  We construct a family of equations of state for QCD in the temperature range
30 MeV $\leq T\leq$ 800 MeV and in the chemical potential range $0\leq \mu_B
\leq$ 450 MeV. These equations of state match available lattice QCD results up
to $\mathcal{O}(\mu_B^4)$ and in each of them we place a critical point in the
3D Ising model universality class. The position of this critical point can be
chosen in the range of chemical potentials covered by the second Beam Energy
Scan at RHIC. We discuss possible choices for the free parameters, which arise
from mapping the Ising model onto QCD. Our results for the pressure, entropy
density, baryon density, energy density and speed of sound can be used as
inputs in the hydrodynamical simulations of the fireball created in heavy ion
collisions. We also show our result for the second cumulant of the baryon
number in thermal equilibrium, displaying its divergence at the critical point.
In the future, comparisons between RHIC data and the output of the hydrodynamic
simulations, including calculations of fluctuation observables, built upon the
model equations of state that we have constructed may be used to locate the
critical point in the QCD phase diagram, if there is one to be found.
