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:
“The difference between the almost right word and the right word is the difference between the lightning- bug and the lightning.”
—Mark Twain [Samuel Langhorne Clemens] (1835–1910)
“Oh, I love Proust. We all learned from him how to go back in time. The difference is that Proust stayed in his room, and he observed himself. He was Proust lying in his bed looking at Proust at the window who was looking at Proust in bed. In our generation’s case, we are always in the middle. We are never on the outside. Whatever happens, happens to us.”
—Elie Wiesel (b. 1928)
“Clay answered the petition by declaring that while he looked on the institution of slavery as an evil, it was ‘nothing in comparison with the far greater evil which would inevitably flow from a sudden and indiscriminate emancipation.’”
—State of Indiana, U.S. public relief program (1935-1943)
“It is difficult to generalize why so many Latino/as moved toward conservative ... views.... for many, I believe it is basically a matter of desiring material acquisitions. It is difficult to maintain a collective ideology in a society where possessions and power-status equal self-worth.”
—Ana Castillo (b. 1953)