Question

78-1. Dimensional Analysis in Mass Transfer. A fluid is flowing in a vertical pipe and mass transfer is occurring from the pipe wall to the fluid. Relate the convective mass- transfer coefficient ke to the variables D, p, μ, ν, DAB, g, and Δρ, where D is pipe di- ameter, L is pipe length, and Δρ is the density difference. kc D AB

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Answer 1

Given lhol , Considey connective moss sonefe co-eMicient is junction Obtin he table hou e dimension of voriobles:r- DIMENSIOn UNIT PARAMETER LT m|s mi3] k9Im3 ml' Al Kgl m. s Majs m S AB kgm3 mL

e totanumlos of Voiobles, n-8 numbe o Pamory dimensions calculate the totof number of dimensonless π term" 8-3 consider 4he repeating vaniobles is D, DAB,? calculale the value oF Ti m AB Equale he co-efciet M, L Ond T e volue o term Ti.

2 ten TTa calculae he volue oS Eqoafe the co-efれcent L ond T of M, AB Calcolate the value oț π3term AB

Equale he co-efcient of M, L and T a O AB calculate the value of η4 term AB 3 C Equate he Co-efficient oM, L and T Ja. a:3

AB Equale he Co-cfficrenl ML and'T Tre vetoh'on t the connechve mass tronsfe coefficient is 9D3 k^O AB