Lecture 20 Notes - EGN 3353C Fluid Mechanics Lecture 20...

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EGN 3353C Fluid Mechanics Lou Cattafesta MAE Dept. University of Florida Lecture 20 Recommendation : Choose CS so velocity vector is & n G Æ r V V ndA ρ = G G G Æ ˆ : x umi ± ± , ˆ : yv m j ± ± , ˆ : zw m k ± ± Usually, only one of , , or uv w is not zero! See example at left. Look at r VV n d A GG G at inlet : only component is in x direction: ( )( ) , ,, , ˆˆ ˆ ˆ in avg in in avg in avg in in avg uAm uiuiA i um i −= ⋅− =− = ± ± ²³³´³³µ at exit : only component is in z direction: ( )( ) , , ˆ ˆ out avg out out avg out avg out out avg wA m wk wkA k wm k = −−⋅ = = ± ± ²³³³´³³³µ Note : We sometimes include 1 β mom. flux correction factor to make r d A G exact. Choice of CV for this problem? Important to consider: o body forces (weight of “stuff” inside CV) Æ often neglected since this is static and we’re interested in the extra forces to the fluid motion o Grey CV: cuts the bolts on the flange so there will be a reaction force on the CV ± pressure forces Æ out atm PP = so only need . in gage in PA ± usually draw reaction force(s) in positive directions if force < 0, force is actually in other direction o Magenta CV: doesn’t cut the bolts so no reaction force
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Lecture 20 Notes - EGN 3353C Fluid Mechanics Lecture 20...

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