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| In [[fluid dynamics]], '''stagnation pressure''' (or '''pitot pressure''') is the [[static pressure]] at a [[stagnation point]] in a fluid flow.<ref name=Clancy3.5>Clancy, L.J., ''Aerodynamics'', Section 3.5</ref> At a stagnation point the fluid velocity is zero and all kinetic energy has been converted into pressure energy (isentropically). Stagnation pressure is equal to the sum of the free-stream [[dynamic pressure]] and free-stream static pressure.<ref>[http://scienceworld.wolfram.com/physics/StagnationPressure.html Stagnation Pressure] at Eric Weisstein's World of Physics (Wolfram Research)</ref>
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| Stagnation pressure is sometimes referred to as pitot pressure because it is measured using a [[pitot tube]].
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| ==Magnitude==
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| The magnitude of stagnation pressure can be derived from a simplified form of [[Bernoulli's principle#Bernoulli equations|Bernoulli Equation]].<ref>[http://www.engineeringtoolbox.com/bernouilli-equation-d_183.html Equation 4], Bernoulli Equation - The Engineering Toolbox</ref><ref name=Clancy3.5/> For [[incompressible flow]],
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| :<math>P_\text{stagnation}=\tfrac{1}{2} \rho v^2 + P_\text{static}</math>
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| where:
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| :<math>P_\text{stagnation}</math> is the stagnation pressure
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| :<math>\rho\;</math> is the fluid density
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| :<math>v</math> is the velocity of fluid
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| :<math>P_\text{static}</math> is the static pressure at any point.
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| At a stagnation point, the velocity of the fluid is zero. If the gravity head of the fluid at a particular point in a fluid flow is zero, then the stagnation pressure at that particular point is equal to [[total pressure]].<ref name=Clancy3.5/> However, in general total pressure differs from stagnation pressure in that total pressure equals the sum of stagnation pressure and gravity head.
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| :<math>P_\text{total}=0 + P_\text{stagnation}\;</math>
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| In [[compressible flow]] the stagnation pressure is equal to static pressure only if the fluid entering the stagnation point is brought to rest [[Isentropic flow|isentropically]].<ref>Clancy, L.J. ''Aerodynamics'', Section 3.12</ref> For many purposes in compressible flow, the stagnation [[enthalpy]] or [[stagnation temperature]] plays a role similar to the stagnation pressure in incompressible flow.
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| ==Compressible flow==
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| Stagnation pressure is the static pressure a fluid retains when brought to rest [[isentropic process|isentropical]]ly from [[Mach number]] ''M''.<ref>[http://www.grc.nasa.gov/WWW/K-12/airplane/Images/naca1135.pdf Equations 35,44], Equations, Tables and Charts for Compressible Flow</ref>
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| :<math>\frac{p_t}{p} = \left(1 + \frac{\gamma -1}{2} M^2\right)^{\frac{\gamma}{\gamma-1}}\, </math>
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| or, assuming an [[isentropic]] process, the stagnation pressure can be calculated from the ratio of stagnation temperature to static temperature:
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| :<math>\frac{p_t}{p} = \left(\frac{T_t}{T}\right)^{\frac{\gamma}{\gamma-1}}\,</math>
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| where:
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| :<math>p_t</math> is the stagnation pressure
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| :<math>p</math> is the static pressure | |
| :<math>T_t</math> is the stagnation temperature
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| :<math>T</math> is the static temperature
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| :<math>\gamma</math> ratio of [[specific heat]]s
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| The above derivation holds only for the case when the fluid is assumed to be calorically perfect. For such fluids, specific heats and <math>\gamma</math> are assumed to be constant and invariant with temperature (a thermally perfect fluid).
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| == See also ==
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| *[[Hydraulic ram]]
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| ==Notes==
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| {{Reflist}}
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| == References ==
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| *Clancy, L.J. (1975), ''Aerodynamics'', Pitman Publishing Limited, London. ISBN 0-273-01120-0
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| *Cengel, Boles, "Thermodynamics, an engineering approach, McGraw Hill, ISBN 0-07-254904-1
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| == External links ==
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| *[http://www.spaceagecontrol.com/pm/uploads/Main.Freepubs/ADA320216.pdf Pitot-Statics and the Standard Atmosphere]
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| *[http://www.spaceagecontrol.com/pm/uploads/Main.Litroom2/naca-tn-616.pdf The Measurement of Air Speed in Airplanes]
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| [[Category:Fluid dynamics]]
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