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Impact pressure

Summary

In compressible fluid dynamics, impact pressure (dynamic pressure) is the difference between total pressure (also known as pitot pressure or stagnation pressure) and static pressure.[1][2] In aerodynamics notation, this quantity is denoted as ${\displaystyle q_{c}}$ or ${\displaystyle Q_{c}}$.

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.[citation needed]

Some authors in the field of compressible flows use the term dynamic pressure or compressible dynamic pressure instead of impact pressure.[3][4]

Isentropic flow

In isentropic flow the ratio of total pressure to static pressure is given by:[3]

${\displaystyle {\frac {P_{t}}{P}}=\left(1+{\frac {\gamma -1}{2}}M^{2}\right)^{\tfrac {\gamma }{\gamma -1}}}$

where:

${\displaystyle P_{t}}$  is total pressure

${\displaystyle P}$  is static pressure

${\displaystyle \gamma \;}$  is the ratio of specific heats

${\displaystyle M\;}$  is the freestream Mach number

Taking ${\displaystyle \gamma \;}$  to be 1.4, and since ${\displaystyle \;P_{t}=P+q_{c}}$

${\displaystyle \;q_{c}=P\left[\left(1+0.2M^{2}\right)^{\tfrac {7}{2}}-1\right]}$

Expressing the incompressible dynamic pressure as ${\displaystyle \;{\tfrac {1}{2}}\gamma PM^{2}}$  and expanding by the binomial series gives:

${\displaystyle \;q_{c}=q\left(1+{\frac {M^{2}}{4}}+{\frac {M^{4}}{40}}+{\frac {M^{6}}{1600}}...\right)\;}$

where:

${\displaystyle \;q}$  is dynamic pressure