2" piping
1.57 x 2 = 3.14 sq in
300 cfm = 156 mph = 0.20 mach
400 cfm = 208 mph = 0.27 mach
500 cfm = 261 mph = 0.34 mach
585 cfm max = 304 mph = 0.40 mach

JUST WANTED TO UPDATE THAT MORE ACCURATE NUMBERS ARE IN THE MAKING. =)

here ya go bud.

*.4 Mach is the point at which air becomes turbulent and losses in efficiency start to occur exponentially. The key is to stay under that speed. You want to use the smallest piping possible that still flows enough to meet your needs. Larger than necessary piping increases lag time with no measurable gain

The velocities are in miles per hour and mach, and the flow rates are in cfm. Measurements for the piping are in inches.


2" piping
1.57 x 2 = 3.14 sq in
300 cfm = 156 mph = 0.20 mach
400 cfm = 208 mph = 0.27 mach
500 cfm = 261 mph = 0.34 mach
585 cfm max = 304 mph = 0.40 mach


2.25" piping
3.9740625 sq in = 1.98703125 x 2
300 cfm = 123 mph = 0.16 mach
400 cfm = 164 mph = 0.21 mach
500 cfm = 205 mph = 0.26 mach
600 cfm = 247 mph = 0.32 mach
700 cfm = 288 mph = 0.37 mach
740 cfm max = 304 mph = 0.40 mach


2.5" piping
4.90625 sq in = 2.453125 x 2
300 cfm = 100 mph = 0.13 mach
400 cfm = 133 mph = 0.17 mach
500 cfm = 166 mph = 0.21 mach
600 cfm = 200 mph = 0.26 mach
700 cfm = 233 mph = 0.30 mach
800 cfm = 266 mph = 0.34 mach
900 cfm = 300 mph = 0.39 mach
913 cfm max = 304 mph = 0.40 mach


2.75" piping
5.9365625 sq in = 2.96828125 x 2
300 cfm = 82 mph = 0.10 mach
400 cfm = 110 mph = 0.14 mach
500 cfm = 137 mph = 0.17 mach
600 cfm = 165 mph = 0.21 mach
700 cfm = 192 mph = 0.25 mach
800 cfm = 220 mph = 0.28 mach
900 cfm = 248 mph = 0.32 mach
1000 cfm = 275 mph = 0.36 mach
1100 cfm max = 303 mph = 0.40 mach


3.0" piping
7.065 sq in = 3.5325 x 2
300 cfm = 69 mph = 0.09 mach
400 cfm = 92 mph = 0.12 mach
500 cfm = 115 mph = 0.15 mach
600 cfm = 138 mph = 0.18 mach
700 cfm = 162 mph = 0.21 mach
800 cfm = 185 mph = 0.24 mach
900 cfm = 208 mph = 0.27 mach
1000 cfm = 231 mph = 0.30 mach
1100 cfm = 254 cfm = 0.33 mach
1200 cfm = 277 mph = 0.36 mach
1300 cfm max= 301 mph = 0.39 mach


In order to convert from Lb/Min to CFM for the equation above, you take the flow rate in Lb/Min for your turbo (generally an educated guess based on the pressure ratio and power created) and multiply it by 14.27. That will yield the CFM flow for your setup.

For Example:
T3/T04e 57trim .63ar @ 21psi makes 452 whp
This turbo is known to have a 50lb/min compressor wheel which will make ~500bhp. Since we're using whp above, we can assume this turbo is pretty close to its max of 50lb/min.

Now to convert that to CFM, you take 50lb/min x 14.27 = 713.5 CFM. When you refer to the table above, you can see that we're starting to max 2.25" piping, but we're still in the "good" range for 2.5"

but it also depends on how smooth the piping is inside... and all the bends. this i would say is " perfect piping conditions" and if you would pick a number to upsize your piping at it would be when you hit about the .3 maximum .35 mach region.

