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Fluid Mechanics (0905241)Fluid Mechanics (0905241)

Fl O B di D d Lift

D E Z d Al H

Flow Over Bodies: Drag and Lift

Dr.-Eng. Zayed Al-Hamamre

Chemical Engineering Department | University of Jordan | Amman 11942, Jordan

Tel. +962 6 535 5000 | 22888

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Content

Overview

Drag and Lift

Flow Past Objects Flow Past Objects

Boundary Layers

Laminar Boundary Layers

Transitional and Turbulent Boundary Layers Transitional and Turbulent Boundary Layers

Drag on Immersed Objects

Lift on Immersed Objects

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External Flows: OverviewIf a body is immersed in a flow, we call it an external flow.

External flows involving air are typically termed

aerodynamics

Some important external flows include airplanes, motor

vehicles, and flow around buildings, under water

aerodynamics.

, g ,

submarine.

In internal flows, the entire flow field is dominated by viscous effects, while

In external flow, the viscous effects are confined to a portion of the flow field such as the

boundary layers and wakes.

When a fluid moves over a solid body, it exerts pressure forces normal to the surface and shear

forces parallel to the surface along the outer surface of the body.

The component of the resultant pressure and shear forces that acts in the flow direction is The component of the resultant pressure and shear forces that acts in the flow direction is

called the drag force (or just drag), and the component that acts normal to the flow direction is

called the lift force (or just lift).

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External Flows: OverviewOften flow modeling is used to determine the flow fields in a wind tunnel or water tank.

Fuel economy, speed, acceleration, maneuverability,

stability, and control are directly related to the

aerodynamic/hydrodynamic forces and moments.

correct design

Typical quantities of interest are lift and drag acting on these objects.

The flow fields and geometries for most external flow problems are too complicated to be

solved analytically, and thus we have to rely on correlations based on experimental data

Such testing is done in wind tunnels

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Example: Automobile Drag

Development of the Cw

value for motor vehicles

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External Flows: OverviewTypes of External Flows:

Two-Dimensional: infinitely long and of constant cross-y g

sectional size and shape the flow is normal to the body. the

end effects are negligible

Axisymmetric: formed by rotating their cross-

sectional shape about the axis of symmetry.

Three-Dimensional: may or may not possess a line of

symmetry.

The bodies can be classified as streamlined or blunt, tends to block the flow, buildings.

Streamlined object typically move more easily through a fluid, airfoils, racing cars.

The force a flowing fluid exerts on a body in the flow direction is called drag

A fluid may exert forces and moments on a body in and about various directions

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External Flows: Drag and Lift When any body moves through a fluid, an interaction

between the body and the fluid occurs; forces at the

fl id b d i t f

Pressure Distributions around an object lead to lift and drag.

fluid–body interface.Normal stresses due to the pressure,

Shear Stresses on the surface also lead to lift and drag.

D Ali d ith th FlDrag: Aligned with the Flow Lift: Normal to the Flow

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Example: Automobile Drag

Scion XB Porsche 911

CD = 1.0, A = 25 ft2, CDA = 25ft2 CD = 0.28, A = 10 ft2, CDA = 2.8ft2

Drag force FD=1/2V2(CDA) will be ~ 10 times larger for Scion XB

Source is large CD and large projected area

Power consumption P = F V =1/2V3(C A) for both scales with V3!

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8Power consumption P = FDV =1/2V3(CDA) for both scales with V3!

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Example Air at standard conditions flows past a flat plate as is indicated. In case a the plate is parallel to

the upstream flow, and in case b it is perpendicular to the upstream flow. If the pressure and

shear stress distributions on the surface are as indicated obtained either by experiment orshear stress distributions on the surface are as indicated, obtained either by experiment or

theory, determine the lift and drag on the plate.

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Example Cont.

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Example Cont.

The friction drag is zero for a flat surface normal to flow and maximum for a flat surface The friction drag is zero for a flat surface normal to flow, and maximum for a flat surface parallel to flow

Th d i ti l t th f t l d t th diff b t th The pressure drag is proportional to the frontal area and to the difference between the

pressures acting on the front and back of the immersed body.

