When solving fluid flow problems using finite elements you typically end up requiring that $p\in L^2$.
For Darcy flow problems, a popular choice of elements is the Raviart-Thomas element and discontinuous pressure elements.
For Stokes/Navier-Stokes flow a popular choice of elements is the Taylor-Hood element which has piecewise continuous pressure elements. This is actually more continuity than is required, because for a function to be in $L^2$ it does not have to be continuous.
Is there some reason that discontinuous pressure elements are preferred (or necessary) for Darcy flow problems, but not for Stokes/Navier-Stokes flow problems?