# ch712 - CHAPTER 7 FLOW PAST IMMERSED BODIES(unbounded flows...

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CHAPTER 7: FLOW PAST IMMERSED BODIES *(unbounded flows)

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Chapter 7: Flow Past Immerses Bodies 7.1 Reynolds Number and Geometry Effects 7.2 Momenum Integral Estimates 7.3 The Boundary Layer Equations 7.4 The Flat Plate Boundary Layer 7.5 Boundary Layers with Pressure Gradients 7.6 Experimental External Flows
Internal flow: viscous boundary layer grow from pipe walls, meet downstream, and fill entire pipe. Forces on pipe due to viscous shear stresses on pipe walls (skin friction), no wake. External flow: viscous boundary layer (laminar then turbulent) at surface and can separate and form wake. Flow outside boundary layer and wake acts as if inviscid. Forces on body due to skin friction and pressure.

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adverse pressure gradient leads to separation difficult to use theory • Re = U x/ ν ; Re = U c/ ν ; … • laminar and turbulent boundary layers • displaced inviscid outer flow • adverse pressure gradient and separation = separated boundary layer CHAPTER 7: FLOW PAST IMMERSED BODIES
Re = 20,000 Angle of attack = 6 o Symmetric Airfoil 16% thick imposes unfavorable pressure gradient on boundary layer

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Note – throughout figures the boundary layer thickness * , δ , is greatly exaggerated! ( disturbance layer* ) Airline industry had to develop flat face rivets.
Re D = 1.5 Re D = 2000 Ma = 1.5 FLOW OVER CYLINDER

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In August of 1904 Ludwig Prandtl, a 29-year old professor presented a remarkable paper at the 3 rd International Mathematical Congress in Heidelberg. Although initially largely ignored, by the 1920s and 1930s the powerful ideas of that paper helped create modern fluid dynamics out of ancient hydraulics and 19 th -century hydrodynamics. only 8 pages long , but arguably one of the most important fluid-dynamics papers ever written
• Prandtl assumed no slip condition • Prandtl assumed thin boundary layer region where shear forces are important because of large velocity gradient • Prandtl assumed inviscid external flow • Prandtl assumed boundary so thin that within it p/ y 0; v << u and / x << / y • Prandtl outer flow drives boundary layer, boundary layer can greatly effect outer outer “inviscid” flow if separates

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Theodore von Karman - 1904 Prandtl Fluid Motion with Very Small Friction 2-D bdy layer equations - 1908 Blasius The Boundary Layers in Fluids with Little Friction Solution for laminar, 0-pressure gradient flow - 1921 von Karman Integral form of bdy layer equations - 1924 Sir Horace Lamb Hydrodynamics ~ one paragraph on bdy layers - 1932 Sir Horace Lamb Hydrodynamics ~ entire section on bdy layers BOUNDARY (BDY) LAYER HISTORY
PRESSURE GRADIENT TURBULENT EXPERIMENT GROWING BOUNDARY LAYER? THEORY LAMINAR WAKE? FULLY

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ch712 - CHAPTER 7 FLOW PAST IMMERSED BODIES(unbounded flows...

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