This is an equation free, "not ready for prime time", post because I've just started working on the exhaust system part of my PSD computer model. I've added a few comments on three recent exhaust system threads, and I thought it might be useful to summarize those and a few other things I've learned so far. I'm planning on collecting measurements on various configurations of PSD exhaust systems so I can hopefully understand and quantify their performance differences in more detail.

The following discussion concerns the exhaust flow path from the exhaust valve port to the end of the tailpipe. By extrapolating some reference data I found on another engine to a 7.3L displacement, I estimate that engine HP is reduced by as much as 5 HP for each additional 1 psi increase in Exhaust Back Pressure, EBP, at the exhaust valve port. Therefore, an exhaust system which produces the lowest EBP will result in the highest engine HP, everything else being equal.

The flow path from the exhaust valve port to the turbo is usually the stock configuration for most trucks. I'd like to hear from anyone that's replaced their stock exhaust manifold with a set of custom headers. The only other mod that comes to mind is insulating the up-pipes and the turbine housing to more efficiently use a given EBP to generate the most high temperature expansion pressure possible to drive the turbo. The goal here is to generate to most BP with the least amount of EBP, and of course better turbos help do this, but I'm talking about "everything else being equal" when I discuss the various exhaust system configurations.

The flow path from the turbo outlet to the end of the tailpipe is where most mods are done, and any additional restriction here directly adds to the EBP at the exhaust valve port, and thereby reduces HP. My research suggests it's best to run a constant diameter pipe over the entire distance from the turbo to the end of the tailpipe, because any change in diameter results in turbulence at the junction, and this increases the restriction to flow, and increases EBP. This holds true even if you go from a smaller to a larger diameter, because the turbulence effect more than offsets the reduced friction from the larger diameter. From here on, tailpipe refers to this entire length.

The EBP generates a pushing force that overcomes friction to move the gas along the pipe. The EBP required to maintain a given flow in a straight section of horizontal pipe is proportional to the length. The EBP is significantly increased by bends. One way to see the adverse effect of bends is to consider the mass flow. A mass has inertia and wants to keep going in the same direction. A force is required to change the direction of a mass and make it flow around a bend, and that force is generated by increased EBP. The sharpness of a bend increases the rate of change in direction, and this means even more force and an even higher EBP.

Most performance exhaust systems tout their use of "mandrel-formed" bends, and they kind of imply that their special bends don't cause much more restriction than a straight piece of pipe. However, this type of bend does nothing whatsoever to circumvent or reduce the EBP increase required to change the direction of a mass, which is purely based on the force, mass, and acceleration requirements of Newtonian physics. Mandrel bends do keep the diameter constant, and this is the first requirement I mentioned for keeping the EBP as low as possible. So if you must have a bend, a mandrel bend is the best way to minimize the adverse effect on EBP due to a bend.

Now to address the interesting issue of the "optimum diameter" that a tailpipe should have to minimize its EBP for a given exhaust flow. The precise value is hard to calculate, and it depends on RPM, BP, and other factors, but I at least want to discuss why there is an "optimum diameter", and that larger diameter tailpipes don't necessarily give lower EBP, and might even give higher EBP than smaller diameters.

To make this easier to discuss, consider the following terms... D=Tailpipe Diameter, EBP=Exhaust Back Pressure, EGP=Exhaust Gas Pressure, EGT=Exhaust Gas Temperature, EGD=Exhaust Gas Density, and EGV=Exhaust Gas Velocity. Except for D, all the other parameter values vary along the length of the tailpipe, which is what makes exhaust flow so difficult to analyze. Also, EGP and EGT determine EGD, whereas EBP is the net effect that reduces HP.

A larger D reduces friction which reduces EBP, however, a larger D also reduces EGV, which allows more time for the gas to cool, which reduces EGT, and this increases EGD, which means that a heavier volume of gas must be pushed along each segment of the pipe, and this requires a higher EBP. So if the D is too large, the favorable reduction in friction is more than offset by the increase in EGD, and the net effect is to increase EBP. I'll give several quotes that might explain this better.

In summary, all the exhaust system information I've come across suggests that a straight, short, horizontal tailpipe with a constant diameter that's optimized for the actual gas flow will provide the minimum possible EBP, and therefore the most HP. Any changes to this diameter, increased length, addition of bends, or uphill runs will increase the EBP above this level.

