Stagnation pressure

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. In an incompressible flow, stagnation pressure is equal to the sum of the free-stream static pressure and the free-stream dynamic pressure.[2]

Stagnation pressure is sometimes referred to as pitot pressure because it is measured using a pitot tube.

MagnitudeEdit

The magnitude of stagnation pressure can be derived from Bernoulli Equation[3][1] For incompressible flow and no height changes. For any two points 1 and 2:

 

The two points of interest are 1) in the freestream flow at relative speed   where the pressure is called the "static" pressure, (for example well away from an airplane moving at speed  ); and 2) at a "stagnation" point where the fluid is at rest with respect to the measuring apparatus (for example at the end of a pitot tube in an airplane).

Then

 

or[4]

 

where:

  is the stagnation pressure
  is the fluid density
  is the speed of fluid
  is the static pressure

So the stagnation pressure is increased over the static pressure, by the amount   which is called the "dynamic" or "ram" pressure because it results from fluid motion. In our airplane example, the stagnation pressure would be atmospheric pressure plus the dynamic pressure.

In compressible flow however, the fluid density is higher at the stagnation point than at the static point. Therefore,   can't be used for the dynamic pressure. For many purposes in compressible flow, the stagnation enthalpy or stagnation temperature plays a role similar to the stagnation pressure in incompressible flow. [5]

Compressible flowEdit

Stagnation pressure is the static pressure a gas retains when brought to rest isentropically from Mach number M.[6]

 

or, assuming an isentropic process, the stagnation pressure can be calculated from the ratio of stagnation temperature to static temperature:

 

where:

  is the stagnation pressure
  is the static pressure
  is the stagnation temperature
  is the static temperature
  ratio of specific heats

The above derivation holds only for the case when the gas is assumed to be calorically perfect (specific heats and the ratio of the specific heats   are assumed to be constant with temperature).

See alsoEdit

NotesEdit

  1. ^ a b 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. ^ Houghton, E.L and Carpenter P.W. Aerodynamics (2003), Section 2.3.1
  5. ^ Clancy, L.J. Aerodynamics, Section 3.12
  6. ^ Equations 35,44, Equations, Tables and Charts for Compressible Flow

ReferencesEdit

  • L. J. Clancy (1975), Aerodynamics, Pitman Publishing Limited, London. ISBN 0-273-01120-0
  • Cengel, Boles, "Thermodynamics, an engineering approach, McGraw Hill, ISBN 0-07-254904-1

External linksEdit