Response of Pitot probes in turbulent streams

Abstract

The response of a Pitot probe in a uniform laminar stream is commonly expressed in the form \[ P_s = P+{\textstyle\frac{1}{2}}C_{\rho} U^2, \] where P_s is the probe signal pressure, P is the stream static pressure, U is the stream speed and ρ is the fluid density. It has been found that for ordinary sphere-nosed, round-nosed and square-nosed probes \[ 1-C = K(\sin^2\theta)^m = K(U^2_n/U^2)^m, \] where θ is the angle between the velocity vector and the probe axis, and U_n ≡ U sin θ is the transverse velocity component. The parameters m and K are functions of the probe geometry. These formulae also describe the performance in a turbulent stream when the probe is small compared with the turbulence scale. The evaluation of the time-averaged response is treated, and an answer is developed to the question of what it is that a Pitot probe measures in a turbulent stream. In a turbulent shear flow having the properties of a boundary layer, the reference pressure is best taken to be the static pressure at the shear-layer edge. It is shown that round-nosed probes with D_i/D≃0·45 and square-nosed probes with D_i/D≃0·15 then detect ${\textstyle\frac{1}{2}}\rho\overline{U}^2_x$ with good accuracy, where D_i/D is the ratio of the inside and outside diameters of the Pitot tube. When measurements are made with two probes of dissimilar geometry, the differential response can be used to find the mean-square level of the transverse velocity fluctuations. Turbulence levels so measured agree closely with results from hot-wire anemometry.