1.
web notes: lect4.ppt

2. 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?
Why is honey sticky?

3. “VISCOSITY IS DIFFERENT TO DENSITY”
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”

4. L stationary wall plate moves with speed v vx = v high speed vx
A useful model: Newtonian fluids water, most gases
plate moves with speed v
vx = v
high speed Z vx
linear velocity gradient L X
vx / d = v / L d
low speed
stationary wall
vx = 0

5. (F/A) =  (v / L) over area A velocity gradient shear
A useful model: Newtonian fluids water, most gases
plate exerts force F
over area A
velocity gradient
shear
stress
is proportional to
(F/A) =  (v / L)
stationary wall

6. (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.

7. (F/A) =  (v / L) toothpaste grease shear stress F / A wet sand
corn flour
shear stress F / A
Newtonian fluid
velocity gradient Dv/DL
(F/A) =  (v / L)
slope

8. 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.

9. SI unit is (N.m-2)(m).(m-1.s)  Pa.s
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  (mPa.s)
water (0 °C)
water (20 °C)
water (100 °C)
white blood (37 °C) ~4
blood plasma (37 °C) ~1.5
engine oil (AE10) ~ 200
air
Viscosity is very temperature dependent.
Viscosity of a liquid decreases with increasing temp.
Viscosity of a gas increases with increasing temp.
1 mPa = 10-3 Pa

10. 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?

11. 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.

12. What happens to the velocity profile when a
Newtonian fluid flows through a pipe?
Parabolic
velocity
profile
Linear
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)

13. h 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 h p1 p2 2R L
Dp = p1 - p2
assumptions ?

14. p1 > p2 pressure drop along pipe
A useful model: Poiseuille’s Law
Q = dV = Dp p R 4
8 h L dt h Dp 2R
Q = dV/dt L
p1 > p2 pressure drop along pipe
 energy dissipated (thermal) by friction between streamlines moving past each other

15. Pipes from Warragamba Dam Respiratory system Circulatory system
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)

16. 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 h L dt
What happens to the flow as viscosity changes ?
what happens to the flow as the radius changes ?

17. How do we apply conservation of energy in a flow system?
FLUID FLOW
STREAMLINE – LAMINAR FLOW
TURBULENT FLOW
REYNOLDS NUMBER
How do we apply conservation of energy in a flow system?

18. LAMINAR FLOW Streamlines for fluid passing an obstacle streamlines v
Velocity of particle
Velocity profile for the laminar flow of a non viscous liquid -
tangent to streamline

19. 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

20. 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 < ~ laminar flow
~ < Re < ~ unstable laminar
to turbulent flow
Re > ~ turbulent flow

21. Sydney Harbour Ferry
Re =  v L / 

22. Re =  v L /  turbulent flow r = 103 kg.m-3
v = 5 m.s-1
L = 10 m
 = Pa.s
Re = (103)(5)(10) / (10-3)
Re = 5x107
turbulent flow

23. Spermatozoa swimming
Re =  v L / 

24. Re =  v L /  laminar flow Spermatozoa swimming r = 103 kg.m-3
v = m.s-1
L = 10 mm
 = Pa.s
Re = (103)(10-5)(10x10-6) / (10-3)
Re = 10-4
laminar flow

25. Household plumbing pipes
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 …