Limitations of the standard Bernoulli equation method for evaluating Pitot/impact tube data

The inaccuracies of Pitot or impact tubes for the measurement of low fluid velocities have been demonstrated by several experimental investigations. However, owing to considerable data scatter, there does not exist a definitive criterion for establishing when these instruments are inaccurate with respect to low velocities. It is not that the instruments themselves are faulty, but rather that the methodology for extracting velocity information from the measured pressures fails. The standard method for extracting velocities from the pressure data is the application of Bernoulli's equation. That equation is, however, based on an inviscid model. At low Reynolds numbers, the viscosity exerts a strong effect on the flow pattern and, thereby, invalidates the use of the Bernoulli equation. In the present investigation, a painstaking numerical simulation has been performed to establish criteria at which the Bernoulli interpretation of Pitot/impact tube data is not valid. Two types of nose pieces for Pitot/impact tube were investigated. One of these is a hemispherical nose, while the other is a flat-faced nose. It was found that for the former, the Bernoulli interpretation should not be used when ρU_∞R_outer/μ < 45, while for the latter, the corresponding criterion is ρU_∞R_outer/μ < 65. These values correspond to a 2% error in the pressure coefficient c_p and a 1% error in the value of the extracted velocity measurement.