Assumptions
Like any mathematical model of the real world, fluid mechanics makes some basic assumptions about the materials being studied. These assumptions are turned into equations that must be satisfied if the assumptions are to be held true.
For example, consider a fluid in three dimensions. The assumption that mass is conserved means that for any fixed control volume (for example a sphere) – enclosed by a control surface – the rate of change of the mass contained is equal to the rate at which mass is passing from outside to inside through the surface, minus the rate at which mass is passing the other way, from inside to outside. (A special case would be when the mass inside and the mass outside remain constant). This can be turned into an equation in integral form over the control volume.
Fluid mechanics assumes that every fluid obeys the following:
- Conservation of mass
- Conservation of energy
- Conservation of momentum
- The continuum hypothesis, detailed below.
Further, it is often useful (at subsonic conditions) to assume a fluid is incompressible – that is, the density of the fluid does not change.
Similarly, it can sometimes be assumed that the viscosity of the fluid is zero (the fluid is inviscid). Gases can often be assumed to be inviscid. If a fluid is viscous, and its flow contained in some way (e.g. in a pipe), then the flow at the boundary must have zero velocity. For a viscous fluid, if the boundary is not porous, the shear forces between the fluid and the boundary results also in a zero velocity for the fluid at the boundary. This is called the no-slip condition. For a porous media otherwise, in the frontier of the containing vessel, the slip condition is not zero velocity, and the fluid has a discontinuous velocity field between the free fluid and the fluid in the porous media (this is related to the Beavers and Joseph condition).
Read more about this topic: Fluid Mechanics
Famous quotes containing the word assumptions:
“What a man believes may be ascertained, not from his creed, but from the assumptions on which he habitually acts.”
—George Bernard Shaw (1856–1950)
“All of the assumptions once made about a parent’s role have been undercut by the specialists. The psychiatric specialists, the psychological specialists, the educational specialists, all have mystified child development. They have fostered the idea that understanding children and promoting their intellectual well-being is too complex for mothers and requires the intervention of experts.”
—Elaine Heffner (20th century)
“Unlike Boswell, whose Journals record a long and unrewarded search for a self, Johnson possessed a formidable one. His life in London—he arrived twenty-five years earlier than Boswell—turned out to be a long defense of the values of Augustan humanism against the pressures of other possibilities. In contrast to Boswell, Johnson possesses an identity not because he has gone in search of one, but because of his allegiance to a set of assumptions that he regards as objectively true.”
—Jeffrey Hart (b. 1930)