STAGNATION PRESSURE

Stagnation pressure (also referred to as total pressure) is the pressure which would exist if the air were brought to rest isentropically. It exists only where the air has been so brought to rest, in which ase it is a state condition, and is simultaneously, then, the static pressure at the stagnation point (in subsonic flows). Note that "brought to rest" means that the velocity is zero in the frame of reference of the flow. Stagnation "lines" or "points" refer to places where the air has come to zero velocity isentropically.

Note that flow is not isentropic while passing through propellers, shock waves, boundary layers or gas turbine compressors and turbines, or where heat is added via combustion. These involve a change in the entropy level.

The free-stream stagnation pressure is obtained when the air is isentropically brought to rest from the free-stream velocity. For incompressible flow (density is constant) this is calculated by , called the subsonic Bernoulli equation, and where density varies

Note that shock waves are irreversible, so if the flow is supersonic, the free-stream stagnation pressure above will not physically exist anywhere. However, that pressure is a useful reference in numerous problems. Stagnation conditions on bodies in supersonic flow are not free-stream stagnation, but are actually the stagnation conditions behind the bow shock. The flow behind the bow shock is brought to rest isentropically.

TEMPERATURES

The static temperature is also a state property which always exists; it is defined the same way as static pressure except that a weightless thermometer replaces the weightless pressure gage.

The stagnation temperature is obtained by bringing the air to rest adiabatically rather than isentropically. Shock waves do not add or remove heat and thus are adiabatic, and the free-stream stagnation temperature does exist for supersonic flight. It is calculated by

Although equations (1) and (2) above are in terms of Mach number, they are equally valid for low-speed flows.

Return to ASE 120K Homepage