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The horizontal pressure gradient is a two-dimensional vector resulting from the projection of the pressure gradient onto a local horizontal plane. Near the Earth's surface, this horizontal pressure gradient force is directed from higher toward lower pressure. Its particular orientation at any one time and place depends strongly on the weather ...
Here we assumed the local pressure gradient is not too great to have any compressibility effects. Though locally we ignored the effects of pressure variation due to density variation, over long distances these effects are taken into account. Since μ is independent of pressure, the above equation can be integrated over the length L to give
In fluid mechanics, the pressure-gradient force is the force that results when there is a difference in pressure across a surface. In general, a pressure is a force per unit area across a surface. A difference in pressure across a surface then implies a difference in force, which can result in an acceleration according to Newton's second law of ...
This ordinary differential equation is what is obtained when the Navier–Stokes equations are written and the flow assumptions applied (additionally, the pressure gradient is solved for). The nonlinear term makes this a very difficult problem to solve analytically (a lengthy implicit solution may be found which involves elliptic integrals and ...
Equations Fluid statics, pressure gradient: r = Position; ... Bernoulli's equation: p constant is the total pressure at a point on a streamline + ...
The second equation expresses that, in the case the streamline is curved, there should exist a pressure gradient normal to the streamline because the centripetal acceleration of the fluid parcel is only generated by the normal pressure gradient. The third equation expresses that pressure is constant along the binormal axis.
Vertical pressure variation is the variation in pressure as a function of elevation.Depending on the fluid in question and the context being referred to, it may also vary significantly in dimensions perpendicular to elevation as well, and these variations have relevance in the context of pressure gradient force and its effects.
The pressure gradient can be positive (adverse pressure gradient) or negative (favorable pressure gradient). In the limiting case of stationary plates ( U = 0 {\displaystyle U=0} ), the flow is referred to as Plane Poiseuille flow , and has a symmetric (with reference to the horizontal mid-plane) parabolic velocity profile.