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External Flows: Flow Past Objects The fluid velocity ranges from zero at the surface (the no-slip condition) to the free-

stream value away from the surface

The character of the flow field is a function of the shape of the body size orientation s peed The character of the flow field is a function of the shape of the body size, orientation,s peed,

and fluid properties.

Low Reynolds , Number: Re = 0.1Medium Reynolds Number: Re = 10

Large Reynolds

N b R 105

strong viscous effects, Large Boundary Layer

Number: Re = 105

Thin Boundary Layerviscous effects are negligible

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Boundary layer: a thin region on the surface of a body in which viscous effects are very important

and outside of which the fluid behaves essentially as if it were inviscid

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Flow Over Flat Plate :

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External Flows: Flow Past Objects

Symmetric

The viscous effects are important several diameters in any direction

from the cylinder.

The streamlines are essentially symmetric about the center of the

cylinder the streamline pattern is the same in front of the cylinder as

i i b hi d h li dit is behind the cylinder.

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External Flows: Flow Past Objects

Separationp

As the Reynolds number is increased, the region ahead of the cylinder in which viscous effects

are important becomes smaller,are important becomes smaller,

The viscous region extending only a short distance ahead of the cylinder.

The flow loses its symmetry and the flow separates from the body at the separation location The flow loses its symmetry and the flow separates from the body at the separation location

With the increase in Reynolds number, the fluid inertia becomes more important and at some

location on the body, denoted the separation location, the fluid’s inertia is such that it cannot

follow the curved path around to the rear of the body.

The result is a separation bubble behind the cylinder in which some of the fluid is actually

fl i i h di i f h fl

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15flowing upstream, against the direction of the upstream flow

External Flows: Flow Past Objects

Wake

At larger Reynolds numbers, the area affected by the viscous forces is forced farther

downstream until it involves only a thin boundary layer on the front portion of the cylinder

Irregular, unsteady perhaps turbulent wake region that extends far downstream of the cylinder.

The fluid in the region outside of the boundary layer and wake region flows as if it were

inviscid.

Th l i di i hi h b d l d k i h l h h The velocity gradients within the boundary layer and wake regions are much larger than those

in the remainder of the flow field

The viscous effects are confined to the boundary layer and wake regions

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16 The viscous effects are confined to the boundary layer and wake regions.

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Streamlining

• Streamlining reduces drag by reducing FD,pressure, at the cost of increasing wetted surface areaincreasing wetted surface area and FD,friction.

• Goal is to eliminate flow i d i i i lseparation and minimize total

drag FD

• Also improves structural pacoustics since separation and vortex shedding can excite structural modesstructural modes.

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Streamlining

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Streamlining The friction drag is zero for a flat surface normal to flow, and maximum for a flat surface

parallel to flow

Th d b t i ifi t h th l it f th fl id i t hi h f th

The pressure drag is proportional to the frontal area and to the difference between the

pressures acting on the front and back of the immersed body.

The pressure drag becomes most significant when the velocity of the fluid is too high for the

fluid to be able to follow the curvature of the body, and thus the fluid separates from the body at some point and creates a very low pressure region in the back.

The part of drag that is due directly to wall shear stress τw is called the skin friction drag (or

friction drag FD, friction) since it is caused by frictional effects,

The part that is due directly to pressure P is called the pressure drag (also called the form drag because of its strong dependence on the form or shape of the body)

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Streamlining The first thought that comes to mind to reduce drag is to streamline a body in order to reduce

flow separation and thus to reduce pressure drag

Streamlining has opposite effects on pressure and friction drags. It decreases pressure drag by

delaying boundary layer separation and thus reducing the pressure difference between the

front and back of the body and increases the friction drag by increasing the surface areay g y g

Optimization study to reduce the drag of a body must consider

both effects and must attempt to minimize the sum of the twoboth effects and must attempt to minimize the sum of the two

The minimum total drag

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CD of Common Geometries

At higher Reynolds numbers, the drag coefficients for

most geometries remain essentially constant

This is due to the flow at high Reynolds numbers

becoming fully turbulent.

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CD of Common Geometries

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CD of Common Geometries

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CD of Common Geometries

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Example

As part of the continuing efforts to reduce the drag coefficient and thus to improve the fuel

efficiency of cars, the design of side rearview mirrors has changed drastically from a simple

circular plate to a streamlined shapecircular plate to a streamlined shape.

