pressure and friction drag i - lth and friction drag i ... synopsis 1. general description 2....
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Pressure and Friction Drag I
Hydromechanics VVR090
ppt by Magnus Larson; revised by Rolf L Jan 2014
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SYNOPSIS
1. General description
2. Applications
3. Forces on immersed bodies
4. Dimensional analysis
5. Drag coefficients and lift coefficients
6. Examples/Problems
7. Flow separation. Introduction.
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1. General Description
Fluid Flow About Immersed Objects
Flow about an object may induce:
• drag forces
• lift forces
• vortex motion
Asymmetric flow field generates a net force
Drag forces arise from pressure differences over the body (due to its
shape) and frictional forces along the surface (in the boundary layer)
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D’Alemberts Paradox
Jean d’Alembert
(1717-1783)
Ideal fluid no viscosity (implies no friction, no separation)
No net force on an object submerged in a flowing fluid.
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2 Applications
• Naval architecture and aerodynamics.
• Structural engineering (e.g., houses, bridges)
• Vehicle design (e.g., cars, trains).
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Applications
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3. Forces on an Immersed Body
sin cos
cos sin
o
o
dD pdA dA
dL pdA dA
Drag and lift on a small element:
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Total drag and lift force on the body:
sin cos
cos sin
o
A A
o
A A
D dD p dA dA
L dL p dA dA
Effects of the shear stress on lift negligible:
cos A
L p dA
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sin cos o
A A
D p dA dA
Drag force:
Pressure drag (Dp) Frictional drag (Df)
(form drag)
Dp = function of the body shape and flow separation
Df = function of the boundary layer properties (surface
roughness etc)
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Examples of Flow around Bodies I
sin 0, cos 1
0,
p f o
A
D D dA
No pressure drag
sin 1, cos 0
, 0
p f
A
D pdA D
No frictional drag
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Examples of Flow around Bodies II
Dp >> Df Dp Df Dp << Df
D1 >> D2 >> D3
1. 2. 3.
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4. Dimensional Analysis of Drag and Lift
Assumed relationships:
1
2
, , , ,
, , , ,
o
o
D f A V E
L f A V E
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Derived -terms:
1
2 22
2 2
3 2
3 2
Re
M
o
o o
o
o
AV
V V
E a
D
A V
L
A V
(drag)
(lift)
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Results of Dimensional Analysis
2 2
3
3
1 1Re,M
2 2
Re,M
o D o
D
D f AV C AV
C f
Total drag force:
Total lift force:
2 2
4
4
1 1Re,M
2 2
Re,M
o L o
L
L f AV C AV
C f
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5. Drag coefficients CD and lift coefficients CL
Bodies of same shape and alignment with the flow have the
same CD and CL, if Re and M are the same.
Re describes the ratio between intertia forces and viscous
forces
M describes the ratio between inertia forces and elastic
forces
M only important at high flow velocities
(e.g. supersonic flows)
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Drag Coefficient for Various Bodies
2D3D
Re Re
CDCD
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Drag Coefficient for a Sphere
Mach number effects
Ernst Mach
(1838-1916)
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Drag Coefficient at Sound Barrier
CD as a function of M
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Example I: Drag Force on an Antenna Stand
30 m
0.3 m
What is the total drag force on the stand and
moment at the base?
wind
35 m/s
Standard atmosphere
(101 kPa, 20 deg)
6. Examples / problems
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Example II: Sphere Dropped from an Airplane
Plastic sphere falling in air – what is the
terminal speed?
FG
FD
50 mm
Relative density of
sphere S = 1.3
Standard atmosphere
(101 kPa, 20 deg)
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7. Flow Separation
contraction expansion
airfoilcylinder
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Flow around an airfoil
small angle of attack large angle of attack
(drag from frictional losses) (drag from pressure losses)