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'In [[fluid mechanics]] the term '''static pressure''' has several uses: * In the design and operation of [[aircraft]], ''static pressure'' is the air pressure in the aircraft’s [[Pitot-static system#Static pressure|static pressure system]]. * In [[fluid dynamics]], many authors use the term ''static pressure'' in preference to just ''pressure'' to avoid ambiguity. Often however, the word ‘static’ may be dropped and in that usage [[pressure]] is the same as static pressure at a nominated point in a fluid. * The term ''static pressure'' is also used by some authors in [[fluid statics]]. == Static pressure in design and operation of aircraft == An aircraft’s [[altimeter]] is operated by the [[Pitot-static system#Static pressure|static pressure system]]. An aircraft’s [[airspeed indicator]] is operated by the static pressure system and the [[Pitot-static system#Pitot pressure|pitot pressure system]].<ref>Lombardo, D.A., ''Aircraft Systems'', 2nd edition – chapter 2</ref> The static pressure system is open to the exterior of the aircraft to sense the pressure of the atmosphere at the [[Altitude#Altitude in Aviation|altitude]] at which the aircraft is flying. This small opening is called the [[Pitot-static system#Pitot-static pressure|static port]]. In flight the air pressure is slightly different at different positions around the exterior of the aircraft. The aircraft designer must select the position of the [[Pitot-static system#Pitot-static pressure|static port]] carefully. There is no position on the exterior of an aircraft at which the air pressure, for all [[angle of attack|angles of attack]], is identical to the atmospheric pressure at the altitude at which the aircraft is flying.<ref>"It is virtually impossible to find a position where the static pressure is always exactly the same as the pressure in the free airstream away from the aircraft". Kermode, A.C., ''Mechanics of Flight'', 10th edition – page 65</ref> The difference in pressure causes a small error in the altitude indicated on the altimeter, and the [[airspeed]] indicated on the airspeed indicator. This error in indicated altitude and airspeed is called [[position error]].<ref>Kermode, A.C., ''Mechanics of Flight'', 10th Edition – page 65</ref><ref>"Of these errors the error in detection of static pressure is generally the most serious and has the special name, ''position error''." Dommasch, D.O., Sherby, S.S., and Connolly, T.F. (1967) ''Airplane Aerodynamics'', 4th edition – page 51, Pitman Publishing Corp., New York</ref> When selecting the position for the static port, the aircraft designer’s objective is to ensure the pressure in the aircraft’s static pressure system is as close as possible to the atmospheric pressure at the altitude at which the aircraft is flying, across the operating range of weight and airspeed. Many authors describe the atmospheric pressure at the altitude at which the aircraft is flying as the ''[[freestream]] static pressure''. At least one author takes a different approach in order to avoid a need for the expression ''freestream static pressure''. Gracey has written "The static pressure is the atmospheric pressure at the flight level of the aircraft".<ref>Gracey, William, [https://ntrs.nasa.gov/archive/nasa/casi.ntrs.nasa.gov/19800015804_1980015804.pdf ''Measurement of aircraft speed and altitude''] NASA, RP-1046, page 1</ref><ref>Gracey, William, ''Measurement of Aircraft Speed and Altitude'', page 1</ref> Gracey then refers to the air pressure at any point close to the aircraft as the ''local static pressure''. == Static pressure in fluid dynamics == The concept of [[pressure]] is central to the study of fluids. A pressure can be identified for every point in a body of fluid, regardless of whether the fluid is in motion. Pressure can be [[Pressure measurement|measured]] using an [[Barometer#Aneroid barometers|aneroid]], [[Pressure measurement#Bourdon|Bourdon tube]], mercury column, or various other methods. The concepts of ''total pressure'' and ''[[dynamic pressure]]'' arise from [[Bernoulli's equation]] and are significant in the study of all fluid flows. (These two pressures are not pressures in the usual sense - they cannot be measured using an aneroid, Bourdon tube or mercury column.) To avoid potential ambiguity when referring to [[pressure]] in fluid dynamics, many authors use the term ''static pressure'' to distinguish it from ''total pressure'' and ''dynamic pressure''; the term ''static pressure'' is identical to the term ''pressure'', and can be identified for every point in a fluid flow field. In ''Aerodynamics'', L.J. Clancy<ref>Clancy, L.J., ''Aerodynamics'', page 21</ref> writes: "To distinguish it from the total and dynamic pressures, the actual pressure of the fluid, which is associated not with its motion but with its state, is often referred to as the static pressure, but where the term pressure alone is used it refers to this static pressure." [[Bernoulli's equation]] is fundamental to the dynamics of incompressible fluids. In many fluid flow situations of interest, changes in elevation are insignificant and can be ignored. With this simplification, Bernoulli’s equation for incompressible flows can be expressed as<ref>Clancy, L.J., ''Aerodynamics'', equation 