From some of the questions I'm encountering my text, it seems like the writers are implying that there always needs to be a difference in pressure for a fluid to accelerate (by this I mean a difference between the Pi and Pf values on either side of Bernoulli's equation). But is this really true? For instance, in Toricelli's result, the velocity(f) is different from the velocity(i), but the Pi and Pf values are the same. Thus the fluid has experienced a change in velocity, but there is no difference in pressure. Am I misunderstanding this concept? Thank you all so much in advance!