# Impact pressure

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 $q_c$ or $Q_c$.

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]

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

where:

$P_t$ is total pressure

$P$ is static pressure

$\gamma\;$ is the ratio of specific heats

$M\;$ is the freestream Mach number

Taking $\gamma\;$ to be 1.4, and since $\;P_t=P+q_c$

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

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

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

where:

$\;q$ is dynamic pressure

## References

1. ^ DoD and NATO definition of impact pressure Retrieved on 2008-10-01
2. ^ The Free Dictionary Retrieved on 2008-10-01
3. ^ a b Clancy, L.J., Aerodynamics, Section 3.12 and 3.13
4. ^ "the dynamic pressure is equal to half rho vee squared only in incompressible flow."
Houghton, E.L. and Carpenter, P.W. (1993), Aerodynamics for Engineering Students, Section 2.3.1