Random Fluid Mechanics

\fbox{\textbf{\Large Viscosity}}

Resistance of a fluid to deformation at a given rate. It is better to visualize in a shear flow.

The force F acting on the top plate is proportional to the speed u and the area A of the plate, and inversely proportional to the separation y

F = \mu A \frac{u}{y} \tau = \frac{F}{A} = \mu \frac{\partial u}{\partial y} \fbox{\textbf{\Large Dynamic viscosity}}

= pressure multiplies time

= energy per unit volume multiplies time

\mu/\eta = \Big[\frac{kg}{m\cdot s}\Big] = \Big[\frac{N}{m^2}\cdot s\Big] = Pa \cdot s \fbox{\textbf{\Large Kinematic viscosity}}

= specific energy multiplies time

= energy per unit mass multiplies time

\nu = \Big[\frac{m^2}{s}\Big] = \Big[\frac{N\cdot m}{kg}\cdot s\Big] = \frac{J}{kg}\cdot s