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Density Ratio and CFM

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When properly sizing a turbo for a particular application one of the last steps is computing the density ratio and then multiplying the density ratio by the N/A CFM airflow to find the CFM airflow after turbocharging. For example: N/A cfm= 300. Density Ratio= 1.90 Turbo cfm = 570. How is it that multiplying the Density Ratio by the N/A Cfm results in the CFM after Turbocharging? What is the relationship?

Thank You

Don't quite follow your query, but I think what you're confused by is the PVT (Pressure Volume Temperature) relationship, as described by Boyle's Law - http://www.docbrown.info/page03/3_52gaslaws.htm

In short, if you have one unit of gas at one value of PVT, if you use Boyle's Law you can work out how changing one, or two, of those values by a known amount you can calculate the third. You can use imperial units, but it is MUCH easier to use metric, or Kelvin!

Ah, re-reading it, this may make more sense.

The turbo-charger is more likely to be rated as a pressure ratio, than a density ratio - are you sure that was correct - but it means that whatever air is taken in will be compressed to 1/1.90 times the volume, making it denser - taking up less volume inside the engine. Because the engine can use 300cfm, but the turbocharger has compressed the air into a smaller volume, it has to suck in 1.9 times as much air to squeeze down to 300CFM.

Here is an example of what I’m referring to: http://www.turbominis.co.uk/forums/attachments/213848-1.pdf

You can see where the NA Cfm is multiplied by the Density Ratio

Not 100% sure on the question here, but as Gord mentioned above, I think the wording is throwing you off. Given the units and numbers you used above, the turbo will take 570 cubic feet of atmospheric air, and squish it down into 300, so the engine can swallow it. This will increase it's pressure by 1.9 times in the process.

If you were to monitor this with an airflow meter pre turbo, it would still show 570cfm of airflow even though the engine is only moving 300 through it (because they are at different densities)

I think you answered my question, thank you

You need to be very careful when looking at density and pressure - they are NOT the same, as temperature MUST be considered.

The classic experiment is to use a closed container with a pressure guage connected to it. At room temperature, 20C, it may show 0 PSIG (gauge), but if it's placed over a gas burner and brought up to 100C, the pressure will increase by 27.3% (383K/293K) to 4 PSIG ((14.7 PSIA*1.273) - 14.7).

The volume, and density, are still the same, as the container is sealed,but the pressure is increased.

If you now release the pressure, at the same temperature it will now be the same volume but only 78.6% as dense. This is a big part of why charge cooling is SO important - it is actually possible to increase boost and get less actual air into the cylinders, if the temperature increase is great enough - plus all the other efficiency losses that will also be introduced.


If your question is what is density ratio then looking at the example you provided its basically inter cooler efficiency and how that effects volumetric flow rate. As the temperate of the compressor discharge air is reduced in the inter cooler the density will increase creating more volumetric flow rate. this is calculated using the formula supplied and the pre and post inter cooler temperature and pressure for inputs. In that example the compressor discharge flow rate of 158cfm is increased by 16% to 183cfm.

Its worth taking the time to build a spreadsheet with all the commonly used formulas in so you can just throw numbers around to see what you could achieve. http://www.epi-eng.com/piston_engine_technology/engine_technology_contents.htm is a good source of engine calcs without spending a fortune on text books but if you were so inclined the John Hayward fundamentals book is a good starter.

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