Fluid Mechanics-ISpring 2010

Lecture #02

2

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

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