Pressure fluctuations of liquids under short-time acceleration

This study investigates experimentally the pressure fluctuations of liquids in a column under short-time acceleration. It demonstrates that the Strouhal number $St=L/(c\,\Delta t)$ , where $L$ , $c$ and $\Delta t$ are the liquid column length, speed of sound, and acceleration duration, respectively, provides a measure of the pressure fluctuations for intermediate $St$ values. On the one hand, the incompressible fluid theory implies that the magnitude of the averaged pressure fluctuation $\bar {P}$ becomes negligible for $St\ll 1$ . On the other hand, the water hammer theory predicts that the pressure tends to $\rho cu_0$ (where $u_0$ is the change in the liquid velocity) for $St\geq O(1)$ . For intermediate $St$ values, there is no consensus on the value of $\bar {P}$ . In our experiments, $L$ , $c$ and $\Delta t$ are varied so that $0.02 \leq St \leq 2.2$ . The results suggest that the incompressible fluid theory holds only up to $St\sim 0.2$ , and that $St$ governs the pressure fluctuations under different experimental conditions for higher $St$ values. The data relating to a hydrogel also tend to collapse to a unified trend. The inception of cavitation in the liquid starts at $St\sim 0.2$ for various $\Delta t$ , indicating that the liquid pressure goes lower than the liquid vapour pressure. To understand this mechanism, we employ a one-dimensional wave propagation model with a pressure wavefront of finite thickness that scales with $\Delta t$ . The model provides a reasonable description of the experimental results as a function of $St$ .