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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 ...
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 ...
The pressure force pushing the liquid through the tube is the change in pressure multiplied by the area: F = −A Δp. This force is in the direction of the motion of the liquid. The negative sign comes from the conventional way we define Δp = p end − p top < 0. Viscosity effects will pull from the faster lamina immediately closer to the ...
Flux F through a surface, dS is the differential vector area element, n is the unit normal to the surface. Left: No flux passes in the surface, the maximum amount flows normal to the surface.
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.
Every point in a steadily flowing fluid, regardless of the fluid speed at that point, has its own unique static pressure p and dynamic pressure q. Their sum p + q is defined to be the total pressure p 0. The significance of Bernoulli's principle can now be summarized as "total pressure is constant in any region free of viscous forces".
The pressure gradient force causes an acceleration forcing air from regions of high pressure to regions of low pressure. Mathematically, this can be written as: =. The gravitational force accelerates objects at approximately 9.8 m/s 2 directly towards the center of the Earth.
At all points, the pressure gradient points to the direction of maximum increase of p and is always normal to the isobar at that point. Since the flow packet feels a push from the higher to the lower pressures, the effective pressure vector force is contrary to the pressure gradient, whence the minus sign before the gradient vector. Friction.