The total pressure tube, or Pitot tube, provides a common method of measuring the stagnation pressure within a pipe, channel or duct flow. In its simplest form this instrument consists of a symmetrical body such as a cylinder, cone, or hemisphere with a small hole or piezometric opening drilled along its central axis. If this is aligned with its central axis in the direction of the flow (Figure 1a) the fluid will accelerate around the upstream face with minimal energy losses, and a stagnation point arises at the piezometric opening. In this case the tapping point, typically connected to some form of manometer, provides a direct measure of the stagnation pressure, or total pressure, Ps. If a second piezometric opening records the static pressure in the undisturbed flow (P0), the velocity of the flow may be inferred from the pressure difference (Ps-P0).
The Bernoulli Equation states that for an incompressible fluid the dynamic pressure accounts for the difference between the stagnation pressure and the static pressure:
where u is the velocity of the flow field.
An alternative arrangement, usually referred to as a Pitot-static tube, is indicated in Figure 1b. In this case the static pressure is recorded on the same instrument through a series of tapping points located at section B-B. This approach is often more convenient and, in particular, overcomes the difficulty experienced in curved flow where the transverse pressure gradient renders u indeterminate from (Ps-P0). However, this latter approach suffers from the disadvantage that the static pressure P0' measured at section B-B may be slightly less than that recorded in the free stream. This effect may be eliminated in the detailed design of the Pitot tube, or incorporated within an empirical coefficient (C1) such that:
Since P0' < P0, C1 is always less than 1.0. However, for most practical engineering purposes C1 = 1.0 is appropriate for many conventional Pitot-static tubes.
Pitot tubes may also be used in compressible flows. If M0 defines the Mach Number of the undisturbed flow, the Euler equation appropriate to a subsonic flow (M0 < 1) yields:
where Ps is obtained from the Pitot tube, P0 from the static tube (piezometer) and Ts is the temperature at the stagnation point which is usually measured using a thermocouple. In this equation cp is the specific heat at constant pressure and γ is the ratio (cp/cv) or the adiabatic exponent.
For supersonic flow (M0 > 1) a normal shock wave will be located upstream of the stagnation point. In this case the free stream velocity (u) is given by:
where R is the gas constant (or energy per unit mass per Kelvin).