In this article, on the basis of the stochastic theory of turbulence and the regularity of equivalence of measures, the calculation of the friction coefficient is presented for the laminar–turbulent transition on the flat plate. As a result, the formula for the friction coefficient depending on the turbulence intensity, the scale of turbulence, the velocity-profile index, and the Reynolds number for the laminar–turbulent regime of flow of an incompressible fluid along a smooth flat plate is proposed. For each of the listed parameters included in the equation for the drag coefficient, the relations determining these parameters for each Reynolds number in the region of the laminar–turbulent transition are obtained. It is also determined that the equation for the friction coefficient obtained previously on the basis of stochastic equations for a fully developed turbulent flow can be obtained on the basis of a new dependence for the laminar–turbulent transition with taking into account the initial perturbations in the deterministic motion. The parameters of these perturbations may be determined from the well-known experimental data for the initial turbulence in the flow on the flat plate. Using new dependence of the friction coefficient for the laminar–turbulent transition, it is possible to understand that the differences between the experimental results both for the laminar–turbulent transition and for a fully developed turbulent flow with the same Reynolds number are caused by the difference in the magnitudes of flow fluctuations for concrete experiment instead of only due to the systematic error in the processing of experimental data. The friction coefficient for a laminar–turbulent transition on a smooth flat plate is calculated in the of Reynolds number range of \(5\times 10^{5}\div 2\times 10^{7}\) up to the region of developed turbulent flow. The results of calculations of the friction coefficient show both qualitative and quantitative agreement with the experimental data. So, the law of equivalence of measures and stochastic equations presents both the physical and mathematical essence between interacting deterministic and random states. Thus, “the discovery of the interplay of disorder and fluctuations in physical systems from atomic to planetary scales” does not reflect the law of mechanism of interaction of a deterministic state with the fluctuation.

本文根据湍流随机理论和测度等价规律，提出了平板上层流-湍流过渡的摩擦系数计算方法。因此，在不可压缩流体沿光滑平板的层流-湍流状态下，提出了取决于湍流强度、湍流尺度、速度剖面指数和雷诺数的摩擦系数公式。 . 对于阻力系数方程中包含的每个列出的参数，获得了确定层流-湍流过渡区域中每个雷诺数的这些参数的关系。还确定了先前基于完全发展的湍流的随机方程获得的摩擦系数方程可以在考虑层流-湍流转变的新依赖性的基础上获得，同时考虑到初始扰动确定性运动。这些扰动的参数可以从平板上流动的初始湍流的众所周知的实验数据中确定。使用摩擦系数对层流-湍流过渡的新依赖性，可以理解，层流-湍流过渡和具有相同雷诺数的充分发展的湍流的实验结果之间的差异是由具体实验的流动波动幅度的差异引起的，而不仅仅是由于实验数据处理过程中的系统误差。光滑平板上层流-湍流过渡的摩擦系数在雷诺数范围内计算\(5\times 10^{5}\div 2\times 10^{7}\)直到发展的湍流区域。摩擦系数的计算结果与实验数据定性和定量一致。因此，测度等价定律和随机方程既体现了相互作用的确定性状态和随机状态之间的物理本质，也体现了数学本质。因此，“发现物理系统从原子尺度到行星尺度的无序和涨落相互作用”并不能反映确定性状态与涨落相互作用的机制规律。