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
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1
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!
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
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.
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.
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
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
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