Pipe size, velocity, and backpressure - some fluid dynamics

[zlexiss]

I'm posting this in Advanced because I sat down and paged through my fluid dynamics texdtbooks for a few hours, so it darn well is advanced :)

I was spec'ing out my new exhaust, and there's lots of talk of how bigger pipes will reduce backpressure and velocity the bigger you go. I decided to plug the numbers and find out. Calculations are for turbulent flow in a drawn (almost smooth) metal pipe.

Flow rate is based on an engine producing 220hp. Flow rate in CFM is 2.2 times hp, I checked this rule of thumb with some chemistry and it's pretty good. Much nicer than figuring fuel flow rates for a certain hp and calculating exhaust flow rate, adjusted for pressure and temperature.

Here's the numbers. The numbers are for the pipe only (no cat/muffler), and have adjustments made for effects of bends on flow.

Some notes:
Both velocity and backpressure scale linearly with flow rate and length. This means that no matter what horspower I put in, or what length and bends of pipe I assumed, the ratios of velocity and backpressure remain constant - 3" pipe will always have about 1/2 the velocity and 1/4 the backpressure of the 2.25" pipe.

So, how much backpressure is needed? I'm not sure. Dynomax calculates their "Loss Free Airflow Capacity" with a 20.3" drop for the just the muffler. If we assume the cat to be about the same drop, moving from 2.25" pipe to 3" pipe reduces the total system backpressure by about a third. I think it's fair to say that highflow cat, 3" pipe, and aftermarket muffler would cut backpressure by at least half from stock.

Any thoughts? I'm trying to rationalize an equation that tries to balance out the effects of the reduced backpressure against the lower velocity, which would both affect the scavenging of exhaust from the cylinders (which affects power).

-Jeff

[Bliggida]

Those are some good numbers. Good work. While I don't know specifically for a L36 motor.

Back pressure is measured at the tail-pipe in IPSI or PSI, I'm sure it's IPSI due to the fact that the numbers I know in PSI would be like a fan on the back of your car....

A (high performance street based) Small Block Chevy needs about 8 IPSI. From there, the level of tune requires less and less backpressure until you get to the point of just running open headers.

My educated guess for a V6 would be around 10-15 IPSI, but could be far less?

[zlexiss]

I'm not sure what IPSI is, not a unit of pressure I'm used to.

Most stuff is in PSI or inches of water, which is what I was working in here, standard unit for air handling and flow testing of low pressure gas systems.

If you've got a site that talks about the 8 IPSI for a SBC, let me know - I can probably make some sense on it and extend it to a good range for our engines.

-Jeff

[Arctc Wolf]

ur math is good, but do u know how mufflers and resonators affect velocity and backpressure? I know they both increase backpressure and increase velocity, however, how much does it increase these by? this would be good info to use to pick ur exhaust system.

[zlexiss]

Not sure about velocity, but Dynomax does publish the airflow at a certain pressure drop, including both the Super Turbo and Ultra Flo SS popular for F-Bodies. Not too bad from there to calc the pressure drop at a different airflow. This is found on the pdf sheets they publish.

I'm not sure about the other manufacturers. I also admit that for certain design, this may be simplistic since the muffler can be "tuned" to scavenge the pulsing exhaust better than its straight flow rating can show (see the lectures at www.n2performance.com)

<blockquote>quote:</font><hr>Originally posted by Arctc Wolf:
ur math is good, but do u know how mufflers and resonators affect velocity and backpressure? I know they both increase backpressure and increase velocity, however, how much does it increase these by? this would be good info to use to pick ur exhaust system.<hr></blockquote>

[Jason McCallister]

Is measuring backpressure with H2O a proper method considering water is not compressible and exhaust gases are?

Thanks for the effort! [img]graemlins/thumbsup.gif[/img] Looking forward to reading this thread as it progresses! :cool:

[zlexiss]

Inches of water is just a unit of pressure, much as barometer measurements are performed in inches/mm of mercury. We're not flowing water through the system, just using it in the gauge.

Take a U-shaped tube (manometer), and pour some water (or other fluid) in it. attach a hose from the the sampling point (a hole in the y-pipe) and tie it to one end of the manometer, while leaving the other end open to ambient air pressure. The pressure in the exhaust will force the water down on its side (and rising up the air side). The difference in height is where the "H20 comes from. A denser fluid like mercury will have less rise for the same pressure difference, water works well for air handling.

See here for a diagram and better explanation.

<blockquote>quote:</font><hr>Originally posted by Jason McCallister:
Is measuring backpressure with H2O a proper method considering water is not compressible and exhaust gases are?

Thanks for the effort! [img]graemlins/thumbsup.gif[/img] Looking forward to reading this thread as it progresses! :cool: <hr></blockquote>

[Ike]

One thing I found interesting when attempting exhaust design, is to try to account for the changes undergone by the gas as it flows through the pipe (contraction, expansion--slowing, speeding of the gas--maybe, depends on the flow--difficult to quantify depending on your assumptions). Consult your thermo text for more information on this. Be aware though, that lower level classes such as those given to bachelors of engineering require lots of assumptions that make the problem easier. It's hard to quantify how that would effect the predictions short of hands on testing...but you probably know this [img]smile.gif[/img]

It's a good start, though. Good luck [img]smile.gif[/img] [img]graemlins/thumbsup.gif[/img]

[ August 20, 2003: Message edited by: Ike ]</p>

[zlexiss]

Yeah, I did take an addiitonal semester during my master's degree which covered the adanvced part of this.

