Stagnation pressure

In fluid dynamics, stagnation pressure (or total pressure) is the static pressure at a stagnation point in a fluid flow.

At a stagnation point the fluid velocity is zero and all kinetic energy has been converted into pressure energy (isentropically). Stagnation pressure is equal to the sum of the free-stream dynamic pressure and free-stream static pressure. Stagnation pressure is sometimes referred to as pitot pressure because it is measured using a pitot tube.

Magnitude

The magnitude of stagnation pressure can be derived from the Bernoulli Equation. For incompressible flow,

Total Pressure = Dynamic Pressure + Static Pressure

or

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

where:	$P_\text{total}\;$	is the total pressure
	$\rho\;$	is the fluid density
	$v\;$	is the velocity of fluid
	$P_\text{static}\;$	is the static pressure 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.
$P_\text{total}=0 + P_\text{stagnation}\;$

In compressible flow the stagnation pressure is equal to static pressure only if the fluid entering the stagnation point is brought to rest isentropically. 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.

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

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 $\gamma$ are assumed to be constant and invariant with temperature (See also, a thermally perfect fluid).

See also

• Hydraulic Ram

References

• Clancy, L.J. (1975), Aerodynamics, Pitman Publishing Limited, London. ISBN 0 273 01120 0
• Cengel, Boles, "Thermodynamics, an engineering approach, McGraw Hill, ISBN 0072549041

External links

• Pitot-Statics and the Standard Atmosphere
• The Measurement of Air Speed in Airplanes