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physicsFluid.jpg ![]() |
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physicsFluid.jpg
The Navier-Stokes Equations for the velocity in a compact vector notation (top) and the equation for a density moving through the velocity field (bottom). Mathematically, the state of a fluid at a given instant of time is modeled as a velocity vector field: a function that assigns a velocity vector to every point in space. Imagine the air that occupies a room, its velocity will vary due to the presence of heat sources, air drafts, etc. For example, the velocity of the air near a radiator will predominantly be pointing in the upward direction due to heat rising. The distribution of velocities within a room is also quite complex as is evident when watching the smoke rising from a cigarette or the motion of dust particles in the air.The Navier-Stokes Equations are a precise description of the evolution of a velocity field over time. Given the current state of the velocity and a current set of forces, the equations tell us precisely how the velocity will change over an infinitesimal time step. Figure 1 (top) depicts these equations in a compact vector-like notation. Very roughly the equation states that the change in velocity is due to the three terms on the right hand side of the equal sign. |
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