Stagnation pressure

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Total Pressure redirects here. Total pressure may also refer to a sum of partial pressures.

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.

Contents

[edit] Definition

The definition for Stagnation pressure can be derived from the Bernoulli Equation[2]


Stagnation (Total) Pressure = Dynamic Pressure + Static Pressure

or

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

where: Pstagnation 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/s1
Pstatic is the static fluid pressure away from the influence of the moving fluid in Pascals

[edit] Thermal Definition

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It is the pressure a fluid retains when brought to rest isentropically from mach number M.

\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 kelvin

T =\, static temperature in kelvin

\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).

[edit] See also

[edit] References

  1. ^ Stagnation Pressure at Eric Weisstein's World of Physics (Wolfram Research)
  2. ^ Equation 4, Bernoulli Equation - The Engineering Toolbox

[edit] External links


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