A barotropic fluid has pressure determined by density alone, , so pressure and density surfaces coincide in hydrostatic equilibrium.
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A barotropic fluid is a type of fluid whose pressure is a function solely of its density. In simpler terms, for a barotropic fluid, if you know the density at a given point, you can determine the pressure without needing to know any other state variables, such as temperature or specific internal energy. In mathematical terms, the relationship can be expressed as: \[ P = P(\rho) \] where \( P \) is the pressure and \( \rho \) is the density.