Turbulent Flow in a Plane Channel

Qualitatively, the picture of stabilized turbulent flow in a plane channel is similar to that in a circular tube. Indeed, in the viscous sublayer adjacent to the channel walls, the velocity distribution increases linearly with the distance from the wall V(Y)/U = y+. In the logarithmic layer, the average velocity profile can be described by the expression [289] 

In the flow core, the average velocity distribution in a plane channel of width 2h can be approximately described by formulas of the form [212, 289] 

In the region of stabilized turbulent flow, the drag coefficient can be determined from the implicit relation [289] 

The drag coefficient A for turbulent flows in rectilinear tubes of noncircular cross-section can also be computed using relations (1.6.12) and (1.6.13), where the equivalent diameter 

More detailed information about the structure of turbulent flows in a circular (noncircular) tube and a plane channel, as well as various relations for determining the average velocity profile and the drag coefficient, can be found in the books [138, 198, 268, 276, 289], which contain extensive literature surveys. Systematic data for rough tubes and results of studying fluctuating parameters of turbulent flow can also be found in the cited references. 

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Zhaphashaev, U.K., Isakhanova, G.Z., 1998. Developed turbulent flow in a plane channel with simultaneous injection through one porous wall and suction through the other. J. Appl. Mech. Tech. Phys. 39, 53-59. 

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