  Parametrizations of Equation of state parameter as a function of the scale
factor or redshift are frequently used in dark energy modeling. The question
investigated in this paper is if parametrizations proposed in the literature
are compatible with the dark energy being a barotropic fluid. The test of this
compatibility is based on the functional form of the speed of sound squared,
which for barotropic fluid dark energy follows directly from the function for
the Equation of state parameter. The requirement that the speed of sound
squared should be between 0 and speed of light squared provides constraints on
model parameters using analytical and numerical methods. It is found that this
fundamental requirement eliminates a large number of parametrizations as
barotropic fluid dark energy models and puts strong constraints on parameters
of other dark energy parametrizations.
