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Unformatted text preview: ME309 Fall 2009 Lecture 23: External Incompressible Viscous Flow
Andrew Lee Maurice J. Zucrow Laboratories Purdue University West Lafayette, Indiana Boundary Layer Thicknesses Disturbance thickness (): distance from surface to point where velocity is 0.99U Displacement thickness (*): distance by which a solid boundary would have to be moved in a frictionless flow to give the mass flow deficit that exists in BL * 0 u 1  U dy Momentum thickness (): thickness of a layer of fluid with velocity U for which momentum flux is equal to the deficit of momentum flux through BL 11/11/2009 0 u U u 1  U dy 2 Andrew Lee Momentum Integral Equation
How do we find at x? Momentum equation applied to a differential control volume inside a boundary layer
U(x) b c (x+dx) (x) u(x) y x a dx
11/11/2009 u(x+dx) d
Andrew Lee Solid surface
3 Momentum Integral Equation
Assumptions: incompressible steady twodimensional flow (no flow in the zdirection) The xdirection momentum equation results in the momentum integral equation w d dU 2 = (U ) + *U dx dx
This equation can be used to find /x and w
11/11/2009 Andrew Lee 4 Laminar BL flow over a flat plate
Find (x) and Cf when dP/dx=0 (Chap. 9.5) 11/11/2009 Andrew Lee 5 ...
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This note was uploaded on 04/28/2010 for the course ME 309 taught by Professor Merkle during the Spring '08 term at Purdue University.
 Spring '08
 MERKLE

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