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[edit] Static pressure in fluid dynamics
The use of the expression static pressure in fluid dynamics is very common, although it can easily create ambiguity. In order to avoid that, alternative unambiguous expressions that could be used are free-stream pressure, fluid pressure, thermodynamic pressure or sometimes just pressure. The ambiguity arises from the fact that static pressure can be used (correctly) to refer to the free-stream pressure in external flows, but it is more often (incorrectly) used to refer to the pressure in a generic point of a flow field, when discussing the Bernoulli equation.
[edit] Equivalence of static and free-stream pressure
We consider as an example the atmosphere, at rest relatively to the ground. An observer standing on the ground would see a generic fluid element as not moving, and subject to the local static pressure (which, in this case, is the atmospheric pressure).
We now consider an aircraft that flies straight and level with speed 
(airspeed and ground speed are the same, in this example), approaching the same fluid element from great distance. The distance is such that the fluid element is not perturbed by the approaching aircraft. To an observer on board the aircraft, the fluid element, like all the fluid elements at the same distance, appear as being in free-stream conditions, where all the fluid elements flow straight towards the aircraft with the same constant velocity and there are no pressure gradients inside the fluid (that is the pressure is constant anywhere in that region of fluid).[1] Given that the fluid element is the same for both observers, so is the pressure the element is subject to, therefore what an observer at rest calls static pressure is in fact the free-stream pressure to an observer moving relatively to the fluid. This is the only case in fluid dynamics where the expression static pressure can be used appropriately, i.e. to refer to the free-stream pressure.
Note that when the fluid element comes in proximity to the aircraft, free-stream conditions are lost, its velocity changes and pressure gradients develop. The pressure exerted on the element, therefore, will not be, in general, equal to the static pressure anymore.
[edit] Static pressure and the Bernoulli equation
[edit] References
- ^ A pressure gradient would in fact cause an acceleration, and so the velocity would not be constant anymore. Note also that we are neglecting the variation of atmospheric pressure with altitude.
