The paper compares the results of Eulerian hydrodynamic simulations of cluster formation with analytic scaling relations between four bulk quantities: cluster mass, dark matter velocity dispersion, gas temperature, and cluster luminosity. The comparison is made for a large number of clusters at various redshifts in three different cosmological models (CHDM, CDM, and OCDM). The analytic formulae provide a good description of the relations between three of the four numerical quantities, and the luminosity also agrees when a procedure to correct for fixed numerical resolution is introduced. The normalizations for the virial relations are compared extensively with existing literature, showing good agreement. The Press-Schechter prescription is calibrated with the simulations, finding results consistent with other authors. The paper also examines issues such as the scatter in the virial relations, the effect of metallicity with a fixed pass-band, and the structure of halos. These comparisons aim to establish a firm foundation for using clusters as cosmological probes.The paper compares the results of Eulerian hydrodynamic simulations of cluster formation with analytic scaling relations between four bulk quantities: cluster mass, dark matter velocity dispersion, gas temperature, and cluster luminosity. The comparison is made for a large number of clusters at various redshifts in three different cosmological models (CHDM, CDM, and OCDM). The analytic formulae provide a good description of the relations between three of the four numerical quantities, and the luminosity also agrees when a procedure to correct for fixed numerical resolution is introduced. The normalizations for the virial relations are compared extensively with existing literature, showing good agreement. The Press-Schechter prescription is calibrated with the simulations, finding results consistent with other authors. The paper also examines issues such as the scatter in the virial relations, the effect of metallicity with a fixed pass-band, and the structure of halos. These comparisons aim to establish a firm foundation for using clusters as cosmological probes.