Difference Between Incompressible Flow and Material
As defined earlier, an incompressible (isochoric) flow is the one in which
This is equivalent to saying that
i.e. the material derivative of the density is zero. Thus if we follow a material element, its mass density will remain constant. Note that the material derivative consists of two terms. The first term describes how the density of the material element changes with time. This term is also known as the unsteady term. The second term, describes the changes in the density as the material element moves from one point to another. This is the convection or the advection term. For a flow to be incompressible the sum of these terms should be zero.
On the other hand, a homogeneous, incompressible material is defined as one which has constant density throughout. For such a material, . This implies that,
- and
- independently.
From the continuity equation it follows that
Thus homogeneous materials always undergo flow that is incompressible, but the converse is not true.
It is common to find references where the author mentions incompressible flow and assumes that density is constant. Even though this is technically incorrect, it is an accepted practice. One of the advantages of using the incompressible material assumption over the incompressible flow assumption is in the momentum equation where the kinematic viscosity can be assumed to be constant. The subtlety above is frequently a source of confusion. Therefore many people prefer to refer explicitly to incompressible materials or isochoric flow when being descriptive about the mechanics.
Read more about this topic: Incompressible Flow
Famous quotes containing the words difference between, difference, flow and/or material:
“I parted from my beloved because there was one thing which I had to tell her. She questioned me. She should have known all by sympathy. That I had to tell her it was the difference between us,—the misunderstanding.”
—Henry David Thoreau (1817–1862)
“There is as much difference between the counsel that a friend giveth, and that a man giveth himself, as there is between the counsel of a friend and of a flatterer. For there is no such flatterer as is a man’s self.”
—Francis Bacon (1561–1626)
“But even suppose blood should flow. Is there not a sort of blood shed when the conscience is wounded? Through this wound a man’s real manhood and immortality flow out, and he bleeds to an everlasting death. I see this blood flowing now.”
—Henry David Thoreau (1817–1862)
“The only happy talkers are dandies who extract pleasure from the very perishability of their material and who would not be able to tolerate the isolation of all other forms of composition; for most good talkers, when they have run down, are miserable; they know that they have betrayed themselves, that they have taken material which should have a life of its own, to dispense it in noises upon the air.”
—Cyril Connolly (1903–1974)