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Dynamic pressure is one of the terms of Bernoulli's equation, which can be derived from the conservation of energy for a fluid in motion. [1] At a stagnation point the dynamic pressure is equal to the difference between the stagnation pressure and the static pressure, so the dynamic pressure in a flow field can be measured at a stagnation point ...
The above equations suggest there is a flow speed at which pressure is zero, and at even higher speeds the pressure is negative. Most often, gases and liquids are not capable of negative absolute pressure, or even zero pressure, so clearly Bernoulli's equation ceases to be valid before zero pressure is reached.
Then for an ideal gas the compressible Euler equations can be simply expressed in the mechanical or primitive variables specific volume, flow velocity and pressure, by taking the set of the equations for a thermodynamic system and modifying the energy equation into a pressure equation through this mechanical equation of state. At last, in ...
Is zero-referenced against a perfect vacuum, using an absolute scale, so it is equal to gauge pressure plus atmospheric pressure. absolute scale Any system of measurement that begins at a minimum, or zero point, and progresses in only one direction. The zero point of an absolute scale is a natural minimum, leaving only one direction in which to ...
In fluid dynamics, a flow is considered incompressible if the divergence of the flow velocity is zero. However, related formulations can sometimes be used, depending on the flow system being modelled. Some versions are described below: Incompressible flow: =. This can assume either constant density (strict incompressible) or varying density flow.
Specific examples of vector flows include the geodesic flow, the Hamiltonian flow, the Ricci flow, the mean curvature flow, and Anosov flows. Flows may also be defined for systems of random variables and stochastic processes, and occur in the study of ergodic dynamical systems. The most celebrated of these is perhaps the Bernoulli flow.
In Einstein's theory of general relativity, the interior Schwarzschild metric (also interior Schwarzschild solution or Schwarzschild fluid solution) is an exact solution for the gravitational field in the interior of a non-rotating spherical body which consists of an incompressible fluid (implying that density is constant throughout the body) and has zero pressure at the surface.
The irrotationality of a potential flow is due to the curl of the gradient of a scalar always being equal to zero. In the case of an incompressible flow the velocity potential satisfies Laplace's equation, and potential theory is applicable. However, potential flows also have been used to describe compressible flows and Hele-Shaw flows. The ...