Transcript Coefficient of viscosity, η AS PHYSICS

Coefficient of viscosity, η
Before we can define the coefficient of viscosity, we need to look
at viscosity in more detail.
What causes viscosity in liquids?
We need to consider what is happening on a
molecular level.
As we have discussed already, streamline flow behaves as if there
are layers of liquid passing over each other.
In a liquid with very low viscosity, there will be little interaction
between the layers.
In more viscous liquids, there will be interaction. As one layer
passes over another, energy will be transferred.
How does this interaction happen?
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Coefficient of viscosity, η
Before we can define the coefficient of viscosity, we need to look
at viscosity in more detail.
What causes viscosity in liquids?
We need to consider what is happening on a
molecular level.
One model suggests that the molecules in in adjacent layers are
attracted to each other.
As the molecule in layer B passes the molecule in layer A, their
mutual attraction speeds up A and slows down B.
There is an exchange of energy between the layers. Layer B slows
down and layer A speeds up.
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Coefficient of viscosity, η
Before we can define the coefficient of viscosity, we need to look
at viscosity in more detail.
What causes viscosity in liquids?
We need to consider what is happening on a
molecular level.
A viscous liquid is “thick” because the layers seem to stick a little as
they pass over each other due to intermolecular attractions.
Increasing the temperature would make the molecules’ random
thermal energy greater. They would be in each other’s near vicinity
for a shorter time so the attractive forces would be less and the
viscosity would decrease.
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Coefficient of viscosity, η
Before we can define the coefficient of viscosity, we need to look
at viscosity in more detail.
What causes viscosity in gasses?
We need to consider what is happening on a
molecular level.
In a gas, molecules can drift under thermal motion as well as travel
in the direction of bulk fluid flow.
What happens to the layers of gas in streamline flow if a molecule
passes from a slower layer to a faster one?
•A faster molecule entering a slower layer will, on average, speed
the slower layer up
•A slower molecule entering a faster layer will, on average, slow the
faster layer down
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Coefficient of viscosity, η
Before we can define the coefficient of viscosity, we need to look
at viscosity in more detail.
What causes viscosity in gases?
We need to consider what is happening on a
molecular level.
In a gas, molecules can drift under thermal motion, as well as travel
in the direction of bulk fluid flow.
What happens to the layers of gas in streamline flow, if a molecule
passes from a slower layer to a faster one?
•This manifests itself as an apparent frictional force between the
adjacent layers, with energy being transferred between adjacent layers
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Coefficient of viscosity, η
Tangential stress:
The force due to one plane within a streamline, on another
adjacent plane, will be a viscous force.
It will act tangentially against the streamline.
Retarding
force -F
Relative
velocity, Δv
Area of contact, A
Accelerating
force F
In this diagram, the upper streamline is travelling faster than the lower
one and their relative velocity is Δv.
The viscous drag forces between them form a Newton’s third law pair.
The force on the upper streamline is in the opposite direction to the
relative velocity so is a retarding force. The force on the lower
streamline accelerates the streamline.
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Coefficient of viscosity, η
Tangential stress:
The force due to one plane within a streamline, on another
adjacent plane, will be a viscous force.
It will act tangentially against the streamline.
Retarding
force -F
Relative
velocity, Δv
Area of contact, A
Accelerating
force F
The tangential stress is sometimes called the shear or shearing stress
and is defined by:
Tangential stress = force / area
τ =F/A
The units of tangential stress are Pa (pascal).
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Coefficient of viscosity, η
Δv
Velocity gradient:
y
Δy
This tangential stress creates
varying velocities, perpendicular
to the direction of streamline
flow, as represented by the
Velocity vectors
vectors in this diagram.
The rate of change of velocity across the streamlines is called the
velocity gradient.
Velocity gradient = Δv/Δy = Change in velocity / Change in y
What are the units of velocity gradient?
From the definition, they will be ms-1 / m.
The units of velocity gradient are s-1.
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Coefficient of viscosity, η
Δv
Velocity gradient:
The greater the viscosity of the
liquid, the smaller the velocity
gradient.
y
Δy
Velocity vectors
Imagine a really viscous liquid, like treacle. If you have a cup full
and spin it around, all the treacle moves too.
This is due to the high viscosity. A large Δy would be required for
even a small Δv.
If you spin a cup of water, the water at the edge will turn
immediately but as there is low viscosity and a high velocity
gradient, the water further into the cup might not spin at all at first.
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Coefficient of viscosity, η
Coefficient of viscosity:
So, viscosity is related to the tangential stress and the velocity
gradient.
We can define the coefficient of viscosity as follows:
Coefficient of viscosity, η = tangential stress
velocity gradient
Where η = (F/A) / (Δv/Δy).
What are its units?
Pa s (pascal seconds)
This is also Nsm-2
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Coefficient of viscosity, η
Coefficient of viscosity:
If we plot tangential stress against velocity gradient, we should
obtain a straight line. The gradient (slope) of the line will be the
coefficient of viscosity.
Note that the coefficient
of velocity is extremely
temperature dependent.
Tangential
stress
Velocity gradient
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Coefficient of viscosity, η
Coefficient of viscosity:
Fluids which obey this relationship are called Newtonian fluids.
Fluids that do not are
called non-Newtonian
fluids. The graph will be
non-linear for nonNewtonian fluids.
Tangential
stress
Non-Newtonian
fluid
Velocity gradient
Non-drip paint is a non-Newtonian fluid. With small tangential
stresses, there is a large velocity gradient but this soon falls as
the tangential stress increases.
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Coefficient of viscosity, η
Coefficient of viscosity:
Imagine the contrast between running through paint and running
through water.
Water is a Newtonian fluid. The faster you run, the greater the
resistance you would feel from the water.
It would be harder to overcome the resistive force of the water, the
faster you ran.
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Coefficient of viscosity, η
Coefficient of viscosity:
Imagine the contrast between running through paint and running
through water.
Running in non-drip paint, although a lot more messy, might
actually be easier.
Once you started moving, the viscous drag would decrease as nondrip paint is a non-Newtonian fluid.
We would recommend that you do not try this experiment at home!
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Coefficient of viscosity, η
Coefficient of viscosity:
The coefficient of viscosity of several fluids at 20°C is given below in
Nsm-2.
Air
1.8 x 10-5
Water
1.0 x 10-3
Mercury
1.6 x 10-3
Olive oil
8.4 x 10-2
Golden syrup
1.0 x 102
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