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You cannot convert it. Liters per minute is volume while feet per minute is velocity. There is a similar looking term - Standard Cubic Feet Per Minute, if this is what you meant, then the conversion can be done as it is also volume (volume of gas or liquid flowing per minute to be presice).

use this conversion factor STANDARD CUBIC FEET PER MINUTE - scfm

(at 14.696 psia and 60F) x 0.4474 = Litres per second (l/s) at standard conditions

(760 mmHg and 0oC)

source: http://www.oiltech.com.au/library/library_text/text_files/units.txt

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