To add a bit more info and maybe answer your questions and a few that people are probably thinking of typing...general equation and explanation for the calculations of finding mach for your setup are here. Mach number - Wikipedia, the free encyclopedia
mach is dependent on temperature directly. which is accounted for by the speed of sound in the equation. sound is a factor all in itself.
i would recommend readin up on this page. lol.. i know. im tired. maybe can explain a little better for ya tomorrow.
Speed of sound - Wikipedia, the free encyclopedia you need to adjust for this as far as temp goes also to be accurate enough. since there are such great variances. REASONING WHY A QUALITY INTERCOOLER IS A GOOD IDEA

another quick show of speed of sound... simple terms VERY GOOD TO READ THRU. ESPECIALLY THE LINKS ON THE RIGHT

http://www.ndt-ed.org/EducationResou...mpandspeed.htm


read this also. lol
Machmeter - Wikipedia, the free encyclopedia

as to answer the question:

And are those calculations assuming a parabolic flow through the pipes? With a no slip (zero velocity) condition along the walls.

Yes.
Also add to it that is in a straight pipe no bend situation. at a general given temperature ~60*F. which is also affecting the equation and accuracy. (have to throw that into your equation. there are so many variables that unless you feel like doing all the math. you go off a general bases.) these variables are why i adjusted the max mach value of the air/pipes. to account for imperfections, bends, and slight temp changes. but an accurate equation would require accurate numbers from the beginning based on your setup to be honest. this just gives you a general idea.

here is an explanation of the figures in the equation used above and Affecting variables.

1) The speed of sound is a function of the gas temperature. The numbers quoted above are using the speed of sound at ~60*F. The speed of sound is higher pre and post intercooler (unless you have an ideal intercooler) and needs to be considered.

2) You cannot convert directly from Lb/min to CFM. One is a mass flow rate and one is a volume flow rate (different units). Correct me if I am wrong. Or just guide/ link me to the info and I will learn myself. =).To get from one to the other, you need to know the density of the flow. My guess is that if you found a conversion factor online somewhere, they are using the density of air at ambient conditions (temp/pressure). Obviously if you are in a compressed environment, the density increases and your volume flow would decrease for a given mass flow.

Another consideration that goes with this topic comes up:

1) Pressure Drop: Pdrop = 4UuLR^2 (<-- Centerline Laminar flow solution)
*U: Velocity
*u: viscosity
*L: Length
*R: radius

To sustain a high velocity flow you need a large pressure drop. Losses associated with bends and area transitions are also a function of 1/2*Velocity^2... so smaller piping results in higher pressure drop and higher flow losses. temperature also affects when your transition from hot to cold side of the intercooler. thus why i never understood why people will go with the same piping size all the way pre/post intercooler. or just run giant oversized interccolers with bad designs. such as the proven GReddy crap.

I really can't see lag with larger piping being a concern. Just the ability to run as effiecient as possible. yes lag is affected but it is other performance variables that matter more. The turbos people are using respond fast, flow lots, and the piping is never fully evacuated. I would always err on the side of too big vs. too small. which is why i say to switch at a mach value (calculated) of 0.3 rather then 0.4

If you want help estimating conditions pre/post intercooler to get a better approximation or anything like that... just ask i will try to help or try to find the time to figure it all out. lol. i barely had the free time to gather all this together just found it a very important topic and set other things aside.

THERE ARE SO MANY VARIABLES THAT YOU MUST TAKE THE MOST ACCURATE (GENERAL EQUATION) ASSES YOUR SETUP AND GO FROM THERE. IT IS KIND OF HARD TO CALCULATE EVERY SINGLE LITTLE VARIABLE. SO WHAT YOU DO INSTEAD IS GET AS ACCURATE AS YOU CAN WITH GIVEN INFO AND THEN GO FOR A SLIGHTLY LOWER (THEN MAX) MACH NUMBER.


If I missed anything or if I need to answer any other questions I will try to do so tomorrow. IM TIRED. lol

HOPE THIS HELPS GUYS.

