Stagnation pressure
Encyclopedia
In fluid dynamics
, stagnation 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
.
,
Total Pressure = Dynamic Pressure + Static Pressure
or
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.
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.
ly from Mach number
M.
or, assuming an isentropic process, the stagnation pressure can be calculated from the ratio of stagnation temperature to static temperature:
where:
stagnation (or total) pressure
static pressure
stagnation (or total) temperature in kelvin
static temperature in kelvins
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
are assumed to be constant and invariant with temperature (See also, a thermally perfect fluid).
Fluid dynamics
In physics, fluid dynamics is a sub-discipline of fluid mechanics that deals with fluid flow—the natural science of fluids in motion. It has several subdisciplines itself, including aerodynamics and hydrodynamics...
, stagnation pressure is the static pressure
Static pressure
In fluid mechanics the term static pressure has several uses:* In the design and operation of aircraft, static pressure is the air pressure in the aircraft’s static pressure system....
at a stagnation point
Stagnation point
In fluid dynamics, a stagnation point is a point in a flow field where the local velocity of the fluid is zero. Stagnation points exist at the surface of objects in the flow field, where the fluid is brought to rest by the object...
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
Pitot tube
A pitot tube is a pressure measurement instrument used to measure fluid flow velocity. The pitot tube was invented by the French engineer Henri Pitot Ulo in the early 18th century and was modified to its modern form in the mid-19th century by French scientist Henry Darcy...
.
Magnitude
The magnitude of stagnation pressure can be derived from the Bernoulli Equation. For incompressible flowIncompressible flow
In fluid mechanics or more generally continuum mechanics, incompressible flow refers to flow in which the material density is constant within an infinitesimal volume that moves with the velocity of the fluid...
,
Total Pressure = Dynamic Pressure + Static Pressure
or
| where: |  |
is the total pressure |
 |
is the fluid density | |
 |
is the velocity of fluid | |
 |
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.
In compressible flow
Compressible flow
Compressible flow is the area of fluid mechanics that deals with fluids in which the fluid density varies significantly in response to a change in pressure. Compressibility effects are typically considered significant if the Mach number of the flow exceeds 0.3, or if the fluid undergoes very large...
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
Enthalpy
Enthalpy is a measure of the total energy of a thermodynamic system. It includes the internal energy, which is the energy required to create a system, and the amount of energy required to make room for it by displacing its environment and establishing its volume and pressure.Enthalpy is a...
or stagnation temperature
Stagnation temperature
In thermodynamics and fluid mechanics, stagnation temperature is the temperature at a stagnation point in a fluid flow. At a stagnation point the speed of the fluid is zero and all of the kinetic energy has been converted to internal energy and is added to the local static enthalpy...
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 isentropicalIsentropic process
In thermodynamics, an isentropic process or isoentropic process is one in which for purposes of engineering analysis and calculation, one may assume that the process takes place from initiation to completion without an increase or decrease in the entropy of the system, i.e., the entropy of the...
ly from Mach number
Mach number
Mach number is the speed of an object moving through air, or any other fluid substance, divided by the speed of sound as it is in that substance for its particular physical conditions, including those of temperature and pressure...
M.
or, assuming an isentropic process, the stagnation pressure can be calculated from the ratio of stagnation temperature to static temperature:
where:
stagnation (or total) pressure static pressure stagnation (or total) temperature in kelvinKelvin
The kelvin is a unit of measurement for temperature. It is one of the seven base units in the International System of Units and is assigned the unit symbol K. The Kelvin scale is an absolute, thermodynamic temperature scale using as its null point absolute zero, the temperature at which all...
static temperature in kelvins ratio of specific heatsThe above derivation holds only for the case when the fluid is assumed to be calorically perfect. For such fluids, specific heats and
are assumed to be constant and invariant with temperature (See also, a thermally perfect fluid).