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Gases are composed of molecules which collide with one another and solid objects. The continuity assumption, however, considers fluids to be continuous. That is, properties such as density, pressure, temperature, and velocity are taken to be well-defined at infinitely small points, and are assumed to vary continuously from one point to another. The discrete, molecular nature of a fluid is ignored.
Those problems for which the continuity assumption does not give answers of desired accuracy are solved using statistical mechanics. In order to determine whether to use conventional fluid dynamics (a subdiscipline of continuum mechanicsContinuum mechanics is a branch of physics (specifically mechanics) that deals with continuous matter, including both solids and fluids (i. liquids and gases). The fact that matter is made of atoms and that it commonly has some sort of heterogeneous micro) or statistical mechanics, the Knudsen numberThe Knudsen number Kn is the ratio of the molecular mean free path length to a representative physical length scale. It is defined as: where T, temperature (K) k, Boltzmann's constant P, total pressure (Pa) See also Fluid dynamics Mach number Reynolds num is evaluated for the problem. Problems with Knudsen numbers at or above unity must be evaluated using statistical mechanics for reliable solutions.
The foundational axioms of fluid dynamics are the conservation lawIn physics, a conservation law states that a particular measurable property of an isolated physical system does not change as the system evolves. The following is a partial listing of conservation laws that have never been shown to be inexact. Actually, is, specifically, conservation of massThe law of conservation of mass states that the mass of an isolated system will always remain constant, regardless of the processes acting inside the system. The matter cannot be created or destroyed, it only changes form. Basically this means that in a c, conservation of momentum (also known as Newton's second lawNewton's laws of motion are the three scientific laws which Isaac Newton discovered concerning the behaviour of moving bodies. These laws are fundamental to classical mechanics. Newton first published these laws in Philosophiae Naturalis Principia Mathema or the balance law), and conservation of energyConservation of energy the first law of thermodynamics is one of several conservation laws. It states that the total inflow of energy into a system must equal the total outflow of energy from the system, plus the change in the energy contained within the. These are based on classical mechanicsClassical mechanics is a model of the physics of forces acting upon bodies. It is often referred to as Newtonian mechanics after Newton and his laws of motion. Classical mechanics is subdivided into statics (which models objects at rest), kinematics (whic and are modified in relativistic mechanics .
The central equations for fluid dynamics are the Navier-Stokes equationsIn fluid dynamics, the Navier-Stokes equations named after Claude-Louis Navier and George Gabriel Stokes are a set of nonlinear partial differential equations that describe the flow of fluids such as liquids and gases. For example: they model weather or t, which are non-linear differential equations that describe the flow of a fluid whose stress depends linearly on velocity and on pressure. The unsimplified equations do not have a general closed-form solution, so they are only of use in computational fluid dynamics. The equations can be simplified in a number of ways. All of the simplifications make the equations easier to solve. Some of them allow appropriate fluid dynamics problems to be solved in closed form.