Determine the amount of fuel and money saved per year as a result of replacing a 13-cm-

diameter flat mirror by one with a hemispherical back . Assume the car is driven 24,000 km a d e e o by o e w e sp e c b c . ssu e e c s d ve ,

year at an average speed of 95 km/h.

The densities of air and gasoline are taken to be 1.20 kg/m3 and 800 kg/m3, respectively. The

heating value of gasoline is given to be 44,000 kJ/kg.

Price of gasoline is $0.60/L, and the overall efficiency of the engine to be 30 percent

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Example Cont.

The amount of work done to overcome this drag force and the required energy input for a

distance of

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External Flows: Boundary Layers

Turbine blades

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External Flows: Boundary Layers

divides the flow over a plate into two regions:

h l i h The boundary layer region, in which the viscous effects and the velocity changes are

significant, viscous shearing forces and

The irrotational flow region in which the frictional effects are negligible and the The irrotational flow region, in which the frictional effects are negligible and the

velocity remains essentially constant.

For parallel flow over a flat plate, the pressure drag is zero, and thus the drag coefficient is For parallel flow over a flat plate, the pressure drag is zero, and thus the drag coefficient is

equal to the friction drag coefficient

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External Flows: Boundary Layers

When both sides of a thin plate are subjected to flow, A becomes the total area of the top and

bottom surfaces.

The Reynolds number at a distance x from the leading edge of a flat plate is

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External Flows: Boundary Layers

Friction Coefficient

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Friction Coefficient

the average friction coefficient over the entire plate

The local friction coefficients are higher in turbulent

flow than they are in laminar flow because of the

intense mixing that occurs in the turbulent boundary

layer

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External Flows: Boundary Layers

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Transitional and Turbulent Boundary Layers

Turbulent Spots in Transitional Flow

No real theories for transitional

boundary layersboundary layers.

The turbulent profiles are flatter, have a larger

velocity gradient at the wall and produce a largervelocity gradient at the wall, and produce a larger

boundary layer thickness than do the laminar

profiles

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Transitional and Turbulent Boundary Layers

Flat Plate Drag:

Analogous to Moody

Chart

Surface roughness in generalSurface roughness, in general, increases the drag coefficient in

turbulent flow.

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Drag on Immersed Objects

The critical Reynolds number for flow across a circular cylinder or sphere is about

the fluid completely wraps around the cylinder and the two arms of the fluid meet on the

rear side of the cylinder in an orderly manner.

At higher velocities,

The fluid still hugs the cylinder on the frontal side, but it is too fast to remain attached to the

surface as it approaches the top (or bottom) of the cylinder.

As a result, the boundary layer detaches from the surface, forming a separation region behind

the cylinder

Flow in the wake region is characterized by periodic vortex formation and pressures much

lower than the stagnation point pressure

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35lower than the stagnation point pressure.

The high pressure in the vicinity of the stagnation point and the low pressure on the opposite

side in the wake produce a net force on the body in the direction of flow.

Th d f i i il d f i i d l R ld b (R 10) d The drag force is primarily due to friction drag at low Reynolds numbers (Re < 10) and to

pressure drag at high Reynolds numbers (Re > 5000).

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Drag on Immersed Objects

Drag on a Smooth Sphere and Cylinder:

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Drag on a Smooth Sphere and Cylinder

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Drag on a Smooth Sphere and Cylinder

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Drag on Immersed Objects

If there were not viscous effects acting on an object there would be no friction drag

nor any pressure drag.

i i f i i d i hi h dViscosity causes friction and separation which causes pressure drag.

Friction Drag: the part of drag due directly to the shear stress

/ h f d d di l hPressure Drag/Form Drag: the part of drag due directly to the pressure

The Drag Coefficient is highly dependent on shape and the Reynolds Number:

At the same Reynolds number, the above shapes have the same amount of drag.

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Drag on Immersed Objects

For small Reynolds Number flows, the coefficient of drag varies inversely with

the Reynolds Number, Re < 1.

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Effect of Surface Roughness

This is done by tripping the boundary layer into turbulence at a lower Reynolds

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42 This is done by tripping the boundary layer into turbulence at a lower Reynolds

number, and thus causing the fluid to close in behind the body, narrowing the

wake and reducing pressure drag onsiderably.

