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| The '''Ergun equation''', derived by the [[Turkey|Turkish]] [[chemical engineer]] [[Sabri Ergun]] in 1952, expresses the [[friction factor]] in a [[packed bed|packed column]] as a function of the [[Reynolds number]]:
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| <math>
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| f_p = \frac {150}{Gr_p} + 1.75
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| </math>
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| where <math>f_p</math> and <math>Gr_p</math> are defined as | |
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| <math>f_p = \frac{\Delta p}{L} \frac{D_p}{\rho V_s^2} \left(\frac{\epsilon^3}{1-\epsilon}\right)</math> and <math>Gr_p = \frac{D_p V_s \rho}{(1-\epsilon)\mu}</math>
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| where:
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| <math>\Delta p</math> is the pressure drop across the bed,<br>
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| <math>L</math> is the length of the bed (not the column),<br>
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| <math>D_p</math> is the equivalent spherical diameter of the packing,<br>
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| <math>\rho</math> is the [[density]] of fluid,<br>
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| <math>\mu</math> is the [[dynamic viscosity]] of the fluid,<br>
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| <math>V_s</math> is the [[superficial velocity]] (i.e. the velocity that the fluid would have through the empty tube at the same volumetric flow rate), and<br>
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| <math>\epsilon</math> is the [[void fraction]] of the bed (bed [[porosity]] at any time).
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| Extension of the Ergun equation to fluidized beds is discussed by Akgiray and Saatçı (2001).
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| To calculate the pressure drop in a given reactor, the following equation may be deduced
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| <math>\Delta p=\frac{150\mu (1-\epsilon)^2 V_s L}{\epsilon^3 D_p^2} + \frac{1.75 (1-\epsilon) \rho V_s^2 L}{\epsilon^3 D_p}</math> | |
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| ==See also==
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| [[Kozeny–Carman equation]]
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| ==References==
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| * S. Ergun, Chem. Process Eng. London 48, 89 1952. legacy.library.ucsf.edu/documentStore/e/f/k/.../Sefk76a99.pdf
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| * Ö. Akgiray and A. M. Saatçı, Water Science and Technology: Water Supply, Vol:1, Issue:2, pp. 65–72, 2001.
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| [[Category:Equations]]
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| [[Category:Chemical engineering]]
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