  This study experimentally investigates the pressure fluctuations of liquids
in a column under short-time acceleration and 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 both for limiting cases (i.e.
$St\ll1$ or $St = \infty$) and for intermediate $St$ values. Incompressible
fluid theory and water hammer theory respectively imply that the magnitude of
the averaged pressure fluctuation $\overline{P}$ becomes negligible for
$St\ll1$ (i.e., in the condition where the duration of acceleration $\Delta t$
is large enough compared to the acoustic timescale) and tends to $\rho cu_0$
(where $u_0$ is the change in the liquid velocity) for $St\geq O(1)$ (i.e., in
the condition where $\Delta t$ is small enough). For intermediate $St$ values,
there is no consensus on the value of $\overline{P}$. 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 $St\sim0.2$ 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
becomes negative. 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 $St$. The slight discrepancy between the
model and experimental results reveals additional contributing factors such as
the container motion and the profile of the pressure wavefront.
