drag and lift forces ‘c wp - iit bombay
TRANSCRIPT
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DRAG AND LIFT FORCES ‘C ""wp CDEEP
IIT Bombay
36 Slide
fluid causes a net force to act on the body
• Force acting on an elemental area dA of the body will be
neither normal nor parallel to the surface
• The resultant force can be resolved into components parallel
to the direction of flow i.e. the free stream, and
perpendicular to the flow
• The force parallel to the direction of motion is known as
drag
• The component normal to the flow direction is called the lift
force
• The relative motion between a solid body and the
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DRAG FORCES CDEEP
IIT Bombay
CE 223 I 3L 2.. • In the case of real fluids, both the shear forces and
the pressure forces act simultaneously on the surface
• The part of the drag force arising out of the viscous action is
known as the viscous drag or the skin- friction drag
• The other part of the drag force is caused due to pressure
force acting on the surface and is known as the pressure
drag, or the form drag
• One can write
FD (total drag force) = Fviscous + Fform
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DRAG FORCES (Contd.) CDEEP
IIT Bombay
CE 223 1,31:1 /Slicle3
• The relative importance of the viscous and form
drags depends on the shape and orientation of the body
• When a thin flat plate or a disk is held parallel to the free
stream, viscous force predominates and pressure drag force
is zero
• If the plate is held normal to the direction of flow, the drag
force experienced by the body is due to the pressure
differentials and viscous drag is zero
1
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-4-
> ,C r c ---
> ., T0 (( te r. ;
(r....- c -,:
, - - • Low Pressure C. L- (_ —... 11 . „ \ N ;lc, • ) ,,-
+1
• \ I 1 ..• / t*
W AK . E )
•••■ • J'.., -....Z.:02•- .0
■• • . _••.., . •••• „.....„ .. ••......
y
DRAG FORCES (Contd.)
CDEEP IIT Bombay
CE 223 L3k)
(a) Viscous drag (b) Pressure drag
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COEFFICIENT OF DRAG Co
Body shape CD Range of Re
2-D Circular cylinder 1.2 104 to 1.5x10 5
Elliptical cylinder (4:1) 0.32 2.5x104 to 105
2-D Square cylinder 2.0 3.5x104
Circular disc 1.17 > 103
Open hemisphere (concave
side facing flow) 1.4 > 104
Open hemisphere (convex
side facing flow) 0.4 104
CDEEP IIT Bombay
CE 223 L3L Slide
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CD D rveL
1.328
DRAG COEFFICIENT FOR FLAT PLATES CDEEP
IIT Bombay
CE 223 L34 /Slide
Laminar boundary layer
CD Turbulent boundary layer beginning from R
the leading edge, 5x10 5 < Rey < 10 7
• For ReL <109 , the empirical equation of Schlichting may be
used
CD= 0 . 455/(log Re L) 2.58
0.074
5 eL
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DRAG COEFFICIENT FOR FLAT PLATES (Cont.) CDEEP
IIT Bombay
CE 223 1_315/Slide/
The revised values of the coefficient of drag for a flat
plate, accounting for laminar boundary layer, can be written as
CD 0.074 1740
1 ReL
R eL
(5x105 <Ret_<107 )
CD 9-940 0,45 1610
(Log R e L) 2 . 58
ReL (5x105 <R,L <109 )
Where Rey , is the plate Reynolds number (= VL/v)
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c
- 1010 2
tO 10 0
- IQ 10 •
- -t0101
"Z.:6•■•44"... ••••■■ "•-■
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DRAG COEFFICIENT OF SMOOTH PLATES CDEEP
IIT Bombay
CE 223 L2, /Slide 8/
10 1D6
10'
RF =U * L/V
Variation of the coefficient of drag with the Reynolds number
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DRAG COEFFICIENT OF SMOOTH PLATES (Contd.) CDEEP
IIT Bombay
22:-) [3i2 .'Slide
• The lower straight line is meant for a laminar
boundary layer and the upper curves are for turbulent
boundary layers
• The curve in the middle, connecting the two, represents the
variation of CD in the transition flow regime.
• Contribution of the laminar drag is insignificant for ReL>107.
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TUTORIAL CDEEP
IIT Bombay
CE 223 1,36 -;11(1> to
A super tanker is 360 m long and has a beam width of
70 m and a draft of 25 m. Estimate the force and power
required to overcome skin friction drag at a cruising speed of
13 knots in seawater at 10° C.
