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Fluid Mechanics-ISpring 2010
Lecture #02
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Viscosity Dependence
Coefficient of Viscosity
For Liquids, No effect of pressure on dynamic or Kinematic viscosity.
For gases, viscosity varies with pressure as
( , )p T
p
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Viscosity as a function of Temperature
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Why it is? A drop of blood forms a hump on a
horizontal glass; A drop of mercury forms a near-
perfect sphere and can be rolled just like a steel ball over a smooth surface;
Water droplets from rain or dew hang from branches or leaves of trees;
A soap bubble released into the air forms a spherical shape;
Water beads up into small drops on flower petals
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Interface
Interface
High Density of Molecules
Less dense Molecules
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Interfacial Forces
The liquid molecules tend to minimize their surface area because of surface tension.
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Surface Tension
Surface tension is generated due to intermolecular forces at the interface between two immiscible fluids with density difference.
The interface behaves like a stretched membrane.
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Examples of Surface Tension
Water drops formation on smooth surfaces
Insects walking on Water surface
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Surface Energy
Amount of energy in a stretched membrane.
Energy in a stretched membrane leads to pressure jump in curved surfaces.
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Surface Tension Coefficient ( )
Surface energy per unit area is called surface tension coefficient.
Surface Energy
Area
Force
Distance
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Surface Tension in a Hatched Cylinder
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Surface Tension in a Spherical Droplet
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Surface Tension for a General Curved Surface
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Contact Angle (Liquid-Solid Interface)
If θ<90 Wetting Liquid
If θ>90 Non-wetting Liquid
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Example of Contact Angle
Water wets soap but does not wet wax.
The rise or fall of liquid in a narrow tube is due to the
combined effect of contact angle and surface tension. This is known as Capillary Effect.
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Capillary Tube
Patm
PatmPatm