The following quotes are from several websites on exhaust system design...

"Exhaust Theory... We've seen too much misinformation regarding exhaust theory. What kind of misinformation? For starters, there are a lot of people in the "Bigger is Better" camp. We're talking about exhaust pipe diameters. Even the big magazine editors are boldly smattering statements like, "For a turbo car, you can't get an exhaust pipe that's too big." Also, terms like "back pressure" and the statement, "An engine needs back pressure to run properly!" really rub us the wrong way."

"Pipe Sizing... We've seen quiet a few "experienced" racers tell people that a bigger exhaust is a better exhaust. Hahaha… NOT. As discussed earlier, exhaust gas is hot. And we'd like to keep it hot throughout the exhaust system. Why? The answer is simple. Cold air is dense air, and dense air is heavy air. We don't want our engine to be pushing a heavy mass of exhaust gas out of the tailpipe. An extremely large exhaust pipe will cause a slow exhaust flow, which will in turn give the gas plenty of time to cool off en route."

"When contemplating a modified exhaust system there are those who want the biggest diameter pipe that can be had. Their idea must be that fatter pipes are more effective at venting than narrower pipes. This sounds reasonable but it is not quite correct. Sure wider pipes have greater volume and higher flow capacity, but that is just half of the story. Capacity is one consideration but gas velocity is the other factor."

"An experienced exhaust designer knows that the best exhaust is one that balances flow capacity with velocity. A given volume/time of gasses might travel faster through a 2" pipe than the same volume of gas passing through a 3" pipe. The optimum is where the fastest velocity is achieved with the least constriction possible. This situation will arise when the pipe is wide enough so that there is the least level of positive backpressure possible whilst achieving the highest exhaust gas velocity."

 

WOW thats alot of info. So what do you think is the best dia for our trucks? I have a 02 450 flatbed. I was thinking 4'' straight pipe w/dual outlets,pipes to exit in front of rear tires. If going with straight pipe does it make a difference on the brand? I was thinking MBRP

 

Wow! I just bought the cheapest system.
Bob

 

Which one was that? I am still awaiting Gene's ever present graphical data and/or calculations that usually follow a post like this before I respond here.

 

mindlessly following......

 

You won't find this answer very satisfying, but it's the best one I've got for now. Unlike a nuclear reactor which directly converts mass into energy, the combustion process produces HP by breaking chemical bonds to release energy, and the total mass of all the reactants before and after combustion remains unchanged. This means that all the lbs of air and all the lbs of diesel that go into the combustion chambers must also come out the exhaust ports as an equal number of lbs of waste exhaust gas, and this determines the CFM flow in the tailpipe. By taking these kinds of factors into account, one can in principle scale from the optimum tailpipe diameters that are discussed for different displacements and types of engines to the PSD.

However for a specific PSD, you also have to account for the many other factors that determine its CFM exhaust flow including upgraded turbos which increase the intake CFM, larger injectors, boost levels, and RPM range to optimize for. Even if you know all these parameters for a specific truck, a given tailpipe diameter will only be truly optimum for a given range of RPM and BP, and at this point I'm still trying to figure out all the details, and I'm a long way from being able to calculate the optimum diameter.

Since you mentioned a side exit exhaust, I posted these pics of mine. I modified my 3.5" Banks exhaust about 9 years ago to this configuration because I'm carrying 3,200 lbs of hitch weight and it kept hitting the real axel. The thing in the center is a an exhaust brake, and its got a fitting that I'm going to use to make pressure measurements, and combine those with EGT measurements at the exit and several other points along the tailpipe, and see if I can come up with a way to estimate EGP, EGD, and EGV directly from EGT at different tailpipe locations combined with exhaust manifold EGT, BP, and RPM.

 

Well Gene, ya got me going again. Since Joe is likely sleeping, I am left to respond. I like your exhaust setup although it is somewhat girlie, all small and stuff.

I will be very curious to see how the math works out. I understand that the expanding pipe past the DP allows the exhaust gasses to cool and therefore become more dense/heavy. However there is more space available for it to flow. Would this not negate the difference in back pressure? If not, what you are saying is that stacks are a power robber. Isn't that right? Huge expansion chamber and needs to be pushed out the top? Is this what you are saying in so many words?

 

I understand the thought of cooler temps causing the air to be more dense, but if large stacks caused a power loss every big truck would have a weed burners on them. I know they are not psd, but I dont think the result would be any different.

