Prandtl tube

The local static pressure, equal to that prevailing outside the boundary layer, can be measured in an orifice on the surface of a body immersed in a stream. If, in particular, the static pressure of undisturbed stream, pm, is to be measured, an orifice can be drilled where, from a theoretical point of view, the pressure reaches this value, e. g. in the presence of the boundary layer (Figure 2.2) on a cylinder of circular cross-section in the locations at ±35°. Small deviations from these points, however, lead to large changes in pressure, so, as in the case of stagnation pressure, the use of slender bodies, like tubes, which introduce small disturbances in the stream, is preferred.

The basic concept is that in the absence of curvature of streamlines there is not a centrifugal force to be balanced with a gradient of pressure: keeping streamlines straight equals cancelling the variation in pressure normal to the streamlines themselves. Strictly speaking, only on a flat plate pm could be measured through orifices on the surface because any body disturbs the stream: in practice, a slim body can be used if the pressure is read in a position where the initial disturbances are sufficiently damped and streamlines are straight and parallel to the main flow.

The instrument used, designed by Prandtl, consists of a thin tube aligned with the stream with a closed-end upstream, and backed by a stem perpendicular to it (Figure 2.12). The pressure is detected in a number of orifices in the pipe wall.

Подпись: Figure 2.12

Static pressure probes: top, the Prandtl tube; bottom, the NPL tube

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