Integral Thickness-Basic Fluids Dynamics-Lecture Handout, Exercises of Fluid Dynamics

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Integral Thicknesses 1 Definitions The details of the velocity profile u(y) at any x location are rarely significant in engineering applications. The most significant quantities are integral thicknesses which describe the mass flux, momentum flux, and kinetic energy flux in the shear layer: = / ( _ ) ay displacement thickness Pelle @= [0 - ~) ou dy momentum thickness Ue/ Pele wr pu = / 1-4 dy kinetic energy thickness ~ U2 J Pelle 2 Integral Thickness Interpretation These thicknesses appear when comparing the mass, momentum, and kinetic energy flows in a shear layer and a corresponding potential flow. 2.1 Mass flow comparison Figure 1 shows the mass flux passing between the vertical extent y = 0...y. for inviscid and viscous flows with the same edge velocity. sepa Figure 1: Comparison of inviscid and viscous mass flows . . Ye . mrp = far = [rowdy = Mr = petleYe . . ‘Ye Ye . . my = | dm = f pudy = Pelee — f (pete — pu) dy = thi — pote The viscous mass flow is decreased by an amount equal to the mass defect p,u,0*. _ docsity.com