Stagnation Pressure Calculator

At a glance:Stagnation pressure (total pressure, symbol p₀) is the pressure a flowing fluid reaches when decelerated to rest without loss. For incompressible, inviscid flow along a streamline, Bernoulli's equation gives p₀=p+½ρv², where p₀ is the stagnation (total) pressure (Pa), p the static pressure (Pa), ρ the fluid density (kg/m³) and v the velocity (m/s). Term by term: stagnation pressure is static pressure plus dynamic pressure ½ρv². Static pressure p is the fluid's own pressure (measured normal to the flow); dynamic pressure is the pressure the motion can convert to when stopped. Bernoulli says total pressure is constant along a streamline (no loss), so as velocity rises the dynamic part grows and static pressure must fall — the principle of wing lift, venturi meters and atomisers. Example: sea-level air p=101325 Pa, ρ=1.225 kg/m³, v=50 m/s (180 km/h): dynamic ½×1.225×50²=1531.25 Pa, p₀=101325+1531.25=102856.25 Pa. The Pitot tube uses exactly this: a hole facing the flow reads p₀, a side hole reads p, their difference is the dynamic pressure, from which v=√(2(p₀−p)/ρ). Uses: (1) Pitot and Pitot-static tubes for speed (aircraft airspeed, ventilation); (2) flow measurement (venturi, orifice from total vs static); (3) aerodynamics and turbomachinery energy analysis; (4) Bernoulli demonstrations. Notes: (1) this is the incompressible (Ma<0.3) form — high-speed compressible flow needs the Mach-number correction; (2) Bernoulli assumes inviscid, lossless, steady, along a streamline; (3) static pressure may be absolute or gauge as long as consistent; (4) keep SI units. In short, p₀=p+½ρv² is static plus dynamic pressure — the core of Pitot speed and flow measurement.