Stagnation point

# Stagnation point

Discussion

Encyclopedia
In fluid dynamics
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...

, a stagnation point is a point in a flow field where the local velocity
Velocity
In physics, velocity is speed in a given direction. Speed describes only how fast an object is moving, whereas velocity gives both the speed and direction of the object's motion. To have a constant velocity, an object must have a constant speed and motion in a constant direction. Constant ...

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. The Bernoulli equation
Bernoulli's principle
In fluid dynamics, Bernoulli's principle states that for an inviscid flow, an increase in the speed of the fluid occurs simultaneously with a decrease in pressure or a decrease in the fluid's potential energy...

shows that 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....

is highest when the velocity is zero and hence static pressure is at its maximum value at stagnation points. This static pressure is called the stagnation pressure
Stagnation pressure
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 . Stagnation pressure is equal to the sum of the free-stream dynamic pressure and...

.

The Bernoulli equation
Bernoulli's principle
In fluid dynamics, Bernoulli's principle states that for an inviscid flow, an increase in the speed of the fluid occurs simultaneously with a decrease in pressure or a decrease in the fluid's potential energy...

applicable to incompressible flow
Incompressible 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...

shows that the stagnation pressure
Stagnation pressure
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 . Stagnation pressure is equal to the sum of the free-stream dynamic pressure and...

is equal to the dynamic pressure plus 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....

. Total pressure is also equal to dynamic pressure plus static pressure so, in incompressible flows, stagnation pressure 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...

s, stagnation pressure is also equal to total pressure providing the fluid entering the stagnation point is brought to rest isentropically.)

## Pressure coefficient

This information can be used to show that the pressure coefficient
Pressure coefficient
The pressure coefficient is a dimensionless number which describes the relative pressures throughout a flow field in fluid dynamics. The pressure coefficient is used in aerodynamics and hydrodynamics...

at a stagnation point is unity (plus one):

where: is pressure coefficient
Pressure coefficient
The pressure coefficient is a dimensionless number which describes the relative pressures throughout a flow field in fluid dynamics. The pressure coefficient is used in aerodynamics and hydrodynamics...

is 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 the point at which pressure coefficient is being evaluated is static pressure at points remote from the body (freestream
Freestream
The freestream is the air far upstream of an aerodynamic body, that is, before the body has a chance to deflect, slow down or compress the air. Freestream conditions are usually denoted with a \infty symbol, e.g. V_\infty, meaning the freestream velocity...

static pressure) is dynamic pressure at points remote from the body (freestream dynamic pressure)

Stagnation pressure minus freestream static pressure is equal to freestream dynamic pressure; therefore the pressure coefficient at stagnation points is +1. The pressure at the stagnation point is static plus dynamic.

## Kutta condition

On a streamlined body fully immersed in a potential flow
Potential flow
In fluid dynamics, potential flow describes the velocity field as the gradient of a scalar function: the velocity potential. As a result, a potential flow is characterized by an irrotational velocity field, which is a valid approximation for several applications...

, there are two stagnation points — one near the leading edge and one near the trailing edge. On a body with a sharp point such as the trailing edge
Trailing edge
The trailing edge of an aerodynamic surface such as a wing is its rear edge, where the airflow separated by the leading edge rejoins. Essential control surfaces are attached here to redirect the air flow and exert a controlling force by changing its momentum...

of a wing
Wing
A wing is an appendage with a surface that produces lift for flight or propulsion through the atmosphere, or through another gaseous or liquid fluid...

, the Kutta condition
Kutta condition
The Kutta condition is a principle in steady flow fluid dynamics, especially aerodynamics, that is applicable to solid bodies which have sharp corners such as the trailing edges of airfoils...

specifies that a stagnation point is located at that point. The streamline
Streamlines, streaklines and pathlines
Fluid flow is characterized by a velocity vector field in three-dimensional space, within the framework of continuum mechanics. Streamlines, streaklines and pathlines are field lines resulting from this vector field description of the flow...

at a stagnation point is perpendicular to the surface of the body.