I didn't want to get into the effect of heat transfer out of the pipe over length, which affects both density and viscosity changing just about everything. I made midrange estimates in agreement with the temp/composition of exhaust that I could find. Otherwise I'd be solving about three nested integrals :)

Real world testing will ultimately be the best way to fit something to an engine.

I'm finally getting mine done next weekend, impressions and sound clips will be provided..

[Ike]

I daresay you've made excellent assumptions. And feel I must apologize for being a bit presumptuous about your angle of attack of the problem and your technical knowledge. I didn't mean to come across as a jerk. Also I must thank you for telling us that you've looked at this problem from so many angles. I was beginning to get a little self-conscious about my nerdiness in attempting to do it the hard way, as well.

In your opinion, is the mid-range estimate the best way to handle the gas transition from superheated to *near* ideal? I had a hard time convincing myself of that...or even that it was superheated in the first place. What are your feelings on this?

I would really like to get my hands on some hard data from inside the exhaust pipe, but that sort of thing is too varied from car to car. Plus it is really expensive to perform the tests necessary to get at the real world data. At least, too costly for me to handle [img]smile.gif[/img]

One last thing: I'm very interested in knowing what it is you've decided on for your system. Could you tell me what the plans are for next weekend?

One more one last thing: IPSI--perhaps you mean gauge PSI as opposed to absolute PSI Maybe "Internal"?

[zlexiss]

Hey, I _want_ people to question my methods. I need to learn from this as well, and having people pick at my basic assumptions can make things more correct and get us all futher along in understanding everything. Don't worry about coming across long, I'm trying to compose answers without looking too defensive myself.

I don't think we need to treat the gas as superheated. We're only about 1600F at the headers, and range from 400-1000F at the tailpipe depending on throttle and how long it's been floored :) I picked an average value for this, I forgot which, it's at work, and treated as ideal gas since the pressure is nice and low (we're not much above atmospheric pressure at any point past the exhaust valves).

Data would be cool, but it's tough to get good numbers. Everything changes pretty fast with throttle and rpm and isn't too steady. I might eventually rig something up when I stop spending money on autocross mods.

Gage vs absolute PSI - I'm thinking gage is more useful here. Once the gas hits the exit of the tailpipe, it's at 0 PSIG, which turns into a nice reference point.

My intake/exhaust system:
Intake side: FTRA, whisper lid, !MAF screen, getting a smooth hump hose to connect lid and MAF body next.

Exhaust side: Stock tubular manifolds and Y-pipe, Carsound 94009 cat, 3" S-pipe from 2 mandrel 45's, stock I-pipe, Dynomax Ultra-flo SS 17266 (2.5" in, dual 2.5" out), to dual/dual tips.

I gave up on finding 2.5" mandrel I-pipe I wanted(flowbastard will only sell as a system), so I'm figuring the 3" 45 degree S-pipe mated up to the stock I-pipe will end up about the same overall backpressure.

Anyways, it's good to see some discussion on this. I've got a broad engineering background in chemical, materials, fluids, etc. If people discuss and see some use in stuff like this or my injector cleaner article, I'll try to post more explorations in the future.

-Jeff

[Ike]

Awesome. Listen, I was toying with the idea of having the exhaust system's pipe increase in diameter as you go from header to tip...the thought was that this would ease some of the backpressure from the gas expansion, yet still maintain high velocity at the primaries and y-pipe to keep scavangine high, and possibly keep low-end power. Thinking pacesetter headers & Y (coated), 2.5" in/3" out cat (which i couldn't find), 3" I-pipe (and/or s-pipe, which i also couldn't find), and a 3" inlet/dual 2.5" outlet muffler (again, couldn't find, well, one that i wanted). I thought that this might have been a good setup, but like I've been saying, I couldn't find most of it! *oh well*

Let us know how yours turns out, though!

[Bliggida]

Sorry, IP = Inch-Pounds = in-lbs.

I wrote it incorrectly.

[zlexiss]

Blig: ah, ok. in-lbs are torque though, not pressure. Of course, torque is what this whole topic is really about :)

Ike: that's an interesting idea with the increasing diameter. This is where the whole thermal analysis comes in. The gas is getting denser down the pipe due to heat loss, and I don't know if there's enough expansion from pressure loss to overcome this.

I believe the pacesetters are 2 2.5" collectors that merge to a 3" outlet at the Y-pipe, so you want a 3" cat on both sides.
The s-pipe you'll have to build yourself from a U-pipe or 2 45's.
The I-pipe might be where you start playing with size
And if the muffler is 3" in/out and you want 2.5, either neck down right after the muffler, and maybe use crumple-bent 90's on the 2 tail extensions to add a little more restriction to make it "look like" a nice 2.5" pipe.

Ideally, we'd need both pressure and temperature measurements at several points along the system to figure out what's going on where. Of course, these change as you change components.

Last, what would you be trying to optimize for? Autocross, drag, road racing, or general street fun? In auto-x, I'm stuck in low range a lot which made this all necessary. In drag, you only go through the low once, so optimizing for high (bigger pipes) might gain you in the end.

-Jeff

[Ike]

The overall goal would be to eat my cake and still have it. In otherwords, I would be optimizing for reliability, mileage, and power (read: street acceleration) by increasing torque over all RPM (I know you can't optimize for three very well, so let's just say 2000-4000rpm, still a very broad range, but better than no range at all). I know it's the dream, but some one has to chase it, right?