stagnation point

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In fluid dynamics, a stagnation point is a point in a flow field where the local velocity of the fluid is zero.Clancy, L.J. (1975), Aerodynamics, Pitman Publishing Limited, London. {{ISBN|0-273-01120-0}}{{rp|§ 3.2}} The Bernoulli equation shows that the static pressure is highest when the velocity is zero and hence static pressure is at its maximum value at stagnation points: in this case static pressure equals stagnation pressure.{{cite book |last=Fox |first=R. W. |author2=McDonald, A. T. |title=Introduction to Fluid Mechanics |year=2003 |publisher=Wiley | edition = 4th |isbn=0-471-20231-2}}{{rp|§ 3.5}}

The Bernoulli equation applicable to incompressible flow shows that the stagnation pressure is equal to the dynamic pressure and static pressure combined.Clancy, L.J. (1975), Aerodynamics, Pitman Publishing Limited, London. {{ISBN|0-273-01120-0}}{{rp|§ 3.5}} In compressible flows, stagnation pressure is also equal to total pressure as well, provided that the fluid entering the stagnation point is brought to rest isentropically.{{rp|§ 3.12}}

A plentiful, albeit surprising, example of such points seem to appear in all but the most extreme cases of fluid dynamics in the form of the "no-slip condition" - the assumption that any portion of a flow field lying along some boundary consists of nothing but stagnation points (the question as to whether this assumption reflects reality or is simply a mathematical convenience has been a continuous subject of debate since the principle was first established).

Pressure coefficient

This information can be used to show that the pressure coefficient $C_p$ at a stagnation point is unity (positive one):{{rp|§ 3.6}}

: $C_p={p-p_\infty \over q_\infty}$

where:

: $C_p$ is pressure coefficient

: $p$ is static pressure at the point at which pressure coefficient is being evaluated

: $p_\infty$ is static pressure at points remote from the body (freestream static pressure)

: $q_\infty$ 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 $C_p$ at stagnation points is +1.{{rp|§ 3.6}}

Kutta condition

On a streamlined body fully immersed in a potential flow, 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 of a wing, the Kutta condition specifies that a stagnation point is located at that point.Anderson, John D. (1984) Fundamentals of Aerodynamics, section 4.5 McGraw-Hill Inc. {{ISBN|0-07-001656-9}} The streamline at a stagnation point is perpendicular to the surface of the body.

Notes

Category:Fluid dynamics

stagnation point

Pressure coefficient

Kutta condition

See also

Notes