Problem 88P

Problem 88P

Briefly explain the similarities and differences between the material derivative and the Reynolds transport theorem.

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ANSWER:

Material derivative:-

- 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.

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