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In fluid dynamics, stagnation pressure is the static pressure at a stagnation point in a fluid flow.^[1] At a stagnation point the fluid velocity is zero and all kinetic energy has been converted into pressure energy. Stagnation pressure is equal to the sum of the free-stream dynamic pressure and free-stream static pressure.^[2] Stagnation pressure is sometimes referred to as pitot pressure because it is measured using a pitot tube.

1 Magnitude
2 Compressible flow
3 See also
4 Notes
5 References
6 External links

Magnitude

The magnitude of stagnation pressure can be derived from the Bernoulli Equation.^[3]^[1] For incompressible flow,

Total Pressure = Dynamic Pressure + Static Pressure

$P_\text{total}=\tfrac{1}{2} \rho v^2 + P_\text{static}$

where:	$P_\text{total}\;$	is the total pressure in pascals
	$\rho\;$	is the fluid density in kg/m³
	$v\;$	is the velocity of fluid in m/s at any point
	$P_\text{static}\;$	is the static pressure in pascals at any point.

At a stagnation point, the velocity of the fluid is zero. Therefore the stagnation pressure (which is the static pressure at a stagnation point) is equal to total pressure.^[1]
$P_\text{total}=0 + P_\text{stagnation}\;$

In compressible flow the stagnation pressure is equal to total pressure only if the fluid entering the stagnation point is brought to rest isentropically.^[4] For many purposes in compressible flow, the stagnation enthalpy or stagnation temperature plays a role similar to the stagnation pressure in incompressible flow.

Compressible flow

Stagnation pressure is the static pressure a fluid retains when brought to rest isentropically from Mach number M.^[5]

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

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 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).

Notes

^ ^a ^b ^c Clancy, L.J., Aerodynamics, Section 3.5
^ Stagnation Pressure at Eric Weisstein's World of Physics (Wolfram Research)
^ Equation 4, Bernoulli Equation - The Engineering Toolbox
^ Clancy, L.J. Aerodynamics, Section 3.12
^ Equations 35,44, Equations, Tables and Charts for Compressible Flow

References

Clancy, L.J. (1975), Aerodynamics, Pitman Publishing Limited, London. ISBN 0 273 01120 0

External links

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Stagnation pressure

Contents

Magnitude

Compressible flow

See also

Notes

References

External links