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In Fluid mechanics, and in particular in Fluid statics, the term static pressure (from Greek στατικός, IPA: [stati'kos], causing to stand) refers to the pressure exerted by a fluid at rest. Examples of situations where static pressure is involved are:

  • The air pressure inside a latex balloon is the static pressure and so is the atmospheric pressure (neglecting the effect of wind).
  • The hydrostatic pressure at the bottom of a dam is by definition the static pressure and so is the pressure exerted on one's thumb when stopping the water flow in a garden hose.
  • The pressure inside a ventilation duct is not the static pressure, unless the air inside the duct is still.
  • On an aircraft, the pressure measured on a generic point of the surface of the wing (or fuselage) is not, in general, the static pressure, unless the aircraft is not moving with respect to the air.

[edit] Static pressure in Fluid dynamics

For fluids in motion the term static pressure is still applicable (in particular with regard to external flows), and refers strictly to the pressure in the fluid far upstream of any object immersed into it, i.e. the pressure of the undisturbed flow, or free-stream pressure. The free-stream pressure is the pressure that would be exerted anywhere in the fluid if the fluid was not moving,[1] hence the use of the term static to indicate the free-stream pressure.

On the other hand, when the fluid comes in proximity to a body, its pressure deviates from the free-stream value and should no longer be referred to as static pressure, which is a common mistake. Such quantity should be called simply pressure.

The confusion between pressure and static pressure arises from one of the basic laws of Fluid dynamics, Bernoulli equation, written here assuming incompressible, inviscid flow and negligible gravitational effects:


\frac{1}{2} \rho v^2 \ + \ p \ = \ \mathrm{constant}


Since the term ρv2 / 2 represents the so-called dynamic pressure, the term p, by contrast, is often (incorrectly) called static pressure, irrespective of whether it refers to free-stream pressure or not. In fact, strictly speaking, Bernoulli equation states that "the sum of dynamic pressure and pressure is constant across the flow field".

The only case in which the term p is indeed the static pressure is when Bernoulli equation is referred to a point of the flow field far upstream of any object, where the velocity v takes its free-stream value.[2] In this case, Bernoulli equation can be read as "the sum of free-stream dynamic pressure and static pressure is constant across the flow field".

The distinction can be summarized by applying the Bernoulli equation to three relevant points of the flow field: a point far upstream, a generic point close to a body and a stagnation point on the body's surface:


\frac{1}{2} \rho v^2_\infty \ + \ p_\infty \quad = \quad \frac{1}{2} \rho v^2 \ + \ p \quad = \quad p_T


where:

ρ = density (assumed constant)
v_\infty = free-stream velocity
p_\infty = free-stream pressure (static pressure)
v = velocity in a generic point
p = pressure in a generic point
pT = total pressure (or stagnation pressure)


[edit] See also

[edit] Notes

  1. ^ This is true assuming that the effect of gravity is negligible, otherwise the pressure will vary linearly with height. For air, the former assumption is generally correct.
  2. ^ This case is of particular interest for example when measuring the speed of an aircraft (i.e. the free-stream velocity) by means of a Pitot tube. The problem is how to measure the static pressure when the pressure probe itself is on the body, rather than far upstream of it.
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