## 1 Introduction  
Production activities such as mining and metal smelting produce a large amount of dust, and the health and safety of workers exposed to high concentrations of dust for a long time will face serious risks [1; 2; 3; 4], especially from PM2.5 (particles with aerodynamic diameters of \(\leq\)2.5 \(\upmu\)m) [5; 6; 7; 8; 9; 10]. The main dust control measures are ventilation, vacuum cleaner dust purification, spray dust suppression, fence dust, etc. [11; 12]. Nowadays, the primary technology that deals with dust pollution domestically and abroad is spraying. The atomizing nozzle is an important accessory in spraying [13; 14; 15; 16; 17]. Among various nozzle types, the pressure-atomizing nozzle is the most widely used because of its simple structure and strong adaptability. Due to its simple structure and strong adaptability, pressure atomizing nozzle has become the most widely used nozzle [18; 19; 20; 21; 22; 23]. The principle is that the liquid is transported to the nozzle port by liquid pressure or gas pressure, mixed in the liquid cap of the pressure-atomizing nozzle, and then sprayed through the nozzle hole of the pressure-atomizing nozzle [24; 25]. Among them, the circular-hole rotating core micro-fog nozzle is widely used in fog gun vehicles. Compared with normal pressure atomization, the strengths of the circular-hole rotating core micro-fog nozzle include its low water pressure requirements, low water consumption, and high dust removal efficiency (especially for respirable dust). However, this nozzle is seldom studied at present. A number of scholars have conducted extensive experiments and numerical simulations to discuss the impact factors of droplet size, such as nozzle types, water supply pressure, and the distance between the measurement point and the spray nozzle. [PERSON] et al. used the integral form of the conservation equation to establish a system of equations that can be solved to analyze far-field secondary atomization by predicting the droplet size and velocity distribution of the relevant phases [26]. [PERSON] et al. proposed a theoretical model to combine internal flow dynamics to better predict the deformation of droplets and the resulting breakup in a continuous, uniform air jet under multi-mode breakup conditions [27]. [PERSON] proposed a new model to represent the atomization of pre-hole nozzles [28]. [PERSON] performed a rigorous dimensional analysis of the two-fluid spray characteristics [29]. In China, [PERSON] et al. established the droplet size distribution equation of a swirl nozzle by creating a mathematical model [30; 31; 32]. [PERSON] et al. established a mathematical model of nozzle atomization characteristics and the average droplet diameter and analyzed it [33; 34]. Previously, scholars have focused on one factor to determine droplet size in their studies, and the ultrasonic nozzle with a liquid medium was thoroughly studied for its atomization mechanism; however, there were few studies on the degree of influence of different factors on droplet size and the correlation between the main influencing factors and droplet size. At the same time, it has been reported that some scholars have investigated the droplet size produced by this type of nozzle and have developed a simple mathematical model to predict the droplet size. Nevertheless, the existing mathematical models did not take into account all the factors affecting droplet size. Due to this, the established droplet prediction model cannot be applied to the development of programs at engineering sites. Based on the different parameters of the three nozzles and the customized spraying experimental platform, the SMD (the Sauter Mean Diameter) of three different outlet diameters of round-hole rotating core micro-mist nozzles under three different water supply pressures and three different axial distances were measured.