Stagnation pressure

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In fluid dynamics, stagnation pressure (or pitot 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 (isentropically). 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.

Magnitude[edit]

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

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

where:

P_\text{stagnation} is the stagnation 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. If the gravity head of the fluid at a particular point in a fluid flow is zero, then the stagnation pressure at that particular point is equal to total pressure.[1] However, in general total pressure differs from stagnation pressure in that total pressure equals the sum of stagnation pressure and gravity head.

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.[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[edit]

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 is the stagnation pressure
p is the static pressure
T_t is the stagnation temperature
T is the static temperature
\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 (a thermally perfect fluid).

See also[edit]

Notes[edit]

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

References[edit]

External links[edit]