The paper presents simulations of galaxy cluster formation and evolution in the Cold Dark Matter (CDM) cosmogony, focusing on the effects of radiative cooling on the gas. The simulations, conducted using a combined N-body/Smooth Particle Hydrodynamics (SPH) code, explore clusters with a wide range of masses at higher resolutions compared to previous N-body models. The results show that, despite the ongoing mergers, the density profiles of equilibrium clusters are similar for both gas and dark matter, showing no uniform density core and a gradual steepening from the center outwards. The standard $\beta$-model fits these profiles well over most of the observable radius, with the slope parameter $\beta_f$ increasing with the outermost radius of the fit. Temperature profiles of different simulated clusters are also similar, with the gas temperature dropping at larger radii. The gas temperature and dark matter velocity dispersion in equilibrium clusters give values of $\beta_T \equiv \mu n_e \sigma_{DM}^2 / kT$ that are consistent with unity when an X-ray emission-weighted temperature is used. Larger values of $\beta_T$ are found in merging objects, suggesting that $\beta_T > 1$ may be an observational indicator of merging in real clusters. The similar structure of clusters of different masses results in scaling relations between X-ray and dynamical properties, which are inconsistent with the observed luminosity-temperature relation and the evolution of the cluster luminosity function. This suggests that the central properties of the intracluster medium are determined by non-gravitational processes such as radiative cooling or substantial pre-heating at high redshift. The paper also discusses the sensitivity of the simulations to numerical parameters and compares the results with real clusters, highlighting the "$\beta$-discrepancy" in cluster data.The paper presents simulations of galaxy cluster formation and evolution in the Cold Dark Matter (CDM) cosmogony, focusing on the effects of radiative cooling on the gas. The simulations, conducted using a combined N-body/Smooth Particle Hydrodynamics (SPH) code, explore clusters with a wide range of masses at higher resolutions compared to previous N-body models. The results show that, despite the ongoing mergers, the density profiles of equilibrium clusters are similar for both gas and dark matter, showing no uniform density core and a gradual steepening from the center outwards. The standard $\beta$-model fits these profiles well over most of the observable radius, with the slope parameter $\beta_f$ increasing with the outermost radius of the fit. Temperature profiles of different simulated clusters are also similar, with the gas temperature dropping at larger radii. The gas temperature and dark matter velocity dispersion in equilibrium clusters give values of $\beta_T \equiv \mu n_e \sigma_{DM}^2 / kT$ that are consistent with unity when an X-ray emission-weighted temperature is used. Larger values of $\beta_T$ are found in merging objects, suggesting that $\beta_T > 1$ may be an observational indicator of merging in real clusters. The similar structure of clusters of different masses results in scaling relations between X-ray and dynamical properties, which are inconsistent with the observed luminosity-temperature relation and the evolution of the cluster luminosity function. This suggests that the central properties of the intracluster medium are determined by non-gravitational processes such as radiative cooling or substantial pre-heating at high redshift. The paper also discusses the sensitivity of the simulations to numerical parameters and compares the results with real clusters, highlighting the "$\beta$-discrepancy" in cluster data.