**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

### Other articles related to "assumptions, assumption":

**Assumptions**

... Cochran's Q test is based on the following

**assumptions**A large sample approximation in particular, it assumes that b is "large" ...

... to designate provisional and unendorsed

**assumptions**that will be made at the beginning of an argument in order to explore their implications ... Making an

**assumption**arguendo allows an attorney to pursue arguments in the alternative without admitting even the slightest possibility that those

**assumptions**could be true ... Often, these

**assumptions**would be that the facts or legal arguments endorsed by a hostile party were true ...

**Assumptions**

... The constitutive relations for two-dimensional orthotropic linear elastic materials are The assumptions of sandwich theory lead to the simplified relations and The equilibrium equations in two dimensions are The assumptions for a sandwich beam and the equilibrium equation imply that Therefore, for homogeneous facesheets and core, the strains also have the form. ...

**Assumptions**

... The framework of MPT makes many

**assumptions**about investors and markets ... None of these

**assumptions**are entirely true, and each of them compromises MPT to some degree ... A quadratic utility without any

**assumption**about returns is sufficient ...

**Assumptions**

... For the between-subject effects to meet the

**assumptions**of the analysis of variance, the variance for any level of a group must be the same as the variance for ... If the

**assumptions**are violated, a possible solution is to use the Greenhouse Geisser or the Huynh Feldt adjustments to the degrees of freedom because they can correct for issues ...

### Famous quotes containing the word assumptions:

“Why did he think adding meant increase?

To me it was dilution. Where do these

Innate *assumptions* come from?”

—Philip Larkin (1922–1986)

“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)