Lecture 26 Notes - EGN 3353C Fluid Mechanics Lecture 26...

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EGN 3353C Fluid Mechanics Lou Cattafesta MAE Dept. University of Florida Lecture 26 Dimensional Analysis Examples and Dimensionless Groups Example Steady incompressible pipe flow. In incompressible steady pipe flow, the velocity profile eventually becomes fully-developed, meaning that the velocity profile doesn’t change with x (and, hence, neither does w τ ). A CV analysis shows: Mass conservation : ; avg m const V V const = == ± x-mom : ( ) 0 xo u t i n Fm V V = −= ± or ( ) ( ) ( ) 2 perimeter area 40 w Px Px x D Dx πτ π −+ Δ Δ = ⎡⎤ ⎣⎦ ²³´ ²µ³ µ´ In the limit as 0 x Δ , we obtain ( ) ( ) 0 4 lim w x x x D Δ→ Δ = Δ or 4 w dP const dx D =− = Æ P must decrease in a linear fashion vs. x .
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EGN 3353C Fluid Mechanics Lou Cattafesta MAE Dept. University of Florida Dimensional Analysis for w τ 1. List the parameters in the problem: ( ) ,, w fVD ερμ = . 6 n = 2. List the primary dimensions of each. [ ] [ ] [ ][ ] [] [] 21 31 1 , , , w mLt V Lt D L L mL mL t τε ρμ −− = == = 3. Guess reduction j equal to the number of primary dimensions = 3. So 3 knj = −= .
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This note was uploaded on 08/17/2011 for the course EGN 3353C taught by Professor Lear during the Spring '07 term at University of Florida.

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Lecture 26 Notes - EGN 3353C Fluid Mechanics Lecture 26...

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