Slides for Shell Momentum Balance

Slides for Shell Momentum Balance - Shell Momentum Balance...

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1 An example: molecular-momentum fluxes across an x-plane • Momentum flux due to random motion of molecules (pressure p ) • x-momentum flux due to normal viscous stress τ xx • y-momentum flux due to shear stress τ xy • z-momentum flux due to shear stress τ xz A general summary of molecular momentum fluxes across a plane x y z P (x,y,z) xx p τ xy xz Shell Momentum Balance for Steady Laminar Flow Definitions of momentum fluxes x y z P (x,y,z) A general summary of molecular-momentum-flux components • x-momentum fluxes transferred across x-plane: p and τ xx y-plane: τ yx z-plane: τ zx • y-momentum fluxes transferred across x-plane: τ xy y-plane: p and τ yy z-plane: τ zy • z-momentum fluxes transferred across x-plane: τ x xz y-plane: τ yz z-plane: p and τ zz Definitions of momentum fluxes Shell Momentum Balance for Steady Laminar Flow
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2 xx xy xz yx yy yz zx zy zz p p p ττ τ ⎛⎞ + ⎜⎟ =+ + ⎝⎠ π Molecular x-momentum fluxes transferred across x-, y-, and z- planes Molecular x-, y-, z-momentum fluxes transferred across x- plane Definitions of momentum fluxes A general summary of molecular-momentum-flux components Shell Momentum Balance for Steady Laminar Flow Convective momentum transfer Momentum density can be transferred by bulk flow. This leads to a rather simple way to describe convective momentum transfer: x x u u ρ is defined as the flux of x-momentum transferred by convection (bulk flow) across x-plane (called convective x- momentum flux). Definitions of momentum fluxes x y z P (x,y,z) x x u u y x u u is defined as the flux of y-momentum transferred by convection (bulk flow) across x-plane (called convective y- momentum flux). j i u u is generally defined as the flux of j- momentum transferred by convection (bulk flow) across i-plane (called convective j-momentum flux). y x u u y u Shell Momentum Balance for Steady Laminar Flow
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3 x y z P (x,y,z) x xx yx z yy yz zx zy zz uu ρρρ ⎛⎞ ⎜⎟ ⎝⎠ Convective momentum transfer Definitions of momentum fluxes Convective x-momentum fluxes transferred across x-, y-, and z- planes Convective x-, y-, z-momentum fluxes transferred across x- plane Shell Momentum Balance for Steady Laminar Flow Combination of molecular and convective momentum transfer Definitions of momentum fluxes x x xy x y xz x z y x y y y z z x z y z z pu u u u u u p p τρ ++ + + =+ + + + + + Φ Molecular and convective y- momentum fluxes transferred across x-, y-, and z-planes Shell Momentum Balance for Steady Laminar Flow
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4 Momentum principle for a fixed control volume Momentum principle
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This note was uploaded on 01/27/2011 for the course PGE 323 taught by Professor Johns during the Spring '07 term at University of Texas.

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Slides for Shell Momentum Balance - Shell Momentum Balance...

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