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Fluid Properties

Viscosity

Viscosity or Dynamic Viscosity is used to describe the fluidity property or the internal resistance of a fluid to motion.

From experimental observation, when a fluid flows over a solid surface, it comes to a complete stop at the surface and sticks on it. This is known as the no-slip condition and all liquids and gases satisfy this condition.

When considering a hypothetical experiment in which fluid is located between the small gap of two parallel plates. By fixing the bottom plate at rest and moving the upper plate at a constant velocity, the fluid deforms continuously under the shear force.

Because of the no-slip condition, the fluid contacts with the bottom fixed plate has a zero velocity, while the fluid contacts with the upper moving plate moves with the same upper plate velocity. As , the fluid deformation caused by the applied force to the moving plate is due to the shearing stress.

For steady laminar flow, the velocity profile of the flow varies linearly away from the fixed plate, i.e. . The velocity gradient is then equal to  .

For a small time increment , the upper plate will travel with constant velocity , therefore the shear strain equals to . By rearrangement,  , imply the rate of shearing strain  due to the shear stress is equals to 

From experimental results, the rate of shearing strain is directly proportional to the  shear stress .  i.e or . For some common fluid, the constant of proportionality is called the viscosity of the fluid and expressed as . Every fluid has its own value of viscosity and the value is also highly depending on temperature. And the viscosity of liquid decreases with the temperature i.e ,  while the viscosity of gas increases with temperature. i.e.

Fluids with shearing stress linearly proportion to the rate of shearing strain that can be described by a simple constant are called Newtonian fluids, .  Non-Newtonian fluid, like Bingham plastic, Pseudoplastic and Dilatant cannot be described by a single constant value of viscosity.  i.e.
Pseudoplastic or shear-thinning fluid, ;
Dilatant or shear-thickening fluid, .

The ratio of dynamic viscosity to density usually appears and is named as kinematic viscosity, i.e.