A comprehensive investigation of velocity distribution is presented, and the log law is re-examined using experimental data from a smooth uniform open channel flow. It is widely reported that the coefficients of the log law in channel flows deviate from those obtained from circular pipe flows by Nikuradse (Laws of flow in rough pipes, 1933), but the mechanism is not clear and no theoretical formulae are available to express these deviations. A Laser Doppler Velocimetry system was used to measure velocity profiles at the centre of the channel. The data obtained support previous conclusions that the additive constant B of the log law in channel flows can no longer be considered to be 5.5. Interestingly, the experimental data also support Tracy and Lester’s discovery that the shear velocities on both sides of the log law are different. Better agreement can be achieved if the global shear velocity (U_*1) is used to normalize the measured velocity, and the local shear velocity (U_*2) is used to normalize the distance from the wall. Other researchers’ data in the literature also validates this new relationship. Based on this new relationship, a theoretical value of B is obtained, which agrees well with the observed B, thus a new form of log law for channel flow is suggested. The new relationship developed was verified with present experimental and past literature data suggesting its universality irrespective of wide or narrow open channels, or subcritical or super critical flow conditions. By using the developed relationship the large scatter associated with the additive constant B associated with the log law has been explained. It is found that the additive constant B in the log law is a function of channel aspect ratio. The developed relationship for B is validated from a wide range of data from the literature to confirm its universality.

中文翻译：

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重新检查平滑明渠流中的对数律速度曲线

提出了对速度分布的全面研究，并使用来自平滑均匀明渠水流的实验数据重新检验了对数律。据广泛报道，通道流量中的对数定律系数与尼古拉德斯（Nikuradse）从圆形管道中获得的对数系数（粗糙管道中的流动规律，1933）有所不同，但是其机理尚不清楚，也没有理论公式可用来表达这些定律。偏差。激光多普勒测速系统用于测量通道中心的速度分布。获得的数据支持先前的结论，即通道流中对数律的加性常数B不再视为5.5。有趣的是，实验数据也支持Tracy和Lester的发现，即对数律两侧的剪切速度是不同的。_{* 1}）用于归一化测得的速度和局部剪切速度（U _{* 2}）用于归一化与墙的距离。文献中其他研究人员的数据也验证了这一新关系。基于这种新的关系，获得了与观察到的B吻合良好的B的理论值，因此提出了一种新的对流定律的对数定律。目前的实验和过去的文献数据证实了这种新关系的发展，表明它的普遍性，无论宽阔或狭窄的明渠，还是亚临界或超临界流动条件。通过利用所发展的关系，已经解释了与与对数定律相关的加性常数B相关的大散射。发现对数定律中的加性常数B是通道纵横比的函数。