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Effect of Surface Roughness For blunt bodies such as a circular cylinder or sphere, an increase in the surface roughness

may actually decrease the drag coefficient

Thi i d b t i i th b d l i t t b l t l R ld b d This is done by tripping the boundary layer into turbulence at a lower Reynolds number, and

thus causing the fluid to close in behind the body, narrowing the wake and reducing pressure

drag considerably

This results in a much smaller drag coefficient and thus drag force for a rough-surfaced

cylinder or sphere in a certain range of Reynolds number compared to a smooth one of

identical size at the same velocity

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Drag on Immersed Objects

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Drag on Immersed Objects

Shock waves, which cannot exist in subsonic flows, provide a mechanism for the generation of

drag that is not present in the relatively low speed subsonic flowsdrag that is not present in the relatively low-speed subsonic flows

If the velocity of the object is sufficiently large, compressibility effects become important

The Mach number and Reynolds number effects are often closely connected because both are The Mach number and Reynolds number effects are often closely connected because both are

directly proportional to the upstream velocity.

Independent for Ma < 0.5

Strongly

dependentp

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Drag on Immersed Objects

blunt and sharp bodies

This behavior is due to the nature of the shock

wave structure and the accompanying flow

separation.

The leading edges of wings for subsonic aircraft

are s all q ite ro nded and bl nt hile thoseare usually quite rounded and blunt, while those

of supersonic aircraft tend to be quite pointed

and sharp

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Drag on Immersed Objects

Froude number is a ratio of the free-stream speed to a typical wave speed on the interface of

two fluids, such as the surface of the ocean

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Example Engine oil at 40°C flows over a 5-m-long flat plate with a free-stream velocity of 2 m/s.

Determine the drag force acting on the plate per unit width.

laminar flow over the entire plate, and the average friction coefficient

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Example

A 2.2-cm-outer-diameter pipe is to span across a river at a 30-m-wide section while being

completely immersed in water. The average flow velocity of water is 4 m/s and the water

temperature is 15°C Determine the drag force exerted on the pipe by the rivertemperature is 15 C. Determine the drag force exerted on the pipe by the river.

CD = 1.0.

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Example

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Example Cont.

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Example

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Lift on Immersed Objects

A typical device designed to produce lift does so by generating a pressure distribution that is

The component of the resultant pressure and shear forces that acts normal to the flow direction

is called the lift force (or just lift). A typical device designed to produce lift does so by generating a pressure distribution that is

different on the top and bottom surfacesV is the upstream velocity of the fluid (or, equivalently, the velocity of a flying body in aequivalently, the velocity of a flying body in a

quiescent fluid).

Because of the asymmetry of the

i i f il hnonsymmetric airfoil,the pressure

distributions on the upper and lower

surfaces are different,and a lift is Lift is generated because the flow velocity at

the top surface is higher, and thus theproduced even with

the angle between the upstream flow and the axis of

the object

the top surface is higher, and thus the

pressure on that surface is lower

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53the object

Lift on Immersed Objects

Flow starts out with no lift, but the lower fluid

stream separates at the trailing edge when the

l i h i lvelocity reaches a certain value.

This forces the separated upper fluid stream to

close in at the trailing edge initiating clockwiseclose in at the trailing edge, initiating clockwise

circulation around the airfoil.

This clockwise circulation increases the velocity

of the upper stream while decreasing that of the

lower stream, causing lift

A starting vortex of opposite sign

(counterclockwise circulation) is then shed

downstream and smooth streamlined flow is

established over the airfoil

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Lift on Immersed Objects

since roughness affects the wall shear, not the pressure,

Most common lift-generating devices i.e., airfoils, fans, spoilers on cars, etc. operate in the

large Reynolds number range.

Viscous effects to lift is usually negligible since the bodies are streamlined, and wall shear is

parallel to the surfaces of such devices and thus nearly normal to the direction of lift

i ffChemical Engineering Department | University of Jordan | Amman 11942, Jordan

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55The most important parameter that affects

the lift coefficient is the shape of the object

Lift on Immersed Objects

Airfoils are specifically designed to generate lift while keeping the drag at a minimum

The spoilers and inverted airfoils on racing cars are designed for the opposite purpose of e spo e s d ve ed o s o c g c s e des g ed o e oppos e pu pose o

avoiding lift or even generating negative lift to improve traction and control

Most lift generating devices are not symmetrical.

