http://www.physics.usyd.edu.au/teach_res/jp/fluids09
web notes: lect4.ppt
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What do some liquids splash more?
Why do we need to change brake fluid?
Why do cars need different oils in hot and cold
countries?
Why do engines run more freely as it heats
up?
Have you noticed that skin lotions are easier to
pour in summer than winter?
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Why is honey sticky?
When real fluids flow they have a certain
internal friction called viscosity. It exists in
both liquids and gases and is essentially a
frictional force between different layers of
fluid as they move past one another.
In liquids the viscosity is due to the cohesive
forces between the molecules whilst in
gases the viscosity is due to collisions
between the molecules.
“VISCOSITY IS DIFFERENT TO DENSITY”
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A useful model: Newtonian fluids water, most gases
plate moves with speed v
vx = v
high speed
Z
X
linear velocity
gradient
vx
L
d
vx / d = v / L
low speed
stationary wall
vx = 0
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A useful model: Newtonian fluids water, most gases
plate exerts force F
over area A
shear
stress
is proportional to
velocity
gradient
(F/A) =  (v / L)
stationary wall
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(F/A) =  (v / L)
 = (F / A)(L / v)
coefficient of viscosity  (Greek letter eta).
The greater the coefficient of viscosity , the
greater the force required to move the plate at
a velocity v.
This relationship does not hold for all fluids.
Viscous fluids that obey this equation are
called Newtonian fluids and  = constant
independent of the speed of flow.
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toothpaste
shear stress F / A
grease
wet sand
corn flour
Newtonian fluid
velocity gradient Dv/DL
(F/A) =  (v / L)
slope
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Non-Newtonian or rheological fluids –
viscosity  is a function of the flow velocity
Examples of non-Newtonian fluids
* Blood - it contains corpuscles and other suspended particles. The
corpuscles can deform and become preferentially oriented so that the
viscosity decreases to maintain the flow rate.
* Corn flour and water mixture.
* Certain soils (more clay content) are non-Newtonian when moist to wet.
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Viscosity
SI unit is (N.m-2)(m).(m-1.s)  Pa.s
A common unit is the poise P (1 Pa.s = 10 P)
Fluid
water (0 °C)
water (20 °C)
water (100 °C)
white blood (37 °C)
blood plasma (37 °C)
engine oil (AE10)
air
 (mPa.s)
1.8
1.0
0.3
~4
~1.5
~ 200
0.018
1 mPa = 10-3 Pa
Viscosity is very temperature dependent.
Viscosity of a liquid decreases with increasing temp.
Viscosity of a gas increases with increasing temp.
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Why can't you get all the dust off your car by
just squirting water from a hose onto it?
Why can't you simply remove dust just be
blowing across the surface?
Why does dust cling to a fast rotating fan?
How can a leaf stay on a car moving at high
speed?
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Boundary layer
When a fluid moves over a surface, there is a thin layer of the
fluid near the surface which is nearly at rest. This thin layer is
called the boundary layer.
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What happens to the velocity profile when a
Newtonian fluid flows through a pipe?
Linear
velocity
profile
Parabolic
velocity
profile
Adhesive forces between fluid and surface
 fluid stationary at surface
Cohesive forces between molecules  layers
of fluid slide past each other generating
frictional forces  energy dissipated (like
rubbing hands together)
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What causes a fluid to flow through a pipe?
A useful model: Poiseuille’s Law:
laminar flow of a Newtonian fluid through a pipe
parabolic
velocity profile
volume flow rate
Q = dV/dt
2R
p1

p2
L
Dp = p1 - p2
assumptions ?
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Poiseuille’s Law
A useful model:
Q = dV = Dp p R 4
8L
dt
2R

Dp
Q = dV/dt
L
p1 > p2 pressure drop along pipe
 energy dissipated (thermal) by friction
between streamlines moving past each other
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APPLICATIONS
Irrigation pipes
Pipes from Warragamba Dam
Respiratory system
Circulatory system
Air conditioning, ducting, piping
Soils Water will rise quicker in large grain soils
(Q  R 4) but it will rise to greater height by
capillary attraction on fine grain soils (h  1/R)
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The heart is so responsive to the changing
needs of our body that cardiac output can vary
from as little as 5 to a maximum of 35 litres of
blood per minute, a sevenfold change, over a
very short interval.
Q = dV = Dp p R4
8L
dt
What happens to the flow as viscosity changes ?
what happens to the flow as the radius changes ?
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FLUID FLOW
STREAMLINE – LAMINAR FLOW
TURBULENT FLOW
REYNOLDS NUMBER
How do we
apply
conservation of
energy in a
flow system?
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Streamlines for LAMINAR FLOW
fluid passing an
obstacle
streamlines
v
Velocity profile for the laminar
flow of a non viscous liquid
Velocity of particle
- tangent to streamline
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REYNOLDS NUMBER Re
A British scientist Osborne Reynolds (1842 – 1912)
established that the nature of the flow depends upon a
dimensionless quantity, which is now called the Reynolds
number Re.
Re =  v L / 

density of fluid
v
average flow velocity over the cross section
of the pipe
L
characteristic dimension
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Re =  v L / 
[Re]  [kg.m-3] [m.s-1][m] [Pa.s]-1
 [kg] [m-1][s-1][kg.m.s-2.m-2.s]-1 = [1]
Re is a dimensionless number
As a rule of thumb, for a fluid flowing through a tube
Re < ~ 2000
laminar flow
~ 2000 < Re < ~ 3000 unstable laminar
to turbulent flow
Re > ~ 2000
turbulent flow
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Sydney Harbour Ferry
Re =  v L / 
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Re =  v L / 
 = 103 kg.m-3
Re = (103)(5)(10) / (10-3)
v = 5 m.s-1
Re = 5x107
L = 10 m
 = 10-3 Pa.s
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Spermatozoa swimming
Re =  v L / 
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Spermatozoa swimming
Re =  v L / 
 = 103 kg.m-3
v = 10-5 m.s-1
L = 10 mm
 = 10-3 Pa.s
Re = (103)(10-5)(10x10-6) / (10-3)
Re = 10-4
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Re =  v L / 
Household plumbing pipes
Typical pipes are about 30 mm in diameter and
water flows at about 10 m.s-1
Re ~ (10)(3010-3)(103) / (10-3) ~ 3105
The circulatory system
Speed of blood ~ 0.2 m.s-1
Diameter of aorta L ~ 10 mm
Viscosity of blood say  ~ 10-3 Pa.s
Re ~ (0.2)(1010-3)(103) / 10-3) ~ 2103
Impact
Method of swimming/propulsion
Pump design
Flow systems
…
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