I NEED THE EAMPLES OF APPLICATION OF MATERIAL DERIVATIVE .

Hi

The material derivative is a derivative taken along a path moving with velocity v, and is often used in fluid mechanics and classical mechanics. It describes the time rate of change of some quantity (such as heat or momentum) by following it, while moving with a – space and time dependent – velocity field.

For example, in fluid dynamics, take the case that the velocity field under consideration is the flow velocity itself, and the quantity of interest is the temperature of the fluid. Then the material derivative describes the temperature evolution of a certain fluid parcel in time, as it is being moved along its pathline (trajectory) while following the fluid flow.

The material derivative can serve as a link between Eulerian and Lagrangian descriptions of fluid motion^.

^Thanks

^{Anurag Kishore}