Briefly explain the similarities and differences between the material derivative and the Reynolds transport theorem.
- Material derivative describes the time rate of change of some physical quantities.
- To get the equation of motion by this, we need to solve partial differential equations by which the system is defined.
- It is a lagrangian way of describing the rate of change of properties of the fluid.
- The differentiation has to be taken with respect to time and space in this case.
- For an example by this we can calculate the temperature change in the fluid as the fluid flows in space and time.
- As it is a lagrangian way, it depends on the time and spatial coordinates of individual particles in the fluid.
Reynolds transport theorem:-
- Here we use the differentiation under the integral sign which is not so trivial and we need to follow some rigorous steps without fail.
- It associated with the control volume control system.
- It relates the change in system properties with the change in control volume system.
- It can be used in the laws of thermodynamics as it deals with volume and systems which are parts of thermodynamic variables.