 

Seems to me that with all the other parasitic losses on a tractor, the difference between stacks and weed burners would be negligible. Especially considering the safety aspects of putting those smoke belchers up and out of the way. I'm not a fan of stacks, but I've been considering a single stack in my bed for water crossing purposes, though I'm a long way from needing it now.

 

Yes and no, possibly maybe, even though there is more mass that is cooler to push through the pipe, warm air still rises, and the EGT is still going to be way above ambient AT. IS this effect enough to counter act the redirection of the mass at the 90* elbow? IDK. we also have to take into consideration the spliting of the mass at the T pipe, and the venturi effect of the stack tips way up there in the airflow, wich I am guesing is more airflow than below the truck (at least a cleaner more laminar flow than below the truck with all the lower pressure vortices' from the running gear and tires .


I would think that a straight piece of pipe off the down pipe with a slash cut at the end (no turndows or bends) would be the best at alleviating EBP, and maintaining EGT.

 

Well since the "optimum" diameter is smaller for less CFM exhaust flow, a 3.5" diameter tailpipe might be about optimum for my early 99 truck. Less CFM air flow coming in, and less fuel flow, means less CFM exhaust flow coming out! Well this concept of an optimum tailpipe diameter isn't my idea. I was more familiar with the air flow equations for the intake side, and there you want the airflow to be as cool as possible to maximize the number of O2 molecules going into the engine. It never dawned on me that just the opposite is true on the exhaust side until I started researching, and read multiple references that said you want to keep the exhaust gas as hot as possible so you're pushing lighter gas down the tailpipe.

Here's a few interesting posts from this thread, which you also posted on...

Insulating the turbo and up-pipes?? By 99 7.3 towrig
https://www.ford-trucks.com/forums/590809-insulating-the-turbo-an-up-pipes.html

Now the first part of this is consistent with my current research, but the last part isn't. All the references I've found so far say that less EBP results by keeping the tailpipe a constant diameter, and the most optimum diameter is the one which maintains the velocity and temp as high as possible without causing too much restriction because of friction.

For a given CFM, a larger diameter reduces the flow velocity by 1/D^2, and this allows more cooling, and if you then step up to an even larger D, the velocity gets even slower, which leads to more cooling, etc.., and pretty soon you've got a huge pipe full of cold heavy gas to push along, and that requires a lot more pushing force and EBP than getting the gas down the pipe and out the end quickly, while it's still as hot and light as possible.

Here's what I posted... While this is probably correct for an isolated heat engine, I obviously didn't consider the effect that cooling the tailpipe would have on increasing the EBP, which means that the engine to which the turbo is attached can't breathe as well! So consider the part about cooling the DP in this quote to be officially retracted! I was very careful not to mention the "S" word in my entire post. But now that you brought it up, you'll have to be the test truck with the horizontal tailpipe, and as shown below, I've already signed up a test truck with vertical tailpipes, and I'm offering you the same deal... Jeremy is also going to take a some temp measurements on his exhaust system while doing road testing to measure his CC pressure. Also, anyone who's towing and pulls into a rest stop or to get fuel, pull out your IR thermometer and shoot the temp down the end of your tailpipe, the midpoint, and the DP, then also post your configuration and diameters.

 

Nice work as useual Gene. A couple of comments if you don't mind.

“My research suggests it's best to run a constant diameter pipe over the entire distance from the turbo to the end of the tailpipe, because any change in diameter results in turbulence at the junction, and this increases the restriction to flow, and increases EBP. This holds true even if you go from a smaller to a larger diameter, because the turbulence effect more than offsets the reduced friction from the larger diameter.”

This seems counter intuitive since in the limit the end of the exhust pipe is just a very large/infinite diameter pipe. So your statement implys that the end of the pipe transition causes back pressure due to turbulance. I’d like to see a reference to an actual detailed theory supporting this.

“To make this easier to discuss, consider the following terms... D=Tailpipe Diameter, EBP=Exhaust Back Pressure, EGP=Exhaust Gas Pressure, EGT=Exhaust Gas Temperature, EGD=Exhaust Gas Density, and EGV=Exhaust Gas Velocity. Except for D, all the other parameter values vary along the length of the tailpipe, which is what makes exhaust flow so difficult to analyze. Also, EGP and EGT determine EGD, whereas EBP is the net effect that reduces HP.”