IN OTHER WORDS> YOU GET A BALLPARK FIGURE. TO GET AN ESTIMATE OF WHICH SIZE TO USE, AND TRY IT OUT. SEE HOW IT WORKS FOR YOU.

It is crazy how much thought you can actually put into building a car the right way.

now we see why just bolting up your favorite parts and cool looking shyt isn't always going to yield you better performance then the next guy.

IF I screwed anything up I will reread tomorrow when I am not falling asleep at the computer. so i am able to fix it. Please forgive my blotchy and jacked grammar. I will go through at fix it tomorrow. I am just so tired but wanted to throw this out there for you guys who will sit on here all night figuring this out.

APPROXIMATE CFM'S I WOULD RECOMMEND FOR EACH PIPING SIZE.

2" ~450-500 cfm
2.25" ~575-650 cfm
2.5" ~700-800 cfm
2.75" ~850-950 cfm
3" ~1000-1150 cfm

this is all depending on how much hot air you are pushing from that turbo...how much are you also maxing out your turbo? lol AND I AM NOT SAYING THAT GOING BEYOND THESE NUMBERS WILL NOT NET GOOD RESULTS EITHER. It is all still just a trial and error thing. Turbulance becomes a factor above .40 mach tho. so i would at least stay under that....not saying you have to but umm... ya know

Here is the calculator for pressure losses in a typical throttlebody:

Throttle Body Sizing Calculator | REVTRONIX

Take it for what its worth.

I'll make this quick. Off my spreadsheet, given an airflow of 45 lb/min, turbo outlet temp of 375*F, turbo outlet pressure of 25 psig the following pipes will drop the listed psi:

2.25" O.D. straight tubing: 0.17 psi per foot
2.5" O.D. straight tubing: 0.10 psi per foot
3" O.D. straight tubing: .04 psi per foot

Using a (bend radius/pipe diameter) ratio of 1 which is a pretty tight bend and the worst you will see or the tightest you can bend a tube without rupturing it, the K factor (loss coefficient for a 90* bend) is roughly .25-.4. Using K = .35 I get for the following:

2.25" O.D. 90* bend: 0.27 psi per bend
2.5" O.D. 90* bend: 0.17 psi per bend
3" O.D. 90* bend: .08 psi per bend

Various pipe step ups or step downs will yield various additional K loss factors and you'd need to consult a Fluids text for the appropriate charts.

I use the rule of thumb that every 1 psi drop is roughly 10-11 h.p. lost at the 450 h.p. level. So if I have a 2.25" lower I.C. pipe that has 2 90* bends with 4 feet of straights, I get a psi loss of about 1.22 psi loss. If I upgrade to a 2.5" pipe with the same configuration I get about .74 psi loss. For 3" I get about 0.32 psi total pressure loss. At best, the switch to the 3" pipe on the lower I.C. pipe is worth about 0.9 psi gained back in the intake manifold, or about +9.0 h.p.

Also keep in mind when you switch to bigger I.C. pipes the transition off the turbo outlet has to be taken into consideration, which the psi loss actually increases as the pipe size increases, so the gains going to a bigger lower I.C. pipe are not as great as the case I just illustrated. Which is why you need to sketch out exactly the pipe configuration you have now and what you will have when you uprgrade for an accurate loss analysis.

You can play with the numbers all day long but you get the idea. There are gains to be had optimizing the piping size IF your turbo compressor is already dropping off boost at high rpms. Otherwise the turbo will simply command itself to spin up a little faster to compensate. When the turbo is pinned wide open at high rpms and your already seeing boost drop off due to the engine outflowing the turbo, THIS is where reducing pressure losses in the intake system pays off.

In my case, I saw a +1 lb/min increase and 10 h.p. gain swapping out my lower 1.675" j-pipe to a 2" j-pipe because I was already maxxing out my turbo compressor. Otherwise you won't see gains.