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In compressible fluid dynamics, '''impact pressure''' (dynamic pressure) is the difference between total pressure (also known as [[pitot tube|pitot pressure]] or [[stagnation pressure]]) and [[static pressure]].<ref>[http://www.answers.com/topic/impact-pressure DoD and NATO definition of impact pressure] Retrieved on 2008-10-01</ref> <ref>[http://www.thefreedictionary.com/impact+pressure The Free Dictionary] Retrieved on 2008-10-01</ref>  In [[aerodynamics]] notation, this quantity is denoted as '''<math>q_c</math>''' or '''<math>Q_c</math>'''.  
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When input to an airspeed indicator, impact pressure is used to provide a [[calibrated airspeed]] reading. An [[air data computer]] with inputs of pitot and static pressures is able to provide a [[Mach number]] and, if static temperature is known, [[true airspeed]].
 
Some authors in the field of compressible flows use the term ''dynamic pressure'' or ''compressible dynamic pressure'' instead of ''impact pressure''.<ref name=LJC3.12>Clancy, L.J., ''Aerodynamics'', Section 3.12 and 3.13</ref><ref>"the dynamic pressure is equal to ''half rho vee squared'' only in incompressible flow."<br />Houghton, E.L. and Carpenter, P.W. (1993), ''Aerodynamics for Engineering Students'', Section 2.3.1</ref>
 
==Isentropic flow==
In [[isentropic flow]] the ratio of [[stagnation pressure|total pressure]] to [[static pressure]]  is given by:<ref name=LJC3.12/>
 
<math>\frac{P_t}{P} = \left(1+ \frac{\gamma -1}{2} M^2 \right)^\tfrac{\gamma}{\gamma - 1}</math>
 
where:
<math>P_t</math> is total pressure
 
<math>P</math> is static pressure
 
<math>\gamma\;</math> is the [[Heat capacity ratio|ratio of specific heats]]<br />
 
<math>M\;</math> is the freestream Mach number
 
 
Taking <math>\gamma\;</math> to be 1.4, and since <math>\;P_t=P+q_c</math>
 
 
<math>\;q_c = P\left[\left(1+0.2 M^2 \right)^\tfrac{7}{2}-1\right]</math>
 
 
Expressing the incompressible [[dynamic pressure]] as <math>\;\tfrac{1}{2}\gamma PM^2</math> and expanding by the [[binomial series]] gives:
 
 
<math>\;q_c=q \left(1 + \frac{M^2}{4} + \frac{M^4}{40} + \frac{M^6}{1600}  ... \right)\;</math>
 
where:
 
<math>\;q</math> is dynamic pressure
 
==References==
{{reflist}}
 
== See also ==
* [[Dynamic pressure]]
* [[Pitot-static system]]
* [[Pressure]]
* [[Static pressure]]
 
[[Category:Fluid dynamics]]

Latest revision as of 14:32, 18 August 2014

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