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Briefly explain the similarities and differences between

Fluid Mechanics | 2nd Edition | ISBN: 9780071284219 | Authors: Yunus A. Cengel, John M. Cimbala ISBN: 9780071284219 39

Solution for problem 88P Chapter 4

Fluid Mechanics | 2nd Edition

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Fluid Mechanics | 2nd Edition | ISBN: 9780071284219 | Authors: Yunus A. Cengel, John M. Cimbala

Fluid Mechanics | 2nd Edition

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Problem 88P

Problem 88P

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

Step-by-Step Solution:
Step 1 of 3

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.

Step 2 of 3

Chapter 4, Problem 88P is Solved
Step 3 of 3

Textbook: Fluid Mechanics
Edition: 2
Author: Yunus A. Cengel, John M. Cimbala
ISBN: 9780071284219

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Briefly explain the similarities and differences between