I understand this is the context of “all other terms equal” , I’m sure you will not forget to include length of pipe in your equations/model. Since the longer the pipe the more mass is in the pipe that engine exhaust is having to push against. In the limit, an infinitely long pipe would kill the engine since the engine exhaust is having to push against an infinite mass.

“A larger D reduces friction which reduces EBP, however, a larger D also reduces EGV, which allows more time for the gas to cool, which reduces EGT, and this increases EGD, which means that a heavier volume of gas must be pushed along each segment of the pipe, and this requires a higher EBP. So if the D is too large, the favorable reduction in friction is more than offset by the increase in EGD, and the net effect is to increase EBP. I'll give several quotes that might explain this better.”

Not sure I believe this because the actual mass of the air has not changed. That is, even though the density has increased due to lower temperature, the pressure has also decreased and so you have the same number of atoms in the pipe as before, the are just not moving around as fast. In short, the engine exhaust is working against the same mass which implys the same EBP.

 

So my 5" straight pipe is a restriction? Maybe I am not understanding this. Would a 4" straight pipe been better then a 5"?

 

Note, the shortest, straightest, most horizontal tailpipe is the most optimum for sure. However, when I analyze the exhaust flow using the same set of equations I developed for the cold air intake, I come to different conclusions concerning optimum tailpipe diameters! My intake air flow equations only consider the flow of gas molecules, and not the other effects that are quoted below. The quote below is from a site that recommended a reference book on exhaust systems which I just ordered...

Shipping estimate for these items: November 12, 2007 <TABLE><TBODY><TR vAlign=top><TD> </TD><TD>1</TD><TD>"Scientific Design of Exhaust & Intake Systems (Engineering and Performance)"

Philip H. Smith; Paperback; $19.77

</TD></TR></TBODY></TABLE>
I'll post what I learn from this book, stay tuned to this channel. If anyone comes across any good links or references on this subject, please post them here.

"Two basic phenomenon are at work in the exhaust system: gas particle movement and pressure wave activity. As the gases travel down the pipe and expand, the speed decreases. The pressure waves, on the other hand, base their speed on the speed of sound, and this wave speed also decreases as it travels down the pipe due to gas cooling.

At all times, the speed of the wave action is much greater than the speed of the gas particles. Waves behave much differently than gas particles when a junction is encountered in the pipe. When two or more pipes come together, the waves travel into all of the available pipes - backwards as well as forwards. Waves are also reflected back up the original pipe, but with a negative pressure. The strength of the wave reflection is based on the area change compared to the area of the originating pipe.

Gas speed is a double edged sword as well, too much gas speed indicates that the system may be too restrictive hurting top end power, while too little gas speed tends to make the power curve excessively 'peaky' hurting low end torque. Larger diameter tubes allow the gases to expand; this cools the gases, slowing down both the gases and the waves.

Exhaust system design is a balancing act between all of these complex events. For more detail on the specifics of exhaust theory read ‘The Scientific Design of Exhaust and Intake Systems' by Phillip H. Smith’."

 

Well based on this quote below, it's conceivable that a 4" diameter MIGHT be a better choice than a 5" diameter!

"As a general rule, a normally aspirated MX-5 will get better high RPM performance with a 2 1/4" exhaust system (2 1/2" or above is just too wide to retain exhaust gas velocity for street driving). The general consensus is that a 2 1/4" system is for mid to high RPM petrol heads. Forced induction (turbo or supercharged) MX-5s perform better with the high volume pipes (2 1/2" to 3"), but that’s another story."

Hopefully my new book will have some equations concerning the above statement. The complication with analyzing exhaust gas flow is that it's not a simple mass flow of molecules. Exhaust gas flow consists of a series of high density pulses, and each pulse has a trailing region of lower pressure that helps to pull the pulse following behind it down the pipe. Apparently, a tailpipe diameter that's either too small or too large will not fully exploit this "pulse pulling" effect, and this is basically what leads to the concept of an "optimum" diameter for a given exhaust flow.

It seems to me that passing through the turbine should smooth out much of the pulsations in the exhaust flow? My next idea is to record the sound of the exhaust note at the exit of the tailpipe, and see how distinct each pulse is. Unfortunately what comes out the end is a mix of sound pressure waves, and pulse density variations, so I'm not sure if I'll be able to tell much from this.