Abstract This paper derives a mathematical relation between the damped and undamped waves propagating in a fluid-filled pipe. The damping considered is caused by the steady and unsteady friction and the pipe wall visco-elasticity. The derived relation is solved so that the idealized undamped pressure wave signal is obtained from the measured damped pressure signal. Physically, the proposed transformation is an amplification operation that adds back the energy that was lost due to the damping. This means that measurement errors will also be amplified under the transformation, making the problem ill-posed. The truncated singular value decomposition method is used to regularize the transformation. Both numerical and laboratory experiments are conducted to show the validity of this transformation. The results show that the transformation can accurately predict the shape and size of the reflections that were distorted due to the wave dissipation and dispersion.

中文翻译：

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有阻尼和无阻尼水锤波之间的转换

摘要 本文推导了在充满流体的管道中传播的阻尼波和无阻尼波之间的数学关系。所考虑的阻尼是由稳态和非稳态摩擦以及管壁粘弹性引起的。求解导出的关系以便从测量的阻尼压力信号获得理想化的无阻尼压力波信号。从物理上讲，提议的转换是一种放大操作，可以将由于阻尼而损失的能量加回来。这意味着在变换下测量误差也会被放大，使问题不适定。截断奇异值分解方法用于正则化变换。进行了数值和实验室实验以证明这种转换的有效性。