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Calculating air flow in cubic feet per minute based on speed and intake pipe size and length?

Posted on 2007-10-15
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Hey all,

I am currently designing my own Cold Air Intake for my car, and am doing it in quite a unique way. I enjoy mathematics and have challenged myself to calculate everything on my own and have come up with what seems to be a logical equation.

I am hoping someone more experienced in this type of mathematics can confirm or disprove my formula and tell me any changes that need to be made. Either way I'll give whatever points i can to the most helpful person (:

I am attempting to find the potential air flow in Cubic Feet per Minute based on the following:

Radius of the intake pipe in cm (r)
Speed i am travelling in km/h (s)

My formula is currently ((s/60) x 100000) x Àr²

To explain the formula better, i will give an example. Again if i make any mistakes please point them out.

The first half of the formula is determining the distance travelled in 60 seconds at a given speed.

For example, at 100km/h:

((100/60) x 100000) = 166,666.6667cm

I do this because my final figure i am after is the Cubic Feet per Minute of air that can be pushed into the intake pipe, i will convert the cm to feet later.

The second part of the formula finds the area of the intake pipe.

À x 4.5² = 63.62cm²

I am assuming that for every cm travelled, 63.62cm² of air is moved into the intake pipe. By multiplying the distance travelled in 60 seconds by the area of the intake pipe i get the total volume of air that is forced into the pipe. I am not concerned about back pressure or lost air when the pipe is full. I'm assuming that 100% of the air is used so i can compare the above example to my next example, which will be my own design of intake. The above is my factory intake. Anyway, below is my conclusion on the CFM of my factory intake:

166,666.6667 x 63.62 = 10,603,333.335 cubic centimeters per minute

Converted to cubic feet per minute that is 374.45 CFM

I plan to use a 12.7cm in diameter tube for my design. I will stick with same test speed.

À x 6.35² = 126.61cm²

166,666.6667 x 126.61 = 21,102,108.337 cubic centimeters per minute

Converted to cubic feet per minute that is 745.21 CFM

Of course none of this data has accounted for the air filter or the 7 x 120mm fans i will be installing in the intake but for now i would just appreciate if someone could confirm or correct the above calculations. I'm always open to learning better ways to do things.

Can't wait to hear from you all!

Jay.
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Question by:therealj2k

Author Comment

The À symbols are actually Pi symbols. They got changed when i posted question.
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LVL 26

Expert Comment

I would encourage using a consistent set of units.

If you really want to calculate cubic feet per minute as your final result:

Measure (or convert) the radius of your intake pipe in feet as well.

Measure (or convert) your speed to feet per minute.

Then volume rate is ==>   pi * (r feet)² * (speed ft/s)  which has the right units.
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LVL 26

Accepted Solution

Correction:

Then volume rate is ==>   pi * (r feet)² * (speed ft/min)  which has the right units.

100 km/hr ==> 62.137 mile/hr ==>  5468.066 feet/min

I get 745.592 cu ft per minute
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Author Comment

Good to see we get pretty much the same answer d-glitch (:

I initially did what you said, measured every in ft/minute but because it was all decimal my answers all came out wierd and way too low. I found it easier to do everything using the metric system then just converted my final answer.

Jay.
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