**3. Cavitation number and pressure loss coefficient**

The cavitation number in this study is defined as follows:

$$
\sigma = \frac{p - p\_v}{\rho \mathcal{U}^2 / 2} \tag{1}
$$

where is upstream pressure, is saturated vapor pressure, is density of water, and *U* is average upstream flow velocity. The pressure loss coefficient is defined by the following formula:

$$
\zeta = \frac{\Delta P}{\frac{1}{2}\rho \mathcal{U}^2} \tag{2}
$$

where *P* is the differential pressure across the test valve.
