The turbomachinery used in the sCO\({}_{2}\) power cycle is generally designed to operate in extreme conditions of high temperature, high pressure, and high speed; consequently, the bearings and the lubrication system require high reliability and stability. Therefore, the selection of bearing type and compatible design for the required operating conditions is important for the safe operation of the sCO\({}_{2}\) power cycle. In this manner, the development of a reliable bearing system for the sCO\({}_{2}\) turbomachinery has been identified as the one of the major challenges. In previous research, an appropriate bearing system can be found, from small-scale to commercial-scale systems [7]. For the sCO\({}_{2}\) turbomachinery developed to date, oil lubrication bearings such as tilting pad bearings, of which the reliability has already been demonstrated in steam turbine generation system, have been widely adopted. Additionally, in small0 scale facilities or prototype demonstration cases, various types of bearings such as magnetic bearings [8], bump type foil bearings [1], and hydrostatic bearings have been adopted. Among the aforementioned bearings, hydrostatic bearings are operated by supplying a pressurized lubricant to the bearing. Due to these operating characteristics, hydrostatic bearings can provide high stiffness and damping, which result in the precise operation of the rotating shaft and superior stability of the rotor bearing system. Owing to these advantages, hydrostatic bearings have been widely applied to many rotating machines to date and thorough investigations have been performed to investigate the bearing characteristics. [PERSON] et al. outlined a procedure to optimize the design parameters of multi-recess hydrostatic bearings based on minimum power consumption; they suggested an optimal ratio of the land part to recess of 0.25 [9]. [PERSON] et al. calculated the dynamic coefficients of capillary-compensated bearings in a pure hydrostatic operation [10]. [PERSON] calculated the stiffness and damping coefficients of pure hydrostatic operation according to changes in recess pressure ratio and eccentricity [11]. He showed that there exists an optimum value of the pressure ratio at which load capacity is maximum. [PERSON] compared the dynamic properties caused by the hydrostatic, hydrodynamic and squeeze effects for various types of restrictors [12]. [PERSON] et al. calculated stability threshold speeds for hybrid operation and demonstrated superior stability at a low eccentricity ratio [13]. In addition, [PERSON] et al. reported that the dynamic characteristics of a hydrostatic bearing can change considerably with the compressibility of the lubricant inside the recess [14]. They also analytically showed that there is a break frequency beyond which bearing stiffness increases sharply. Subsequently, [PERSON] et al. extended this study [15]. They showed that the fluid compressibility in the recess affects the dynamic behavior of the hydrostatic bearing, and cross coupled stiffness and damping increase with rotating speed. As application fields for hydrostatic bearings increased, bearings operating in turbulent regions were investigated. Through numerical analysis, [PERSON] described the static and dynamic performance of a hydrostatic bearing, considering turbulent effects [16]. [PERSON] et al. reported the effects of changes in the physical properties of the lubricant on a cryogenic hydrostatic bearing [17]. [PERSON] proposed an approximate solution for the static and dynamic properties of hydrostatic bearings considering the flow inertia effect [18]. He reported that approximate solutions show good agreement with the full numerical solution and that maximum direct stiffness occurs at pressure ratio of 0.6, and that maximum direct damping is present at different pressure ratios depending on the rotor speed. By comparing critical mass, [PERSON] and [PERSON] demonstrated that a lobe bearing with offset factor of more than one can achieve a better stability than that of circular bearings [19; 20].