A regulation on the sulfur emissions of ships sailing in global sea areas has been enforced since 1 January 2020. In this new regulation, ships are required to use low-sulfur fuel oils or to install an after-treatment equipment, such as a scrubber. Open and hybrid scrubbers wash the exhaust gas using seawater and then discharge the wash water overboard. According to the regulation promulgated by the International Maritime Organization (IMO) Marine Environment Protection Committee (MEPC), the wash water must have a pH of 6.5 or higher at 4 m from the discharge point. Wash water is generally acidic, with a pH of 2.5–3.5, whereas seawater is alkaline, with a pH of approximately 8.2. The wash water is dispersed after being discharged overboard through a nozzle, and its pH is restored through dilution with the surrounding seawater. In this study, the pH was calculated by using a theoretical chemical reaction model, and then the dispersion of wash water was analyzed using CFD simulation. This study describes the process of selecting the appropriate turbulent Schmidt number in a wide range of nozzle diameters. Finally, the appropriate nozzle diameter was determined based on the initial pH of the discharged scrubber wash.