3.13</ref><ref>Hurt, H.H. Jr, (1960), ''Aerodynamics for Naval Aviators'', page 9, A National Flightshop Reprint, Florida</ref><ref>Anderson, J.D. Jr, ''Fundamentals of Aerodynamics'', 4th edition – page 212, McGraw-Hill, New York. {{ISBN|978-0-07-295046-5}}</ref> :<math>P + \tfrac12 \rho v^2 = P_0,</math> where: *<math>P\;</math> is static pressure, *<math>\tfrac12 \rho v^2</math> is [[dynamic pressure]], usually denoted by <math>q\;</math>, *<math>\rho\,</math> is the [[density]] of the fluid, *<math>v\,</math> is the [[flow velocity]], and *<math>P_0\;</math> is total pressure which is constant along any [[Streamlines, streaklines, and pathlines|streamline]]. It is also known as the [[stagnation pressure]]. Every point in a steadily flowing fluid, regardless of the fluid speed at that point, has its own static pressure <math>P</math>, dynamic pressure <math>q</math>, and total pressure <math>P_0</math>. Static pressure and dynamic pressure are likely to vary significantly throughout the fluid but total pressure is constant along each streamline. In [[Conservative vector field#Irrotational flows|irrotational flow]], total pressure is the same on all streamlines and is therefore constant throughout the flow.<ref>A.M. Kuethe and J.D. Schetzer (1959), ''Foundations of Aerodynamics'', Section 3.5 (2nd edition), John Wiley & Sons, Inc. New York {{ISBN|0-471-50952-3}}</ref> The simplified form of Bernoulli's equation can be summarised in the following memorable word equation:<ref>Clancy, L.J., ''Aerodynamics'', Section 3.5</ref><ref>”The total pressure is composed of two parts, the static pressure and the dynamic pressure”. Streeter, V.L., ''Fluid Mechanics'' 4th edition – page 404</ref><ref>[http://www.grc.nasa.gov/WWW/K-12/airplane/bern.html NASA's guide to Bernoulli's Equation]</ref> :''static pressure + dynamic pressure = total pressure''. This simplified form of Bernoulli’s equation is fundamental to an understanding of the design and operation of ships, low speed aircraft, and airspeed indicators for low speed aircraft – that is aircraft whose maximum speed will be less than about 30% of the [[speed of sound]]. As a consequence of the widespread understanding of the term ''static pressure'' in relation to Bernoulli’s equation, many authors<ref>For example: Abbott, I.H. and Von Doenhoff, A.E. (1949) ''Theory of Wing Sections'', Navier-Stokes equations - section 5.4. Dover Publications, Inc., New York. Standard Book Number 486-60586-8</ref> in the field of fluid dynamics also use ''static pressure'' rather than ''pressure'' in applications not directly related to Bernoulli’s equation. The [[British Standards Institution]], in its Standard<ref>British Standard BS 185: Part 1: 1950 ''Glossary of Aeronautical Terms''</ref> ''Glossary of Aeronautical Terms'', gives the following definition: :''4412 '''Static pressure''' The pressure at a point on a body moving with the fluid.'' == Static pressure in fluid statics == The term ''[[Hydrostatics#Hydrostatic pressure|(hydro)static pressure]]'' is sometimes used in [[fluid statics]] to refer to the [[pressure]] of a fluid at a nominated depth in the fluid. In fluid statics the fluid is stationary everywhere and the concepts of dynamic pressure and total pressure are not applicable. Consequently, there is little risk of ambiguity in using the term ''pressure'', but some authors<ref>For example: "The pressure in cases where no motion is occurring is referred to as static pressure." Curtis D. Johnson, [http://zone.ni.com/devzone/cda/ph/p/id/190 Process Control Instrumentation Technology], Prentice Hall (1997) {{webarchive |url=https://web.archive.org/web/20080119225401/http://zone.ni.com/devzone/cda/ph/p/id/190 |date=January 19, 2008 }}</ref> choose to use ''static pressure'' in some situations. == See also == * [[Pascal's law]] * [[Stagnation pressure]] * [[Standard conditions for temperature and pressure]] ==Notes== {{Reflist|2}} == References == '''Aircraft design and operation''' * {{Citation | first = William | last = Gracey | title = Measurement of static pressure on aircraft | year = 1958 | place = Langley Research Center | publisher = NACA | url = https://ntrs.nasa.gov/archive/nasa/casi.ntrs.nasa.gov/19930092348_1993092348.pdf | accessdate = 2008-04-26 | id = TR-1364 }}. * {{Citation | first = William | last = Gracey | title = Measurement of aircraft speed and altitude | year = 1980 | place = Langley Research Center | publisher = NASA | url = https://ntrs.nasa.gov/archive/nasa/casi.ntrs.nasa.gov/19800015804_1980015804.pdf | accessdate = 2008-04-26 | id = RP-1046 }}. * {{Citation | last = Gracey | first = William | title = Measurement of Aircraft Speed and Altitude | publisher = John Wiley & Sons | year = 1981 | location = New York | isbn = 978-0-471-08511-9 }} * Kermode, A.C. (1972) ''Mechanics of Flight'', Longman Group Limited, London {{ISBN|0-582-23740-8}} * Lombardo, D.A., ''Aircraft Systems'', 2nd edition, McGraw-Hill (1999), New York {{ISBN|0-07-038605-6}} '''Fluid dynamics''' * [[L. J. Clancy]] (1975), ''Aerodynamics'', Pitman Publishing Limited, London {{ISBN|0-273-01120-0}} * Streeter, V.L. (1966), ''Fluid Mechanics'', McGraw-Hill, New York [[Category:Aerodynamics]] [[Category:Aircraft instruments]] [[Category:Fluid dynamics]]'