Lift can be generated by adjusting the angel of attack of the object.

Lift d d ffi i t f i d d t l f tt k Lift and drag coefficients of wings are dependent on angle of attack.

At large angles of attack, the boundary layer separates and the wing stalls.

The average lift per unit planform area FL/A is called the wing loading, which is simply the

ratio of the weight of the aircraft to the planform area of the wings (since lift equals theratio of the weight of the aircraft to the planform area of the wings (since lift equals the

weight during flying at constant altitude)

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Lift on Immersed Objects

The lift acting on an airfoil can be determined by simply

integrating the pressure distribution around the airfoil

ignoring the very thin boundary layer on the airfoil (zero

vorticity, irrotational flow)

N i f f fl i f il i h Net viscous forces are zero for flow past an airfoil since the

pressure changes in the flow direction along the surface,

but it remains essentially constant through the boundary

layer in a direction normal to the surface

I lif i d i h i i i In many lift-generating devices the important quantity is

the ratio of the lift to drag developed,

To change the lift and drag characteristics of an airfoil is to To change the lift and drag characteristics of an airfoil is to

change the angle of attack.

This represents a change in the shape of the object.

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57p g p j

Lift on Immersed Objects

In general, the lift coefficient increases and the drag coefficient decreases with an increase in

aspect ratio

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58aspect ratio

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Lift on Immersed Objects Other shape changes can be used to alter the lift and drag when desirable.

In modern airplanes it is common to utilize leading edge and trailing edge flapsi h th h f th i f il b th f bli.e. change the shape of the airfoil by the use of movable

leading edge and trailing edge flaps

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Lift on Immersed Objects

High-performance airfoils generate lift that is

perhaps 100 or more times greater than their

ddrag

The minimum flight velocity can be determined

from the requirement that the total weight W offrom the requirement that the total weight W of the aircraft be equal to lift and

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Lift Generated by Spinning

When the ball is not spinning, the lift is zero because of

top–bottom symmetrytop–bottom symmetry.

But when the cylinder is rotated about its axis, the cylinder

drags some fluid around because of the no-slip condition

and the flow field reflects the superposition of the spinning

and nonspinning flows.

The stagnation points shift down, and the flow is no longer

symmetric about the horizontal plane that passes through

the center of the cylinder.y

The average pressure on the upper half is less than the

average pressure at the lower half

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Lift Generated by Spinning

• CL strongly depends on rate of rotation.

• The effect of rate of rotation on CD is small.

• Baseball golf soccer tennis players utilize spin• Baseball, golf, soccer, tennis players utilize spin.

• Lift generated by rotation is called The Magnus Effect.

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Example

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Example Cont.

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Example Cont.

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ExampleA commercial airplane has a total mass of 70,000 kg and a wing planform area of 150 m2. The

plane has a cruising speed of 558 km/h and a cruising altitude of 12,000 m, where the air density

is 0.312 kg/m3. The plane has double-slotted flaps for use during takeoff and landing, but itis 0.312 kg/m3. The plane has double slotted flaps for use during takeoff and landing, but it

cruises with all flaps retracted. Assuming the lift and the drag characteristics of the wings can be

approximated by NACA 23012, determine (a) the minimum safe speed for takeoff and landing i h d i h di h fl (b) h l f k i dil h i iwith and without extending the flaps, (b) the angle of attack to cruise steadily at the cruising

altitude, and (c) the power that needs to be supplied to provide enough thrust to overcome wing

drag.g

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Example

tennis ball with a mass of 0.125 lbm and a diameter of 2.52 in is hit at 45 mi/h with a backspin of

4800 rpm. Determine if the ball will fall or rise under the combined effect of gravity and lift due

to spinning shortly after being hit in air at 1 atm and 80°Fto spinning shortly after being hit in air at 1 atm and 80 F.

The translational and angular velocities of the ball are

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Example Cont.

The ball will drop under the combined

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68The ball will drop under the combined

effect of gravity and lift due to spinning