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Stagnation pressure

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In fluid dynamics, stagnation pressure is the pressure at a stagnation point in a fluid flow, where the kinetic energy is converted into pressure energy. It is the sum of the dynamic pressure and static pressure at the stagnation point.^[1]

Pitot tubes are used to measure stagnation (or total) pressure. A combined pitot-static tube is used on aircraft to determine flight speed. Stagnation quantities (e.g., stagnation temperature, stagnation pressure) are also frequently used in jet engine performance calculations.

1 Definition
2 Thermal definition
3 See also
4 References
5 External links

Definition

The definition for stagnation pressure can be derived from the Bernoulli Equation.^[2] For incompressible flow,

Stagnation (Total) Pressure = Dynamic Pressure + Static Pressure

$P_\text{stagnation}=\frac{1}{2} \rho v^2 + P_\text{static}$

(Only if Bernoulli's conditions are met.)

where:	$P stagnation$	is the stagnation (or total) pressure in pascals
	$ρ$	is the fluid density in kg/m³
	$v$	is the fluid velocity relative to the stagnation point before it becomes influenced by the object which causes stagnation in m·s^-1
	$P static$	is the static fluid pressure away from the influence of the moving fluid in pascals

This definition is not valid for transonic or supersonic flow. The stagnation pressure may still be defined; see below. For many purposes, in transonic flow, the stagnation enthalpy or stagnation temperature plays a role similar to the stagnation pressure in incompressible flow.

Thermal definition

It is the pressure a fluid retains when brought to rest isentropically from Mach number M.^[3]

$\frac{p_t}{p} = \left(1 + \frac{\gamma -1}{2} M^2\right)^{\frac{\gamma}{\gamma-1}}\,$

or, assuming an isentropic process, the stagnation pressure can be calculated from the ratio of stagnation temperature to static temperature:

$\frac{p_t}{p} = \left(\frac{T_t}{T}\right)^{\frac{\gamma}{\gamma-1}}\,$

where:

$p_t =\,$ stagnation (or total) pressure

$p =\,$ static pressure

$T_t =\,$ stagnation (or total) temperature in kelvins

$T =\,$ static temperature in kelvins

$\gamma\ =\,$ ratio of specific heats

The above derivation holds only for the case when the fluid is assumed to be calorically perfect. For such fluids, specific heats and $γ$ are assumed to be constant and invariant with temperature (See also, a thermally perfect fluid).

References

^ Stagnation Pressure at Eric Weisstein's World of Physics (Wolfram Research)
^ Equation 4, Bernoulli Equation - The Engineering Toolbox
^ Equations 35,44, Equations, Tables and Charts for Compressible Flow

External links

Retrieved from "http://en.wikipedia.org/wiki/Stagnation_pressure"

Categories: Fluid dynamics

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