Please notice that Bernoulli equation relates pressure changes to velocity along a streamline (which in a steadyflow is the trajectory traced by a fluid particle) , so it's not restricted to closed systems.
Bernoulli equation in the form
p + (1/2) (density) V^2=constant
was derived with the following restrictions:
-Steady flow
-Imcompressible flow
-Frictionless flow
-Flow along a streamline