Every now and then, I find myself wonder, “how do I figure that out on my own?” What do I mean by that? Well, I mean, how to I do the math to get an outcome, without just relying on what someone else suggests… As you may have seen with my Tire Formula posting, I’m really interested in diving into the numbers and facts; not looking at pictures to make best guesses.
The most recent question was, how do I find the proper dimensions for a well flowing exhaust? While it doesn’t dive too deep into the hard numbers of calculation, this post I recently found does give a pretty good start. I’ve even started following them on Facebook.
The hunt still continues…
Here’s the post content, from above…
How To Calculate Muffler Size and Exhaust Pipe Diameter If you’re a math wiz and/or an engineer, you’re probably going to like this article and the resources we’ve linked to. However, if you find yourself getting stuck (or bored) with the info below, here are the key take-aways:
1. The factory exhaust pipe diameter is usually a good choice for most vehicles.
2. The muffler manufacturers are doing all the math for us – no need to reinvent the wheel. If they say it will work for your vehicle, it will probably work for your vehicle.
3. We’ve got an easy-to-read exhaust system size table that is good for quick calculations.
Breaking Down The Problem While we’re not going to go through and list out all the formulas and calculations you need to figure this exactly, we will break down the problem, explain how you would go about figuring things out scientifically, and then leave you with some good quick-and-dirty exhaust system math as well as some interesting links.
The science goes like this…
1) Mass of air that the engine breathes in + mass of fuel = mass of exhaust gases Conservation of mass, right?
2) To calculate the volume of air the engine takes in, we multiply the displacement of the engine by the engine RPM and then divide by two (it takes two full revolutions for the engine to exhaust it’s entire air volume). We then convert that to volume to mass.
3) To make the calculations easy, you want to assume that combustion is perfect, i.e. there aren’t any byproducts, any unburned fuel, etc. It’s easier to assume perfect combustion and then “back in” to the actual numbers using an estimate after the fact.
4) Since you’re assuming perfect combustion, it’s easy to figure out how much fuel mass is added to the exhaust.
5) Once you know the mass of the exhaust gas, you just figure out how much volume that mass would occupy. Of course, you have to adjust for expansion due to the high exhaust gas temperature.
That’s it! Of course, when you sit down to figure it, you’ll find that getting a good scientific estimate takes a lot of work (which is why we don’t bother with it here).
Quick and Dirty Exhaust System Math Easy Way To Estimate: Your intake system needs to flow 1.5 CFM per engine horsepower, and your exhaust system needs to flow 2.2 CFM per engine horsepower.
Good Way To Estimate: Take engine RPM x engine displacement, then divide by two. This is the intake volume. Use this same volume of air for the exhaust system, but then correct for thermal expansion (you need to know exhaust temps to figure things out).
Exhaust Pipe Size Estimate: A good section of straight pipe will flow about 115 CFM per square inch of area. Here’s a quick table that shows how many CFM each common pipe size will flow, as well as the estimated max horsepower for each pipe size:
Pipe Diameter (inches) Pipe Area (in2) Total CFM (est.) Max HP Per Pipe Max HP For A Dual Pipe System 1 1/2 1.48 171 78 155 1 5/8 1.77 203 92 185 1 3/4 2.07 239 108 217 2 2.76 318 144 289 2 1/4 3.55 408 185 371 2 1/2 4.43 509 232 463 2 3/4 5.41 622 283 566 3 6.49 747 339 679 3 1/4 7.67 882 401 802 3 1/2 8.95 1029 468 935 NOTE: These numbers are just estimates. All pipes are assumed to be 16 gauge steel.
The table above is probably over-estimating pipe size, but you can see that a 400 hp vehicle with a dual exhaust system only needs 2 1/4 – 2 1/2 inch pipes. Anything larger is overkill.
Useful Links Great forum discussion that really discusses the details of the scientific calculations: http://www.eng-tips.com/viewthread.cfm?qid=104735
An interesting discussion of header pipe designs: http://victorylibrary.com/mopar/header-tech-c.htm
A good general article about designing the perfect exhaust system: http://www.popularhotrodding.com/enginemasters/articles/hardcore/0505em_exh/index.html