Bio-fluid Mechanics I

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2007 IntroBiomechanics-- W5 2007/10/8 1 1 Bio-fluid Mechanics I Viscosity, Re, Vortices, Forces of Flow, and Bernoulli’s Principles Introduction to Biomechanics 2008/10/22 2 I. Viscosity 3 Contrast b/w solid and fluid Bernoulli’s principle Cons. of energy Principle of continuity Cons. of mass Drag Frictional force Momentum flux change Force Velocity gradient Shearing plane Streamline Interface Viscosity Elastic modulus Density Mass Fluids Solids … resist to deform … defining boundary 4 Important properties - Density (m/V): air ~ 1.2 kg/m 3 , water ~ 1000 kg/m 3 - Viscosity: Viscous dense, e.g. ρ motor oil < ρ water t k F θ = Fluids: … how fast sheared; shape not returned dz dv S F μ τ = = (unit: kg/m·s or Pa·s) 5 Viscosity : Measuring kinematic viscosity e.g. Ostwald (capillary) viscometer www.greentree.com.tw www.oil.net.tw/lbg2006 /chapter/3-1.htm ρ μ η = ' ' η η = t t 6 ρ μ η =

Transcript of Bio-fluid Mechanics I

Microsoft PowerPoint - 2008F_IBM_W8_Biofluid mechanics I.pptand Bernoulli’s Principles
Introduction to Biomechanics 2008/10/22
DragFrictional force
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- Viscosity: Viscous ≠ dense, e.g. ρmotor oil < ρwater
t kF θ
dz dv
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4. “Steady” flow (i.e. same v @ same location)
5. No fluid-fluid interfaces
When fluids pass through an obstacle…
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l Sv ma
=Re ρ, μ … of the fluid (medium)
l … “Characteristic length” Convention: mostly in the direction of the flow
Exception:
Osborne Reynolds (1883): In circular pipe of certain length, turbulent occurs when
Re > 2000 (l = d=2r) or Re > 1000 (l = r) (our circulatory system, still laminar when Re ~ 4000)
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but usually vair > vwater, ∴Rebird ~ Refish if similar size
μ ρlv
3
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Note: Re is just a crude number, so only look at its order of magnitude (usually significant digits < 2)
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A useful tool for making models:
For two geometrically similar situations, equality of Re Equality of the patterns of flow, whatever the individual
values of length, speed, density, and viscosity
Other use for Re…
@ low Re, viscous force dominates; with no-slip condition shallow velocity gradient
(semi-stagnant fluid surrounding object)
III. Vortices
S1 S2
dl1 dl2
1v 2v
dt dlS
Conservation of mass
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(“pathline”)
3D ~ in tube (Principle of Continuity holds)
2211 vsvs =
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Some problems—
Antenna of the car vibrates use spiral around to break the vortices
Chimney, bridge, tree problematic if vibrating frequency caused by vortices shedding = natural frequency
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Removes momentum from the fluid
Impart momentum to the fluid
[Some vortex phenomena & examples]
“Viscous entrainment”
Use of Ground-Level Vortices
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Fig. 6.12 (b)
Obst, et al. 1996. Kinematics and fluid mechanics of spinning in phalaropes. Nature (+ cover photo). 384: 121.
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Shear motion within a velocity gradient rotation in solid body or fluid itself
Fig. 6.13
Force:
maF =
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S2 < S1
For a propeller or fan Force exerted on the mounting
For a propeller on a craft Thrust
For a passive body Drag (v1 > v2)
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From amount of constriction or Δv:
But in real case, v2 is rarely uniform across the flow
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To get v— Flow sensor Neutrally buoyant particles (photographs, videorecording)
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2007 IntroBiomechanics-- W5 2007/10/8
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dynamic pressure
Dynamic Pressure
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• Bernoulli’s Principle– some assumptions:
1. Viscosity negligible (i.e. Ideal fluid)
2. Steady flow
3. Incompressible fluid
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S Sdlm ρ=
dl dzg
to get rid of t…, assuming steady flow v dldt =
0=++⇒ dl
0)( 2 1 2
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Fig. 7.5
Ex1: Prairie dog burrow
(Work done by Vogel– use geometrically similar model (i.e. same Re) (p. 126 of text)
Applications of Bernoulli’s Principle
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2007 IntroBiomechanics-- W5 2007/10/8
Ventral view
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Dye released upstream of the nares in a dead shark
Experiment setup:
Velocity gradient creates a pressure difference (Bernoulli’s Principle)
Results:
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At some point, upstream
momentum to “turn”
Dominates @ low Re ∴ Streamlining does no good
2. Pressure drag: due to pressure distribution
Drag ∝ Dynamic pressure ( )
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Fig. 7.9
sphere hollow hemisphere solid hemisphere
47.0=dC 38.0 42.1 42.0 17.1
cylinder hollow half-cylinder half-rectangular solid
17.1=dC 20.1 30.2 55.1 98.1
long, flat plate
Area “S”– Different convention for different shapes
High-drag bodies “frontal” (projected) area
Streamlined bodies total surface (“wetted”) area
Lift-producing bodies “plan form” area
Blimps & organisms (eg. fish) Volume2/3
Same drag different Cd if different S is used
∴ Have to be consistent 54
Tricks for dropping one’s drag
Streamlining
(permit fluid to flow further around before
separation narrower wake less drag)
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“Riblets” for racing boats
↓ skin friction at high Re 56
Mucus– long-chain polymeric molecules
The issues—
(1) Well documented in pipes and for flow over test
body: kinds of molecules (fishes & some animals seem to
have the right kind)
(2) Drag reduction by mucus in Nature is difficult to
demonstrate: cost of production + other functions of
mucus just complicate the situations
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calculations suggest it negligible
opercula, drag ↓ 10% for a trout at top speed
Surface roughening– in critical regions seems possible
for some fast fishes
tune its head turning to ↓ drag
[Good reviews see Bushnell & Moore (1991) and Fish (1998)]
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TO BEAR IN MIND…
A claim of drag reduction in a biol. system should be viewed
with skepticism until
(2) shown to work on physical models under biol. relevant
conditions
(3) shown to work by some direct test on real organisms
under controlled and reproducible conditions
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http://web.mit.edu/fluids/www/Shapiro/ncfmf.html
Max-Planck-Institute for Metals Research
Paper written by Professor Stanislav Gorb:
1. Arzt, E., Gorb, S. and Spolenak, R. (2003). From micro to nano contacts in biological attachment devices. PNAS 100, 10603-10606.
2. Arzt, E., Gorb, S. and Spolenak, R. (2003). From micro to nano contacts in biological attachment devices. PNAS 100, 10603-10606.
3. Gorb, S., Varenberg, M., Peressadko, A. and Tuma, J. (2007). Biomimetic mushroom-shaped fibrillar adhesive microstructure. J. R. Soc. Interface 4, 271-275.
4. Gorb, S. N. and Varenberg, M. (2007). Mushroom-shaped geometry of contact elements in biological adhesive systems. J. Adh. Sci. & Tech. 21, 1175-1183.
5. Jiao, Y., Gorb, S. and Scherge, M. (2000). Adhesion measured on the attachment pads of Tettigonia viridissima (Orthoptera, insecta). JEB 203, 1887-1895.
3-page report on 1 paper due on 12/3
2007 IntroBiomechanics-- W5 2007/10/8
present on 12/10