Fluid Dynamics
– Viscosity
Dave Foster
Department of Chemical Engineering
University of Rochester
Email: dafoster@che.rochester.edu
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Chemical Engineering
What do Chemical Engineers Do?
Manufacturing
„ Research
„
Biotech
Chemical
Pharmaceutical
Medical
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OK, first a little background
„
Fluid Mechanics is the study of fluids either in
motion (Fluid Dynamics) or at rest (Fluid Statics)
„
Fluids are either gas or liquid
„
Solids are NOT fluids
„
Properties of the fluid are things like density,
pressure, temperature, and VISCOSITY!
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Fluid – a definition
„
A substance that deforms continuously under
the action of shear stress
‹
Gas or Liquid
‹
Solids can resist a shear stress, a fluid can’t
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Applications of Fluid Mechanics
Explains blood flow in capillaries of a few
microns in diameter to crude oil flow
through an 800 mile long, 4 ft diameter pipe
„ Explains why airplanes are streamlined
with smooth surfaces
„ Explains why golf balls are made will
dimpled surfaces for most efficient travel
„
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Drag (Pounds of Force)
Effect of Dimples on Golf Balls
0.5
0.45
0.4
0.35
0.3
0.25
0.2
0.15
0.1
0.05
0
Drag for Sphere
Drag for Golf Ball
0
100
200
300
400
Velocity (Feet per Second)
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A List of Some Applications
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Coating
Breathing
Blood flow/pipe flow
Swimming
Pumps (traditional and
your heart)
Fans
Turbines
„
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Airplanes & Rockets
Missiles
Ships
Kidney dialysis machines
Heart-Lung bypass
machines
Membrane oxygenators
Engines
And lots more!
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For everything “FLUID” Flow is key
‹ How fast
‹ What direction
‹ How changing with time (differential
equations)
„ Flow properties deal with things like the
velocity, changes in temperature,
concentration.
„
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Isaac Newton
„
„
Key player in much of basic science
Three “Laws”
A body will remain at rest or in motion
1.
unless acted upon by an external force
ΣF=ma
2.
For every action there is an equal and
3.
opposite reaction
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Newton’s Law of Viscosity:
dv
τ =µ
dy
Shear stress
viscosity
Shear Strain
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Viscosity – What is it?
„
„
„
A property of a fluid to resist the rate of
deformation – a quantitative measure of a fluid’s
resistance to flow (water vs. syrup)
Takes place when a fluid is acted upon by a shear
stress
Simply stated, it’s how “thick” a fluid is
‹ We easily move through air
‹ It’s more difficult to move through water which
is 50X higher in viscosity than air
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A couple common examples:
Most Viscous
Air < Water < Paint < Pancake Syrup < Tooth Paste
Least Viscous
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Units
(yep – units, very important)
If we talk about how deep a
swimming pool is and I tell you
that it’s “10”, would you dive in?
„ Not if it’s 10 inches
„ But you might if it was 10 feet
„
Units are key in all of science, never
accept a number without a unit if it’s
supposed to have one
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Units of Viscosity
„
Poise (the most common units used to
describe viscosity, but not the only one)
„
Named after the French physician –
Jean Louis Poiseuille (1799 - 1869)
„
One-hundredth of a Poise is a centipoise or
“cP”
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Viscosity of Some “Common” Materials
(all are in units of Centi-Poise)
Hydrogen
Carbon Dioxide
Air
Blood
Gasoline
Water
Mercury
Corn Oil
SAE 30 oil
Heinz Ketchup
0.0088
0.015
0.018
0.40
0.29
1.0
1.5
72
290
50,000
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Changing a Material’s Viscosity
„
Easiest ways:
‹
‹
Change the Temperature – Heat it Up !
 Strong Effect
Change the Pressure – not as easy…
 Weak Effect: Decrease pressure, viscosity
decreases
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In a perfect world:
„
Fluids obey Newton’s Law of Viscosity
dv
τ =µ
dy
Straight line passing
through the origin
τ
Slope = viscosity
(Format: y = m x + b)
dv/dy
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Newtonian Fluids
Fluids that obey Newton’s Law of Viscosity
„ Linear relationship between shear stress and
shear strain
„ Some Examples of Newtonian Fluids:
‹ Water
‹ Simple Alcohols
‹ Simple Organic Solvents
„
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Everything Else is a
Non-Newtonian Fluid
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Non-Newtonian Fluids
„
Examples: Honey, toothpaste, paint, blood,
ketchup, syrup, many polymers
The list goes on and on………
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Non-Newtonian Fluids
Pseudoplastic – shear-thinningFluid decreases resistance with
increasing stress.
(ex: hair gel)
Newtonian
τ
Dilatant –shear-thickeningfluid increases resistance with
Increasing applied stress
(ex. Rarely encountered,
Cornstarch + water, Silly putty)
dv/dy
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Why do we care?
„
The primary parameter correlating the
viscous behavior of Newtonian Fluids is the
dimensionless Reynolds Number:
velocity * distance
Re =
viscosity
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Why do we care?
„
The first thing a fluids researcher should do
is estimate the Reynolds Number range of
flow under study.
‹ Low Re = laminar flow
(no change with time)
‹ High Re = turbulent flow
(changes with time)
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Reynolds Number and Viscosity
Viscosity
Re
Viscosity
Re
velocity * distance
Re =
viscosity
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How can we use Viscosity
(and Fluid Dynamics)?
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„
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Flow measurements in human body
‹ Heart valve flow volumes
Coating technologies
‹ Lots of applications
Moving fluids from one place to another
‹ Blood flow in your body
‹ Chemicals in pipes
Moving objects through fluids
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Thanks !!
Any Questions ?
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