In order to model the water flow in a nuclear reactor core, the authors carried out several studies coupling the Low Mach nuclear core (Lmnc) model of partial differential equations to the stiffened gas law for the physical behaviour. The Lmnc model is derived from the Navier-Stokes equations through an asymptotic expansion with respect to the Mach number commonly assumed to be small in this domain of application. This simplified system of equations provides qualitative results under the stiffened gas hypothesis such as analytical solutions in dimension 1 and enables a simple numerical treatment no matter what the dimension. In the regime of interest (namely high pressure situations), the stiffened gas law turns out to be inaccurate. That is why this paper is devoted to the coupling of the Lmnc model to an equation of state tuned by means of experimental values (NIST) for thermodynamic variables. The very point in this study consists in fitting tabulated values and derivatives satisfying positivity and monotonicity constraints, showing a clear improvement in the quantitive results.