_1035_1064_1114&products_id=1008&osCsid=999d7ef5fdd15864bae3
> > > > > > 3db41abf5ef9
> > > > > >
> > > > > > The 2 90 degree turns were fabricated in that manner
because it's
> > > > not
> > > > > > easy to bend large diameter pipe in a single 180 degree
bend, thus
> > > > > > they weld 2 90's together, which is the industry standard
for
> > > > > > manufacturing a 180 degree turn in large pipe exhausts.
Well this
> > > > > > ain't the factory and we're not constrained by what is
easy. I
> > > > have
> > > > > > acquired a 14ga 180 degree U-Tube that has the same
external
> > > > > > dimensions as the original pipe. I'm not an engineer but I
> > > > reasonably
> > > > > > certain that with the remaining 90 degree bend and a 45
degree
> > > > bend
> > > > > > there will be sufficient back pressure.
> > > > > >
> > > > > > There will also be a flexible pipe hanger mount behind
the Flex
> > > > > > connector mounted on the ceiling of the engine
compartment that
> > > > will
> > > > > > support the middle section of pipe and will allow for any
movement
> > > > > > and or torque that may be transferred to the pipe by the
motor.
> > > > The
> > > > > > original clamps for the muffler have to go as they are 6"
but the
> > > > > > rubber isolated mounting bars will remain and that's all
that was
> > > > > > there to begin with. So where's the rub? Bub!
> > > > > >
> > > > > > Not to take anything away from the engineers that
designed the
> > > > Bird,
> > > > > > But there are some glaring deficiencies. 7 way trailer
plug, Air
> > > > > > Purge System, Watts valve, Accelerator and Brake peddles,
Front
> > > > Left
> > > > > > Shock Mount, Relay for Jake Brake, W/D Vent for Slendide
2000,
> > > > > > Installation of Refrigerator with inadequate convection,
The seat
> > > > > > belts mounted to floor instead of the seat, That reminds
me I
> > > > still
> > > > > > have to fix that one. Nothing like hitting a road
transition just
> > > > to
> > > > > > have the air ride seat bounce and the seat belts
automatically
> > > > adjust
> > > > > > for the slack then the air ride seat rebounds and the
belts try to
> > > > > > cut you in half at the waist. That's just the 95 PT 42.
I'm not
> > > > > > bitchin! I'm fixin
> > > > > >
> > > > > > Kurt Horvath
> > > > > > 95 PT 42
> > > > > > 10AC
> > > > > >
> > > > > > --- In "WanderlodgeForum%40yahoogroups.com"
> > Forum%40yahoogroups.com>
> > > > Forum%40yahoogroups.com>
> > > > > > Forum%40yahoogroups.com>, David Brady

> > > > > > wrote:
> > > > > > >
> > > > > > > Kurt,
> > > > > > >
> > > > > > > I agree with Greg. I'm gonna keep mine stock. There's a
bunch
> > > > > > > of vibration and movement back there. I figure BB's been
> > > > building
> > > > > > > buses a whole lot longer than I have. Initially I'd
scratch my
> > > > > > > head when looking at the frame and support pieces, but
when
> > > > > > > you consider that something as big as a bus must twist
and flex,
> > > > > > > this flexibility needs to be designed in. Make one piece
> > > > stronger
> > > > > > > and you've created a stress raiser someplace else.
> > > > > > >
> > > > > > > I have a friend who transplanted a honda v-tech motor
into a
> > > > > > > lotus elise. Everything worked but the alternator
mount. The
> > > > mount
> > > > > > > insists on cracking. There can be some weird harmonics
and
> > > > > > > resonant frequencies going on that are difficult to
grasp and
> > > > > > > only trial and error and a 50 year track record of
building
> > > > buses
> > > > > > > can solve (unless you can model it and run high powered
> > > > > > > computer finite element analysis on it). He's still
fighting
> > > > that
> > > > > > > mount...
> > > > > > >
> > > > > > > Okay, I'm off my soap box.
> > > > > > >
> > > > > > > David Brady
> > > > > > > '02 LXi, NC
> > > > > > >
> > > > > > > Gregory OConnor wrote:
> > > > > > > >
> > > > > > > > Kurt, try and figure why there were 4 bends. it may
be that
> > > > it was
> > > > > > > > engineered to alow for swing room between the 'hung
exhaust'
> > > > and
> > > > > > > > the 'torque reaction of the ruber mounted detroit'.
look at
> > > > the
> > > > > > roll
> > > > > > > > of the torque and see that there is a place for the
movement
> > > > to
> > > > > > twist
> > > > > > > > a union. I kinda think this movement was the problem
with the
> > > > > > > > resulting crack.
crack=result ;movement=cause ;facilitate
> > > > movement
> > > > > > > > =repair. may be that BB enginered it correct but
someone
> > > > > > > > overtightened a band to cure an exhaust leak???????
you also
> > > > got
> > > > > > to
> > > > > > > > keep the stack from cantilivering off of the maniford
with
> > > > your
> > > > > > new
> > > > > > > > design. Scavenging is one variable in fuel
efficiency. even
> > > > > > straight
> > > > > > > > pipes some time will result in lower fuel economy
because the
> > > > > > intake
> > > > > > > > variable get screwd. backpressure is mathed into the
computer.
> > > > > > > >
> > > > > > > >
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> > > > > > > > Internal Virus Database is out-of-date.
> > > > > > > > Checked by AVG.
> > > > > > > > Version: 7.5.405 / Virus Database: 270.8.0/1715 -
Release
> > > > Date:
> > > > > > 10/9/2008 12:00 AM
> > > > > > > >
> > > > > > >
> > > > > >
> > > > > >
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> > > > ------
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> > > > > > Checked by AVG.
> > > > > > Version: 7.5.405 / Virus Database: 270.8.0/1715 - Release
Date:
> > > > 10/9/2008 12:00 AM
> > > > > >
> > > > >
> > > >
> > > >
> > > >
> > ----------------------------------------------------------
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> > > > Checked by AVG.
> > > > Version: 7.5.405 / Virus Database: 270.8.0/1715 - Release
Date:
> > 10/9/2008 12:00 AM
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> > Checked by AVG.
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10/9/2008 12:00 AM
> >
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