Velocity Measurement By Pitot Static Tube in Subsonic And Supersonic Regime
Do you know how the velocity of aircraft is measured in the fluid by Pitot-Static Tube? On road vehicles like bus, motor bikes, the car we have a mechanism of magnetic coils which measure the velocity of the vehicle by the number of rotations of the wheels.
Aircraft, have no road from speed-o-meter mechanism measure velocity. In this case, fluid pressure is used for measuring the velocity of the body in a fluid. In fewer words, Pitot-Static tube installed on the aircraft body for measurement of the velocity of the aircraft.
Pitot Static Tube is the air flow measurement instrument which is used for measurement of fluid flow velocity. The Pitot-static tube is the combination of Pitot tube and Prandtl tube. Pitot tube which consists of the total hole (as shown below in image) and Prandtl tube consist of static holes on the periphery of the tube.
The Pitot static tube is the combination of Pitot tube and Prandtl tube design. This design is more working in high Reynolds number fluid flow and at various altitudes and angles of attack. Static holes required to take the static pressure of the local atmosphere for measuring the accurate velocity of a body (aircraft, ship, rocket sled).
Stagnation Pressure= Static Pressure + Dynamic Pressure
PITOT STATIC TUBE AIR FLOW MEASUREMENT IN SUBSONIC AND SUPERSONIC FLOW REGIME
Following are the subsonic to supersonic flow regime information:-
SUBSONIC FLOW REGIME(UP TO MACH 0.3)
For velocity of the free stream up to Mach 0.3 (103 m/s), flow is incompressible here we use the Bernoulli’s equation for velocity measurement which describes the relationship between the velocity and pressure in streamlining.
SUBSONIC COMPRESSIBLE FLOW REGIME MACH 0.3< 1
For velocity more than 0.3 Mach, flow is considered compressible and density of flow changes point to point. When flow strikes the Pitot static tube nose air gets compressed.If we assume the flow is compressed and decelerated from free stream state isentropically.
SUPERSONIC FLOW REGIME MACH 1<M<5
For flow more than Mach 1 a new phenomenon of shock waves formed in the upstream of the nose of Pitot- static tube which decelerated non isentropically flow to subsonic after shock waves and brings zero velocity isentropically near the stagnation point. As shown below
Flow velocity is an implicit function of Pitot tube pressure. Rayleigh formula is used for the velocity measurement in supersonic regime i.e.
- P02 =Pressure of free stream at the stagnation point.
- P1 =Pressure of free stream in front of shock waves(static pressure)
- M1= Free stream Mach number before shock waves
- M2= Free stream Mach number after the shock waves
- x= (Gamma ) Ratio of specific heat at constant pressure to specific heat at constant volume