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Ergun equation

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To isolate this equation I would use the excel solver add in, to get the value of epslon based on the value of the other formula relations.
 
Perhaps you mean epsilon.
Multiply both sides by epsilon cubed and you have a standard cubic equation. There is a general cubic equation analogous to the quadratic equation, see the CRC Math Handbook, etc., or google it up: I've never used it, though. It ie faster to find the one real root by numerical methods on a spreadsheet.
 
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