Fluid Mechanics-I Spring 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

3 Viscosity as a function of Temperature

4

5 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

6 Interface High Density of Molecules Less dense Molecules

7 Interfacial Forces The liquid molecules tend to minimize their surface area because of surface tension.

8 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.

9 Examples of Surface Tension Water drops formation on smooth surfaces Insects walking on Water surface

10 Surface Energy  Amount of energy in a stretched membrane.  Energy in a stretched membrane leads to pressure jump in curved surfaces.

11 Surface Tension Coefficient ( )  Surface energy per unit area is called surface tension coefficient.

12 Surface Tension in a Hatched Cylinder

13 Surface Tension in a Spherical Droplet

14 Surface Tension for a General Curved Surface

15 Contact Angle (Liquid-Solid Interface) If θ<90 Wetting Liquid If θ>90 Non-wetting Liquid

16 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.

17 Capillary Tube P atm