Math 2.0

Fluid mechanics Definition

Stagnation pressure

Builds on Isentropic flowMach numberBernoulli's principleShock wave

Definition

Consider a fluid particle with static pressure pp, density ρ\rho and speed uu. Its stagnation pressure p0p_0 is the pressure it would have after being brought to rest by an isentropic process, that is, adiabatically and reversibly.

  1. For an incompressible fluid, p0=p+12ρu2p_0 = p + \frac{1}{2}\rho u^2.
  2. For an ideal gas with constant ratio of specific heats γ\gamma, at Mach number MM, p0=p(1+γ−12M2)γ/(γ−1).p_0 = p \left(1 + \frac{\gamma - 1}{2} M^2\right)^{\gamma/(\gamma - 1)}.

Remarks

Example: air at p=100 kPap = 100\ \mathrm{kPa} moving at M=1M = 1 with γ=1.4\gamma = 1.4 has p0=100⋅1.23.5≈189 kPap_0 = 100 \cdot 1.2^{3.5} \approx 189\ \mathrm{kPa}. For small MM the binomial expansion gives p0≈p+12ρu2(1+M2/4)p_0 \approx p + \frac{1}{2}\rho u^2 (1 + M^2/4), which recovers formula 1 as M→0M \to 0. In steady inviscid flow without heat exchange p0p_0 is constant along streamlines, which is a form of Bernoulli's principle. Non-example: the static pressure pp is not a stagnation pressure, because it is measured moving with the fluid and does not include the kinetic energy. Across a shock wave the stagnation pressure drops, since the process is not reversible.

Reading path

To understand this page from the ground up, read these 10 pages in order. The foundations come first.

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Euler equations, concept, no evidence levelEuler equationsconceptInviscid flow, concept, no evidence levelInviscid flowconceptIsentropic flow, concept, no evidence levelIsentropic flowconceptMach number, concept, no evidence levelMach numberconceptShock wave, concept, no evidence levelShock waveconceptStreamlines, streaklines and pathlines, concept, no evidence levelStreamlines, streakli…conceptVelocity potential, concept, no evidence levelVelocity potentialconceptVorticity, concept, no evidence levelVorticityconceptBernoulli's principle, statement, no evidence levelBernoulli's principlestatementStagnation pressure, definition, no evidence levelStagnation pressuredefinition
Each page uses the pages above it. The colour of the bar on a box shows how strong the evidence is, and the box also gives it as text. The list has the same pages.
  • no evidence level
  1. Euler equations concept
  2. Inviscid flow concept
  3. Isentropic flow concept
  4. Mach number concept
  5. Shock wave concept
  6. Streamlines, streaklines and pathlines concept
  7. Velocity potential concept
  8. Vorticity concept
  9. Bernoulli's principle statement
  10. Stagnation pressure definition

Further reading

  1. Web https://en.wikipedia.org/wiki/Stagnation_pressure
About this page
Tag3AFWE792TA
URIm2://3AFWE792TA
Kinddefinition
WritingW0 stub
MSC76N15, 76G25
DefinesStagnation pressure
UsesIsentropic flow, Mach number, Bernoulli's principle, Shock wave
Changed3 November 2026

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