The effect of low Reynolds number flows on pitot tube measurements

An investigation on the low Reynolds number effect on hemispherical-tipped Pitot tube measurements was performed by measuring the center-line velocity during the laminar flow of a Newtonian fluid in a 25 mm (1 in.) diameter vertical recirculating pipe loop. The primary objective of the study was to reconsider the available low Reynolds number Pitot tube data in the literature with modern instrumentation. Using the results of this experimental study, a correlation that accurately predicts the low Reynolds number Pitot tube behavior has been developed. The correlation accounts for an additional viscous term in the relationship for the pressure coefficient (C-p) which is not accounted for in Bernoulli's Equation. The correlation is semi-empirical and accurately fits experimental data gathered in this study, as well as a significant body of experimental data available in the literature. The correlation, which is based on a Pitot tube Reynolds number calculated using the opening diameter (d), has been shown to be provide more accurate predictions of Cp for a wide range of opening diameter to outer diameter ratios (0.22 <= d/D <= 0.6) than available correlations based on outer diameter. The transition Pitot tube Reynolds number, below which Bernoulli's Equation is no longer appropriate, was predicted to be approximately 35, compared to a value of 79 obtained from fitting data collected by Barker. The correlation developed in this study provides smoother transitions at both ends of the low Reynolds range. At the low end (Re < 10) it converges with a Stokes Law' analogy, while at the critical transition (Re similar to 35) it converges asymptotically with Bernoulli's Equation. The correlation also accurately predicts the behavior of the pressure coefficient with Reynolds numbers between these ranges. (C) 2015 Elsevier Ltd. All rights reserved.