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**FLAT PLATE Ch 9: EXTERNAL INCOMPRESSIBLE VISCOUS FLOW**

(can’t have fully developed flow) FLAT PLATE

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**BLUNT OBJECT Ch 9: EXTERNAL INCOMPRESSIBLE VISCOUS FLOW**

(can’t have fully developed flow) Unlike pipe and flat plate, flow around blunt objects produce wakes. Because the wake structure changes dramatically with flow, drag will also. BLUNT OBJECT

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**Paradoxes Pipe Flow - hydraulic engineers knew p ~ Uavg2**

- theory and capillary tube showed p ~ Uavg Drag - theory predict no drag (1744 –d’Alembert) Newton (1642 – 1727) in 1687 wrote Principia, entire second book devoted to fluid mechanics. - several other paradoxes for external flows as well

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**Shape and Flow – Irvin Shapiro**

Fluid Dynamics of drag Parts I - IV Newton (1642 – 1727) in 1687 wrote Principia, entire second book devoted to fluid mechanics.

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

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

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**Question #1: sketch the graph of drag**

PARADOX #1 SPHERE 125 MPH 250 MPH Question #1: sketch the graph of drag on sphere vs velocity

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**Drag lower at higher speed! SPHERE D ~ U2 125 mph 250 mph D ~ U**

D = 6RU Drag lower at higher speed!

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

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

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**At “low” speeds, here 120 mph, the rough sphere **

on the left has more drag than the smooth sphere.

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**Above a certain critical speed, here 125 mph, the **

rough sphere has less drag than the smooth sphere.

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**Question #3a: What has more drag at “high speeds”, a **

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

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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 **

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

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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

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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 **

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

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**adverse pressure gradient**

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

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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) CYLINDER Re = UD/ CD = D/( ½ U2A) Flow patterns around smooth cylinder for different Re

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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 **

50 yds 230 yds Smooth Dimpled 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 (1/5th as much at optimum speeds).

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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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**turbulent separation) Smooth: Re = 15,000 (laminar separation)**

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 Smooth

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**f = (dp/dx)D/( ½ U2) CD = D/( ½ U2A) PIPE FLAT PLATE**

Both flat plate and pipe do not have wakes. Both have similar laminar and turbulent trends and function of roughness

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**PIPE FLAT PLATE Both flat plate and pipe do not have wakes.**

SMOOTH SPHERE SMOOTH CYLINDER SMOOTH SPHERE FLAT PLATE Both flat plate and pipe do not have wakes. Both have similar laminar and turbulent trends and function of roughness PIPE

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**Water: Glycerin: High Re Low Re**

(3&4) Sometime streamlining increases drag and sometime it decreases drag. Water: High Re Glycerin: Low Re 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.

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**Viscous flow around sphere Viscous flow around stream- lined body**

From Visualized Flow – Japanese Society of Mechanical Engineers Viscous flow around stream- lined body A 2-D model is installed between the small clearance between two glass plates. The flow of a viscous fluid in this narrow space has sreamlines which coincide with potential flow. [ referred to as Hele-Shaw flow; (h/L)2<<1]

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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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Large wake Small wake

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**First flight of a powered aircraft 12/17/03 120ft in 12 seconds **

Same drag at 210 mph Not until 1907 that a 0ne minute flight was accomplished in Europe ( Henri Farman). By 1905 the Wright brothers were making 30 minute flights. First flight of a powered aircraft 12/17/03 120ft in 12 seconds Orville Wright at the controls

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The End Cd of (a) is 2.0; Cd of (b) is 1.2

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**ASIDE: do you find it odd that viscous drag **

SPHERE D ~ U2 D ~ U D = 6RU ASIDE: do you find it odd that viscous drag does not depend on density or pressure (p = RT)?

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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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