[1 knot = 1852 m per hour; at 10° C viscosity j = 1.4 x 10 -6
M 2 Is]
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SOLUTION CDEEP
IIT Bombay
CE 223 LILSlide I I
L = 360 m, U = 1852x13
= 6.69 m/s, v = 1.4 x 3600
10 -6 m 2/s
RL = 6.69x360 = 1.72 x 10 9 1.4x 10 -6
0.455 CD! = (log RL)2.58
1610 (Valid for 5 x 10 5 < RL < 109 )
R L
= 0.00147 — 0.0000016 = 0.00147
pU2 = Z x 1020 x 6.69 2 = 22825.6 N/m 2
Total area to be considered = bottom + sides
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SOLUTION (Contd.) CDEEP
IIT Bombay
Cr 223 L312.Slidel2
= (360 x 70) + (360 x 25) x 2
= 25,200 + 18,000 = 43,200 m 2
Therefore, F=CDf 1x 2-xpxU2 xA= 0.00147 x
43,200 x 22,825.6
= 1.45 x 10 6 N = 1.45 M-N
Power = F. U = 1.45 x 10 6 x 6.69 = 9.7 x 10 6 N- m/s =
9.7M- W
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FORCES ON BLUFF BODIES C DEEP
IIT Bombay
CL 223 33 I i '3
• Bodies which create a large wake in the flow are classified
as bluff bodies
• Circular cylinders, spheres, elliptical cross sections,
rectangular cross-sections of finite aspect ratios, a flat plate
held normal to the flow, are some examples of the bluff
bodies
• For bluff bodies the frictional drag component is very small
relative to the form drag
• The coefficient of drag CD is independent of the Reynolds
number, above a threshold value of Re .
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FORCES ON BLUFF BODIES (Contd.) CDEEP
IIT Bombay
CE 223 L36 -,1;1(‘ 14
▪ Drag coefficient curve is flat in the range 10 3 <Re<3*10 5
• For Re of around 3x10 5 , the laminar boundary layer on the
font part of the sphere undergoes a change and the
boundary layer becomes turbulent
• In a laminar boundary layer the fluid particles moving close
the surface are able to overcome the resistance, due to
viscous action, in the presence of a favorable pressure
gradient (dp/dx<0) in the front half of the sphere
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T1
4 6110 '! 4 MIMO 1 2 4 210 4 210 2 4 MO. 2 4 Me 2 4 MOS I0
' ' •
SMOOTH SPHERE CDEEP
IIT Bombay
• The Reynolds number for a smooth sphere at which
this sudden drop in Co takes place, as shown in
Figure below is known as the critical Reynolds number
• The drag coefficient with a turbulent boundary layer is
approximately 20% of that with the laminar boundary layer
Variation of Co with Re for a smooth sphere
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FORCES ON BLUFF BODIES (Contd.) CDEEP
IIT Bombay
CE 223 Laix/Slidel5
• The separation of flow occurs just upstream of the
midsection, a little before the fluid particles are subject to a
'pressure-hill' on the rear half
• The pressure difference between the front and the rear is
the main cause for the drag
• Slow moving particles around the midsection acquire more
momentum and the turbulent boundary layer is able to
resist flow separation for some more distance over the
sphere
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Theoretical
(Inviscid)
Turbulent
1.0
C,
0.5 Laminar
1.0
1.5 0 60 120 180
e (degrees)
FORCES ON BLUFF BODIES (Contd.) C DEEP
IIT Bombay
CE 223 L34 /Slide /6
Pressure distribution around a smooth sphere for laminar and turbulent
boundary-layer flow, compared with inviscid flow
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CIRCULAR CYLINDER CDEEP
IIT Bombay
GE 223 L3L/Sliciell
• The velocity is zero at the stagnant points located at the
front and rear of the cylinder
• The maximum value of v 0 =-2U and it occurs for 0=90°
• The pressure is maximum at the upstream stagnation point,
drops to a minimum at 0=90° and recovers to attain a
maximum value at the downstream stagnation point
• The net force due to the differential pressures on the
circular cylinder is zero
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CIRCULAR CYLINDER (Contd.)
Cp -
6.7 x 105
Re =1.1 x 104
20 40 60 eao 100 120 140 160 180
Angle from Forward Stagnation point (degrees)
Pressure distribution around a smooth cylinder
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CIRCULAR CYLINDER (Contd.) CDEEP
IIT Bombay
CE 223 3E) !Side
• The pressure difference on the front and the rear surface of
the cylinder gives rise to a significant drag force, the
pressure drag
• The experimental data of the turbulent boundary layer
follow the potential flow results better than the laminar
boundary layer case
• The total drag experienced by the cylinder drops suddenly
at the critical Reynolds number, Rec = 3 X 10 5
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CIRCULAR CYLINDER (Contd.) CDEEP
III Bombay
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Variation of CD with R e for a circular cylinder (SouRc.C. SChike-h+L1'3,1768)