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Ch 9: EXTERNAL INCOMPRESSIBLE VISCOUS FLOW (can’t have fully developed flow) FLAT PLATE

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Ch 9: EXTERNAL INCOMPRESSIBLE VISCOUS FLOW (can’t have fully developed flow) BLUNT OBJECT

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Paradoxes Pipe Flow - hydraulic engineers knew p ~ U avg 2 - theory and capillary tube showed p ~ U avg Drag - theory predict no drag (1744 –d’Alembert) - several other paradoxes for external flows as well

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Shape and Flow – Irvin Shapiro Fluid Dynamics of drag Parts I - IV

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Air speeds up to 230 mph, drag forces object in jet upwards, causing spring to extend downwards Pressurized settling chamber underneath desk EXPERIMENTAL SET UP

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Tubing leads air from settling chamber to U-tube manometer which is calibrated in mph, so can measure drag force and speed. Can measure U and Drag

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Question #1: sketch the graph of drag on sphere vs velocity PARADOX #1 SPHERE MPH 125 MPH

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D ~ U 2 D ~ U D = 6 RU Drag lower at higher speed! 250 mph125 mph SPHERE

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Question #2: if sphere is roughened, what happens to drag? PARADOX #2

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If pipe walls are roughened, what happens to pressure drop? PIPE

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S R At “low” speeds, here 120 mph, the rough sphere on the left has more drag than the smooth sphere.

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R Above a certain critical speed, here 125 mph, the rough sphere has less drag than the smooth sphere. R S

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Question #3a: What has more drag at “high speeds”, a sphere or streamlined body with the same diameter? PARADOX #3a

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At “high speeds”, a streamlined body has less drag than a sphere with the same diameter.

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Question #3b: What has more drag at “low speeds”, a sphere or streamlined body with the same diameter? PARADOX #3b

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Equal weights in air and water, although in air at “high speeds” more drag on sphere, but in glycerin at “low speeds” more drag on streamlined body

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Equal weights in air and water, in air at “high speeds” more drag on sphere, but in glycerin at “low speeds” more drag on streamlined body

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Summary of Paradoxes (1) In the first experiment we found that sometimes an increase of speed actually produces a decrease of drag. (2) Sometime roughening increases drag and sometime it decreases drag. (3) Sometime streamlining increases drag and sometime it decreases drag.

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(1) In the first experiment we found that sometimes an increase of speed actually produces a decrease of drag. Laminar Boundary Layer, bdy layer separates sooner on body, bigger wake Turbulent Boundary Layer, bdy layer separates later on body, smaller wake

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Components of pressure drag (P) and skin-friction drag (V) for laminar and turbulent flows past an unstreamlined body at high Reynolds number. Viscous forces in turbulent flow greater than laminar, but pressure forces may be reduced enough that total drag goes down!

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IDEAL FLOW LAMINAR FLOW TURBULENT FLOW S e p a r a t i o n adverse pressure gradient Laminar bdy layerTurbulent bdy layer

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Momentum of fluid near surface is significantly greater in turbulent flow than laminar flow, hence turbulent flow is more resistant to separation.

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Ch 9: EXTERNAL INCOMPRESSIBLE VISCOUS FLOW (can’t have fully developed flow) Re = UD/ C D = D/( ½ U 2 A) Flow patterns around smooth cylinder for different Re CYLINDER

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(2) Sometime roughening increases drag and sometime it decreases drag. Roughness causes transition to turbulence sooner, turbulent flow allows boundary layer to remain attached longer; but roughness makes skin friction higher. LAMINAR TURBULENT

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(2) Sometime roughening increases drag and sometime it decreases drag. For U < A, both spheres have laminar bdy layer, greater drag on rough surface due to skin friction For B < U both spheres have turbulent bdy layer, greater drag on rough surface due to skin friction

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Boundary layer becomes turbulent on roughened sphere sooner than it does for smooth sphere. Turbulent boundary layer better at mixing high momentum outer flow with flow in boundary layer. Thus energized by outer flow, turbulent boundary layer separates further back on sphere, resulting in a smaller wake and consequently less drag (1/5 th as much at optimum speeds). 230 yds 50 yds Smooth Dimpled

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In the early days of golf, the balls were smooth, and it was only accidentally discovered that scarred balls travel further than smooth, unscarred ones. If today’s balls are driven, say, 230 yds, a smooth ball similarly struck would travel only 50 yards. Recently golf balls have been designed with randomly spaced hexagonals with the claim of an additional 6 yards.

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Smooth Trip Flow over a sphere. Trip: Re = 30,000 (with trip wire turbulent separation) Smooth: Re = 15,000 (laminar separation) From Van Dyke, Album of Fluid Motion Parabolic Press, 1982 Original photographs by Werle, ONERA, 1980

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PIPE FLAT PLATE C D = D/( ½ U 2 A) f = (dp/dx)D/( ½ U 2 )

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PIPE FLAT PLATE SMOOTH CYLINDER SMOOTH SPHERE

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(3&4) Sometime streamlining increases drag and sometime it decreases drag. At very low Reynolds numbers viscous effects extend far from body, really no boundary layer to speak of. At higher Reynolds number there is form drag due to a pronounced wake. Streamlining will reduce the size of the wake at higher Reynolds numbers. Glycerin: Low Re Water: High Re

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From Visualized Flow – Japanese Society of Mechanical Engineers Viscous flow around sphere Viscous flow around stream- lined body

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Low Re – then friction drag important, want to decrease area High Re – then pressure drag important, want to decrease wake

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Small wake Large wake

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First flight of a powered aircraft 12/17/03 120ft in 12 seconds Orville Wright at the controls Same drag at 210 mph

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The End

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D ~ U 2 D ~ U D = 6 RU ASIDE: do you find it odd that viscous drag does not depend on density or pressure (p = RT)? SPHERE

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“The new law that he {Maxwell ~1862} predicted seemed to defy common sense. It was that the viscosity of a gas – the internal friction that causes drag on a body that moves through it – is independent of pressure. One might expect that a more compressed gas to exert a greater drag.” Turns out that the effect of being surrounded by more molecules is exactly cancelled out by the fact that their mean free path is less. The Man Who Changed Everything – Basil Mahon

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When very small dust particles fall through one column of air at 1 atmospheric, they fall at the same terminal velocity as if it was 0.01 atmosphere.

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Most of the drag due to skin friction, very small wake. Most of the drag due to pressure drop, large wake.

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