# Impact pressure

In compressible fluid dynamics, **impact 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.

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

- ↑ DoD and NATO definition of impact pressure Retrieved on 2008-10-01
- ↑ The Free Dictionary Retrieved on 2008-10-01
- ↑
^{3.0}^{3.1}Clancy, L.J.,*Aerodynamics*, Section 3.12 and 3.13 - ↑ "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

## See also