Experimental evaluation of the mean momentum and kinetic energy balance equations in turbulent pipe flows at high Reynolds number

In light of recent data from hot-wire anemometry and laser Doppler velocimetry, this article explores experimentally the momentum balance and kinetic energy production in fully developed turbulent pipe flow for shear Reynolds numbers in the range from two pipe facilities. It has become common practice to indirectly deduce the Reynolds shear stress via the mean flow data and the mean-momentum balance whenever the simultaneous measurements of the streamwise and wall-normal velocity fluctuations can not be performed precisely. The current assessment underlines, however, the importance of measuring the Reynolds shear stress directly, and the friction velocity independently from the mean-velocity profile to ascertain the quality of the data when utilising the momentum balance. The present analysis also reinforces the universality of the viscous stress gradient to the Reynolds shear stress gradient in the wall vicinity up to the inner limit of the logarithmic layer. The new set of the experimental data shows that Panton's stress function reproduces the measured Reynolds shear stress and kinetic energy production in turbulent pipe flows over a wide Reynolds number range to a high degree.