## 1 Introduction  
Dissipative splitter silencers are the most used mechanical dissipative silencers in industry [1]. These systems are used for a wide variety of applications in different fields of industry, such as noise control in fans [2], vehicles [3, 4] and gas turbine engines [5], among many others. Although they have been studied and developed for decades [6, 7, 8], splitter silencers are still under study, as demonstrated by the analytical model presented by [PERSON] et al. in 2018 [9] in which the homogenization-based theory of sound propagation in heterogeneous media is used to derive the effective acoustic parameters of various types of silencers. Some recent works additionally introduce the possibility of a hybrid approach with active and passive silencers for noise control [10]. Consequently, the challenge nowadays is optimizing the design of silencers to maximize their efficiency in given applications [11]. Dissipative splitter silencers usually consist of a bulk reacting porous material with a given cross section and a perforated plate that protects this material from the conditions in the duct in which a low Mach number flow circulates [12]. This configuration provides them with good performance and effectiveness in the reduction of the propagated sound waves in ducts and, at the same time, simplifies their design and reduces the manufacturing costs. Nevertheless, despite the good performance of splitter silencers for acoustic purposes, placing these devices in ducts reduces the cross-section available for the circulation of air and flow. In those cases in which the flow is circulating through the duct, this leads to the modification of the local behavior of the duct in the vicinity of the silencers. Pressure loss is the main indicator used for evaluating the aerodynamic performance of a silencer, as it has a negative influence on the efficiency of an engine [13]. This parameter is widely considered in the design of silencers, as the pressure loss is an undesired effect of the use of silencers in ducts [14, 15, 16]. Some works have been published in recent years related to the study of the pressure loss in splitter silencers [17; 18]. Nevertheless, most of these publications focus on the numerical [19; 20] and/or experimental study of the silencers, and less attention is paid to the standards applied in industry and their agreement with the numerical models and experimental results. This is especially relevant in those configurations that differ, to a greater or lesser extent, from the cases shown in the standards. In this work, the pressure loss due to the presence of dissipative splitter silencers in a duct is studied. The system to be considered in this work consists of two baffle silencers, made of stainless steel and filled with rockwood as an absorbing material (which is protected by a perforated plate and a veil). The influence of the shape of both terminations of the splitters in the produced pressure loss is studied by considering rectangular and semihexadecagonal shapes. These shapes are chosen in order to study a shape that is considered in the formulations of the standards (rectangular profiles) and a shape that slightly differs from those presented in them (semihexadecagonal profiles, as an approximation of the semicircular profiles defined in the standards). This allows to perform a comparative analysis of the results obtained by using standards (ISO 14136 [21] and VDI 2081-1 [22]), numerical methods (finite element method) and experimental measurements in order to check the validity and accuracy of the standards in the prediction of the pressure loss under given conditions and the suitability of the numerical simulations for improving the predictions of the standards. Additionally, since the pressure loss is dependent on the flow velocity and the flow rate in the duct, four input face velocities (5 m/s, 10 m/s, 15 m/s and 20 m/s) are considered in the study.