On turbulent flow in circular pipe

Abstract

The Reynolds equations of motion of turbulent flow of an incompressible fluid have been studied for turbulent flow in circular pipe. The number of these equations is finally reduced to two. One of these consists of mean velocity and correlation between radial and axial turbulent velocity fluctuations u′w′ only. The other consists of the mean pressure, the radial and the circumferential turbulent velocity intensity only. Some conclusions about the mean pressure distribution and turbulent fluctuations are drawn. The mean velocity distribution and the correlation u′w′ can be expressed in a form of polynomial of the radial distance with the ratio of shearing stress on the wall to that of the corresponding laminar flow of the same maximum velocity as a parameter. These expressions hold true all the way across the tube, that is, both the turbulent region and viscous layer including the laminar sublayer. The mean velocity distribution has been compared with Nikuradse's experimental data to turbulent flow in a circular pipe. It also shows that the logarithmic mean velocity distribution is not a rigorous solution of Reynolds equations.